The advent of widely available computing power has spawned a whole research field that we now call computational physics. Today, we may be on the cusp of a similar paradigm shift as programmable qubit devices enable one to run experiments on a platform of actual physical quantum states. Here we use the commercially available D-Wave DW-2000Q device to build and probe a state of matter that has not been observed or fabricated before. The topological phase that we build has been widely sought for many years and is a candidate platform for quantum computation. While we cannot observe the full quantum regime due to the limitations of the current device, we do observe unmistakable signatures of the phase in its classical limit at the endpoint of the quantum annealing protocol. In the process of doing so, we identify additional features that a programmable device of this sort would need in order to implement fully functional topological qubits. It is a testament to technological progress that a handful of theorists can observe and experiment with new physics while being equipped only with remote access to a commercial device.

At sufficiently low densities, Coulomb energy dominates over the kinetic (Fermi) energy, and the electrons should spontaneously align their spins and become fully magnetized- a classic, textbook problem discussed by Bloch (in 1929), and later on Stoner (in 1947) that eluded experiments for nearly a century. The key challenge was to make the electron system very dilute, and yet keep the disorder to a minimum level. This talk presents an experimental realization of the long-sought, interaction-driven ferromagnetism in a two-dimensional electron system (2DES). At high densities, the 2DES is paramagnetic, and the electrons occupy two conduction band valleys. As the density is sufficiently lowered, the electrons spontaneously valley polarizes. At even lower densities, the 2DES becomes a ferromagnet. This observation of spontaneous ferromagnetism is reminiscent of Bloch's prediction. However, there are key differences, which will be discussed in the talk.

Landau-Fermi liquid theory is commonly associated with the existence of coherent quasiparticles, i.e., of a simple pole in the single-particle Green’s function at the chemical potential with residue Z<1. On the contrary, its quantum impurity counterpart, the Nozières local Fermi liquid theory, remains valid also when the impurity density of states displays a pseudo gap instead of the standard Abrikosov-Suhl Kondo resonance. I will show that this asymmetry is only apparent, namely that Landau’s Fermi-liquid-like expressions of thermodynamic and dynamic quantities can be recovered even in the absence of coherent quasiparticles. Specifically, after a brief historical overview of Landau-Fermi liquid theory and Nozières's local one, I will revisit the standard microscopic derivation of the former, and show that it holds under a more general hypothesis that includes, as a particular case, the conventional Fermi liquids with well-defined quasiparticles.

Since their discovery in 1971 the superfluid phases of Helium-3 have proved to be an ideal testing ground for many fundamental concepts of modern physics. Phenomena such as Cooper pairing, macroscopic quantum coherence, the spontaneous breaking of large symmetry groups, and the formation of exotic topological defects are not only important in condensed matter physics, but provide important links to particle physics and even the structure of the early universe. In my talk I will give a simple introduction into the microscopic and macroscopic physics of superfluid Helium-3.

In quantum mechanics, supersymmetry (SUSY) explicitly relates bosonic and fermionic degrees of freedom — a fundamental concept that has first been introduced in high-energy physics, but which has ingenious applications in many other fields of physics as in the study of disorder phenomena in mesoscopic physics. In this talk, I will highlight settings in condensed matter physics where supersymmetry can make insightful connections to topological states of matter. The principle example will be spin liquids, low-temperature collective states of magnetic moments that defy conventional ordering. In using supersymmetry, we construct (semi)metallic analogues of classical spin liquids and, in reverse, mechanical analogues of quantum spin liquids.

In numerous materials, the electrons exhibit a "strange metal" regime at low temperature, where among other signatures, the resistivity scales proportionally to temperature. A satisfactory theoretical model to explain this behavior has so far been lacking. In this talk, I will describe a new approach to gaining at least a partial understanding of strange metal physics that is not rooted in a specific theoretical model, but rather involves general structural arguments based on a minimal set of experimentally motivated assumptions. These arguments lead to unexpectedly strong conclusions, such as a diverging susceptibility of an order parameter that is odd under time reversal and inversion symmetries, which could be related to experimental observations of spontaneous breaking of these symmetries in the pseudogap phase of cuprates proximate to the strange metal. Time permitting, I will also discuss implications for non-Fermi liquids more generally (beyond the strange metal), such as a general formulation of Lutttinger's theorem.

The talk is based on the following papers:

https://arxiv.org/abs/2007.07896

https://arxiv.org/abs/2010.10523

Density functional theory (DFT) is a popular method for electronic-structure calculations. But while Kohn-Sham eigenvalues can loosely mirror experimental quasiparticle energies, there is formally no connection between the two (except for the HOMO in exact DFT). Furthermore, the presence of self-interaction errors in semi-local DFT can make those eigenvalues an even poorer proxy for quasiparticle energies [1].

This talk will discuss three different methods for addressing these failings of DFT. The first, DFT+U, is a method commonly applied to "strongly correlated" materials such as transition metal oxides [2]. The second, Koopmans spectral functionals, is an efficient approach for recovering spectral properties [3-5]. Finally, I will discuss dynamical mean field theory, with a particular focus on its application to metalloproteins [6-7]. For each of these methods I will present some calculations on real systems in order to demonstrate their strengths and shortcomings.

[1] Cohen et al., Science, 321, 792 (2008)

[2] Linscott et al., Phys. Rev. B, 98, 235157 (2018)

[3] Borghi et al., Phys. Rev. B 90, 075135 (2014)

[4] Nguyen et al., Phys. Rev. X, 8, 021051 (2018)

[5] Colonna et al., JCTC, 15, 1905 (2019)

[6] Linscott et al, JCTC, 16, 4899 (2020)

[7] al-Badri, Linscott, et al., Comm. Phys., 3 (2020)

The fermion sign problem often stymies exploration of strongly correlated quantum systems. Recently, new ideas have emerged on how to construct "designer Hamiltonians" which do not suffer from the sign problem, while still hosting highly entangled phases of matter. In this talk, I will present results on two new directions: (a) A model of competing antiferromagnetism and nodal d-wave superconductivity. (b) Models of non-Fermi liquids in Kondo lattice systems. The corresponding phase diagrams also host interesting critical phenomena, and I will also discuss field-theory approaches to understand the associated universal properties, along with the relevance to experiments. Time permitting, I will discuss new entanglement based approaches to characterize non-Fermi liquids that arise due to Kondo breakdown in frustrated heavy fermion systems.

Space- and time-crystallization effects in multicomponent superfluids—while having the same physical origin and mathematical description as in the single-component case—are conceptually much more straightforward. Specifically, the values of the temporal and spatial periods are absolute rather than relative, and the broken translation symmetry in space and/or time can be revealed with experiments involving only one equilibrium sample. I will discuss two realistic setups—one with cold atoms and another one with bilayer superconductors—for observation of space and time crystallization in two-component counterflow superfluids.

For indistinguishable itinerant particles subject to a superselection rule fixing their total number, a portion of the entanglement entropy under a spatial bipartition of the ground state is due to particle fluctuations between subsystems and thus is inaccessible as a resource for quantum information processing. We derive a measure of the operationally accessible entanglement that is both computationally and experimentally measurable. We quantify the operationally accessible entanglement in a model of interacting spinless fermions on a one-dimensional lattice via exact diagonalization and the density matrix renormalization group. We find that the accessible entanglement exactly vanishes at the first-order phase transition between a Tomonaga-Luttinger liquid and phase-separated solid for attractive interactions and is maximal at the transition to the charge density wave for repulsive interactions. Throughout the phase diagram, we discuss the connection between the accessible entanglement entropy and the variance of the probability distribution describing intra-subregion particle-number fluctuations.

The prototypical superfluid, Helium-4 (4He), transitions to its superfluid state below ~2 K. In contrast, its isotopic counterpart Helium-3 (3He) has a transition temperature of ~2 mK. This thousand-fold disparity is due to the nature of the superfluid transition; while 4He Bose condenses directly, the fermionic 3He atoms must first form composite bosons through Cooper pairing. The p-wave, spin-triplet pairing of the 3He atoms gives rise to many possible superfluid phases, though only two distinct phases are realized in the bulk.

Recent experimental and theoretical advances have suggested that a third phase emerges when superfluid 3He is confined to a slab -- a pair-density-wave (PDW) phase. Analogous to a supersolid, the PDW phase is characterized by the spontaneous breaking of translational symmetry that coexists with superfluid order. This talk will provide an introduction to the phases of superfluid 3He under confinement and the physics that emerges in that geometry.

In 1965, D. J. Thouless, building on earlier ideas, explained magnetism in quantum crystals. Ferromagnetism and antiferromagnatism arise from the rate of cyclic exchange of atoms in quantum crystals. Following work of Roger, Delrieu and Hetherington, we developed “exact” path integral methods to evaluate the quantum exchange frequencies; These methods were an extension of the methods used for superfluid helium. Those calculations supported the conjectured multiple exchange model that had been empirically developed. A delicate cancellation of even and odd body exchanges lead to a broken symmetry magnetic phase. Following that work we also applied this computational method to Wigner crystals and to 4He, a bosonic system conjectured to be a super solid. We found that supersolidity in 4He does not occur, a finding eventually supported by recent experiments.

Quantum-critical strongly correlated systems feature universal collision-dominated collective transport. Viscous electronics is an emerging field dealing with systems in which strongly interacting electrons flow like a fluid. Such flows have some remarkable properties never seen before. I shall describe some recent theoretical and experimental works devoted, in particular, to a striking macroscopic DC transport behavior: viscous friction can drive electric current against an applied field, resulting in a negative resistance, recently measured experimentally in graphene. I shall also describe conductance exceeding the fundamental quantum-ballistic limit, freely-flowing viscous flows, field-theoretical anomalies and other wonders of viscous electronics. Strongly interacting electron-hole plasma in high-mobility graphene affords a unique link between quantum-critical electron transport and the wealth of fluid mechanics phenomena.

Many modern quantum materials display regimes with variable electron density without well-defined quasiparticle excitations. In various solvable models with variable spin and/or charge density, related to the Sachdev-Ye-Kitaev model, the excitation spectra are characterized by infinite sets of operators, almost all with irrational scaling dimensions. I will compare the spectral functions so obtained with numerical studies of random t-J and Hubbard models. The operator associated with time reparameterization symmetry contributes a linear-in-temperature term to the resistivity of a wide class of models.

It was found recently that 2D electron fluids can support collective excitations that are not subject to Landau’s T^2 dissipation [1,2,3]. This surprising collective behavior originates from the head-on carrier collisions, a process that dominates angular relaxation at not-too-high temperatures T << TF due to the interplay of Pauli blocking and kinematic constraints. As a result, a large family of exceptionally long-lived excitations emerges, associated with the odd-parity harmonics of momentum distribution. This leads to ”tomographic” dynamics: fast 1D spatial diffusion along the unchanging velocity direction accompanied by a slow angular dynamics that gradually randomizes velocity orientation. The abnormally slow angular relaxation originates from correlated angular dynamics involving ”lock-step” angular displacements along the Fermi surface occurring in collinear two-particle collisions. The slow loss of directional memory is described as non-Brownian angular random walk, ”superdiffusion” on the Fermi surface. The collective behavior with directional memory dominates at moderately long times, pushing the onset of conventional hydrodynamics to abnormally large timescales. The tomographic regime features an unusual hierarchy of time scales and scale-dependent transport coefficients manifest in fractional-power current flow profiles and unusual conductance scaling vs. temperature and sample size. This exotic behavior can be directly probed by transport measurement techniques, as well as by momentum-resolved tunneling measurements.

[1] P J Ledwith, H Guo, L Levitov, Annals of Physics 411, 167913 (2019)

[2] P J Ledwith, H Guo, A V Shytov, L Levitov, Phys. Rev. Lett. 123, 116601 (2019)

[3] P J Ledwith, H Guo, L Levitov, arXiv:1708.01915 (2019)

The search for topological properties of insulating quantum magnets is an exciting, yet challenging task. While related electronic systems saw a swift verification of the bulk-boundary correspondence because surface sensitive probes like angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) were readily available, similar smoking gun signatures remain elusive for magnetic systems due to the charge-neutral character of spin excitations. Recent years have seen remarkable progress in identifying topological quantum magnets, for example materials potentially realizing a Kitaev quantum spin liquid (QSL). In this talk, I will discuss recent results of Kitaev heterostructures and new proposals for probing charge neutral excitations.

It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I'll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I'll discuss several scenarios for the evolution of the system with N through Nc. One of these scenarios might explain recent numerical results on boundary criticality in 2+1D quantum spin systems with SO(3) symmetry.

The simple moral of eigenstate thermalization is that what we think is the rattling of classical things producing heat is a delusion caused by our incapacity to keep track of the flow of quantum information in the enormous many-body Hilbert space. Are there circumstances where it is impossible to identify such a classical metaphor? The secret of holographic duality is that it makes possible to compute generic properties of extremely densely entangled ”quantum supreme” matter by mapping it onto black hole physics in one higher dimension. According to the holographic incarnation of optical pump probe experiments it takes no time at all to reach thermal equilibrium. Another consequence is that the near equilibrium regime governing transport is governed by ”Planckian dissipation” explaining the famous linear resistivity of the cuprates. We predict that the hydrodynamic flows of the electron fluid in the strange metal regime should be characterized by turbulence on the nanometer scale.

Recent advances in ultra-fast measurement in cold atoms, as well as pump-probe spectroscopy of K3C60 films, have opened the possibility of rapidly quenching systems of interacting fermions to, and across, a finite temperature superfluid transition. However determining that a transient state has approached a second-order critical point is difficult, as standard equilibrium techniques are inapplicable. We show that the approach to the superfluid critical point in a transient state may be detected via time-resolved transport measurements, such as the optical conductivity. We leverage the fact that quenching to the vicinity of the critical point produces a highly time dependent density of superfluid fluctuations, which affect the conductivity in two ways. Firstly by inelastic scattering between the fermions and the fluctuations, and secondly by direct conduction through the fluctuations. The competition between these two effects leads to non-monotonic behavior in the time-resolved optical conductivity. Results are obtained both for a clean system, as well as a strongly disordered system where for the latter connections with Azlamazov-Larkin and Maki-Thompson corrections can be made.

Quantum lattice models with time evolution governed by local unitary quantum circuits can serve as a minimal model for the study of general unitary dynamics governed by local interactions. Although such circuit dynamics exhibit many of the features expected of generic many-body dynamics, exact results generally require the presence of randomness in the circuit. After a short introduction to general unitary circuit models, we discuss the class of dual-unitary circuits characterized by an underlying space-time symmetry. We show how in these models exact results can be obtained and related for the thermalization of correlations and the scrambling of out-of-time-order correlators.

A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing positivity constraints on certain operator expectation values. Complemented with variational upper bounds, ground state observables are constrained to be within a narrow range. The method is demonstrated with the Hubbard model in one and two dimensions, and bounds on ground state double occupancy and magnetization are discussed.

A type II superconducting film with a transverse magnetic field, in contact with a topological insulator, has a Majorana fermion at the centre of every vortex core. A realistic model has a hopping term and a short-range interaction term for the Majorana fermions. By adjusting a chemical potential for the topological insulator, it is possible to tune the hopping term to zero, so that the interaction strength to hopping strength ratio goes too infinity. Adjusting this ratio leads to a fascinating phase diagram which I will discuss in both 1 and 2 dimensions. A supersymmetric phase is shown to occur in both cases.

Our experimental research group at MSU, the Laboratory for Hybrid Quantum Systems (LHQS), is working on a wide variety of exciting experiments at the boundary of condensed matter physics and quantum information science (QIS).

I will describe recent work from our group on creating new hybrid QIS systems based on super- conducting qubits + superfluids, electrons on helium, and quantum acoustic devices. By leveraging the experimental techniques of ultra-low temperature science our experiments reveal insights into the coherence properties of established superconducting qubit systems and single electron devices and potential methods for improving this coherence. Additionally, these systems open the door to developing altogether new qubits based on the quantized motion of electrons trapped on the surface on helium. When coupled to piezoacoustic devices we are also exploring the possibility of developing novel flying qubit platforms based on these electrons. The ability to access low-millikelvin, and even microkelvin temperatures, in micro- and nano-electronic QIS devices and systems brings the exciting possibility of unexpected discoveries and new directions in fundamental and applied QIS.

This talk is based on the idea of representing an interacting system as the combination of two systems with different dynamics coupled in as simple a manner as possible. The idea of treating a single interacting system in this way dates back to the understanding of the 4He superfluid phase and the phenomenological theories of superconductivity, to cite only two of a number of examples. It is sometimes referred to as a ”two fluid description” when one of the quantum liquids is a superfluid or ”s-d coupling model” in electron transport through ferromagnetic conductors. Here one of the systems is chosen to be a paramagnetic Fermi liquid, the other a topological spin texture. The Fermi liquid is described by the standard Landau theory of paramagnetic fermions, while the magnetic texture is assumed to follow a classical Gilbert like equation of motion. There will be some attempts to interpret a few experimental observations. The overall question here is how the presence of interactions in the paramagnetic side of the model influences the dynamics of the texture.

Topological phases of matter in two dimensions support fractionalized quasiparticle excitations. These quasiparticles exhibit a number of fascinating phenomena, such as anyonic braiding statistics and quantum number fractionalization. I will present recent results about fractionalization in topological Z₂ quantum spin liquid (QSL). First I will describe how a complete classification of patterns of symmetry fractionalization can be achieved theoretically. Then I will discuss dynamical signatures of fractionalization across topological phase transitions from a QSL to a conventional symmetry-breaking phase. We show that the (spin) longitudinal conductivity right at the transition becomes fractionally quantized, which is a direct consequence of spin fractionalization. On the other hand, spectroscopic measurements can reveal ”fractional crystal momentum” carried by anyons. These observations are demonstrated in numerical simulations of a spin-1/2 frustrated XXZ model.

Electric and thermal transport in electronic systems has long been described in terms of a single-particle picture, which emphasizes the role of collisions between electrons and impurities or phonons, while electron-electron collisions play a secondary role. It is only in the past two decades that advances in the fabrication of ultra clean samples have refocused the interest on collective hydrodynamic transport - a transport regime which is controlled by the nearly conserved quantities: number, momentum, and energy, and by electron-electron interactions. In this talk I review some of the recent theoretical and experimental progress in our understanding of electronic hydrodynamics in graphene-based materials. I focus on thermal transport and its relation to electric transport, epitomized by the Wiedemann-Franz law which, in its conventional form, predicts a universal ratio between electric and thermal resistivities. Significant deviations from this prediction are found in single layer and double layer graphene, both in the doped case, where the Wiedemann-Franz ratio is reduced, and in the undoped case, where it is greatly enhanced. In the latter case an interesting scenario emerges, in which a small amount of disorder helps to expose an underlying singularity of the transport coefficients: vanishing thermal resistivity, finite electric resistivity, and diverging Wiedemann-Franz ratio and Seebeck coefficient.

We determine the shear viscosity and the dc electrical conductivity of interacting three-dimensional Luttinger semimetals, which have a quadratic band touching point in the energy spectrum, in the hydrodynamic regime. It is well-known that when the chemical potential is right at the band touching point the long-range Coulomb interaction induces the Luttinger-Abrikosov-Beneslavskii (LAB) phase at T = 0, which is an interacting, scale-invariant, non-Fermi-liquid state of electrons. Upon combining the renormalization-group (RG) analysis near the upper critical spatial dimension of four with the Boltzmann kinetic equation, we determine the universal ratio of viscosity over entropy, and the electrical dc conductivity of the system at the interacting LAB fixed point of the RG flow. The projection of the Coulomb interaction on the eigenstates of the system is found to play an important quantitative role for the scattering amplitude in the collision integral, and the so-called Auger-processes make a large numerical contribution to the inverse scattering time in the transport quantities. The obtained leading order result suggests that the universal ratio of the viscosity over entropy, when extrapolated to the physical three spatial dimensions, is above, but could be rather close to, the Kovtun-Son-Starinets lower bound.

In this two-part talk, we will first look at ultracold alkaline earth atoms in optical lattices, which realize the SU(N) Hubbard model. This model is predicted to give many phases of matter, including topological and fractionalized ground states. I will discuss recent unpublished results from an experimental collaboration with the Kyoto group that has observed antiferromagnetic correlations in the SU(6) Hubbard model in 1D and 3D. I will describe how we have been able to understand these rich, strongly correlated systems, and the implications for creating exotic states of matter.

In the second part of the talk, we will see how the size of correlations in a general many-body system can be bounded, and show how to harness this understanding for numerical methods. Though well-studied, these "Lieb-Robinson" bounds have had serious drawbacks: they have been too loose to give realistic estimates of correlations and fail qualitatively in many limits, for example for large spins or bosons. I will discuss our new bounds that remedy these issues and show how these bounds can be used to give rigorous error bars for finite-size effects in numerical calculations.

There is a large and growing list of strongly correlated metals that show so-called ”non-Fermi-liquid” behaviour in the vicinity of a continuous quantum phase transition, usually from a paramagnetic metal to one that is ordered ferromagnetically or antiferromagnetically. Signatures of non-Fermi-liquid behaviour include the absence of a quasiparticle peak in the single-electron spectral function (as measured, for example, by angle-resolved photoemission spectroscopy) and the presence of unusual power laws and logarithms in the dependence of thermodynamic observables (e.g. specific heat capacity, magnetic susceptibility) and transport quantities (e.g. electrical resistivity) on temperature, pressure, and/or magnetic field.

Theoretical work on this problem began in the 1970s, with early work by Hertz [1]. His work and its successors [2] wrote the low-energy theory of such a problem in terms of a single bosonic field representing the fluctuations of the magnetic order parameter; however, I think it is now clear [3] that such approaches yield theories so badly behaved as to be probably of no practical use even if they are formally correct. More recent work has concentrated on theories which contain both bosonic fields (representing the fluctuations of the magnetic order parameter) and fermionic fields (representing the conduction electrons). However, formulating a consistent low-energy theory along these lines has not been straightforward.

A particular problem is Landau damping: the fact that magnetic excitations can decay into electron-hole pairs and thereby dissipate. This is invisible to conventional Wilsonian renormalisation procedures [4], meaning that these treatments tend to give a qualitatively incorrect picture of the low-energy physics. In this talk, I shall discuss two recent pieces of work by my group [5,6] that attempt to investigate what we might do instead, using two different versions of the functional renormalisation group (fRG) technique.

[1] J. A. Hertz, Phys. Rev. B 14, 1165 (1976) [2] A. J. Millis, Phys. Rev. B 48, 7183 (1993) [3] S. C. Thier and W. Metzner, Phys. Rev. B 84, 155133 (2011) [4] A. L. Fitzpatrick, S. Kachru, J. Kaplan, and S. Raghu, Phys. Rev. B 88, 125116 (2013) [5] S. P. Ridgway and CAH, Phys. Rev. Lett. 114, 226404 (2015) [6] M. J. Trott and CAH, Phys. Rev. B 98, 201113(R) (2018)

I will introduce a universal feature of operator evolution in quantum many-body systems known as void formation, and discuss its consequences. In particular, I will explain how void formation is important for ensuring the unitarity of entanglement growth and for the generation of multipartite entanglement. I will also illustrate how void formation explains previously observed differences in the entanglement growth of multiple regions in chaotic and integrable systems. Finally, I will discuss how a simple form of the void formation probability in chaotic systems underlies the unitary evolution of far-from-equilibrium pure states to typical pure states.

In one spatial dimension, enhanced thermal and quantum fluctuations should preclude the existence of any long range ordered superfluid phase of matter. Instead, the quantum liquid should be described at low energies by an emergent hydrodynamic framework known as Tomonaga-Luttinger liquid theory. In this talk I will present details on some orthogonal but complimentary experimental and theoretical searches for this behavior in helium-4 including: (1) pressure driven superflow through nanopores, and (2) the excitation spectrum of a confined superfluid inside nano-engineered porous silica-based structures. For flow experiments, we have devised a framework that is able to quantitatively describe dissipation at the nanoscale leading to predictions for the critical velocity borne out by recent superflow measurements in nanopores. In confined porous media, with radii reduced via pre-plating with rare gases, I will discuss ab initio simulations of phase and density correlations inside the pore that are in agreement with recent neutron scattering measurements. Taken together, these results indicate significant progress towards the experimental observation of a truly one-dimensional quantum liquid.

This work was supported by the NSF through grants DMR-1809027 and DMR-1808440. Some computations were performed on the Vermont Advanced Computing Core supported in part by NSF award No. OAC-1827314.

Because the cuprate superconductors are doped Mott insulators, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. We consider the Hatsugai-Kohmoto model, an exactly solvable system that is a prototypical Mott insulator above a critical interaction strength at half filling. Upon doping or reducing the interaction strength, our exact calculations show that the system becomes a non-Fermi liquid metal with a superconducting instability. In the presence of a weak pairing interaction, the instability produces a thermal transition to a superconducting phase, which is distinct from the BCS state, as evidenced by a gap-to-transition temperature ratio exceeding the universal BCS limit. The elementary excitations of this superconductor are not Bogoliubov quasiparticles but rather superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. An unexpected feature of this model is that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies as seen in the cuprates.

How to construct a holographic model for viscoelastic materials? Why can that be useful and for what purpose? Which is the hydrodynamics behind these models? What do these models have in common with quasicrystals? What is a diffusive Goldstone mode and when does it appear? How and in which sense are solids different from fluids? What do theory and experiments in confined fluids tell us? How do glasses and Weyl semimetals sound? These are the questions that I will discuss with you during my talk!

"Supersolid" is the denomination given to a hypothetical phase of matter, simultaneously displaying crystalline order and flow of matter without dissipation. Whether such a phase could exist, and whether it might be detected experimentally, has been the subject of a long debate and intense investigation. For a long time it was believed that solid helium-4 might be a good candidate for the observation of supersolidity, but it is now accepted that that phenomenon does not take place in such a physical system. Thus, interest has shifted to assemblies of Bose particles possessing a finite electric or magnetic dipole moment. These systems have been extensively explored experimentally in recent times. The long ranged, and isotropic character of the interaction paves the way to the stabilization of novel, exotic phases of matter, including a supersolid one, which consists of ordered arrays of filaments. In this talk, results of first principle theoretical studies of the phase diagram of dipolar bosons carried out in our group will be reviewed, with particular emphasis on aspects directly connected to very recent experimental observations.

We discuss the dependence of the phase diagram of a hypothetical isotope of helium with nuclear mass less than 4 atomic mass units. We argue that with decreasing nucleus mass, the temperature of the superfluid phase transition (about 2.2 K in real He-4) increases, while that of the liquid-gas critical point (about 5.2 K in real He-4) decreases. We discuss various scenarios that may occur when the two temperatures approach each other and the order parameters of the superfluid and the liquid-gas phase transitions interact with each other. The simplest scenario, in which both order parameters become critical at particular values of the nuclear mass, temperature, and pressure can be ruled out based on an analysis of the Landau theory. We argue that in the most likely scenario, as the nuclear mass decreases, first, a tricritical point appears on the line separating the superfluid and the normal fluid phase, then the critical point disappears under the first-order part of superfluid phase transition line, and at the end the tricritical point disappears. The last change in the phase diagram occurs when the two-body scattering length crosses zero, which corresponds to the nuclear mass of about 1.6 u. We develop a quantitative theory that allows one to determine the phase diagram in the vicinity of this point. Finally, we discuss several ways to physically realize such liquids.

It was conjectured over 50 years ago that electrons in a high quality conductor could flow collectively as a viscous fluid, just like air or water. While impurities and umklapp scattering forbid this behavior in conventional metals, it has now become possible to study electrons that flow like classical fluids in high quality devices. I will overview the nature of hydrodynamic transport in electrons together with some recent experiments that allow us to directly probe this behavior.