To get email notifications and obtain the Zoom links, subscribe to one of the following mailing lists:
Some of these talks are recorded and uploaded to our youtube channel:
https://www.youtube.com/channel/UCiNi2o6w8Mom061kMDTTLIw/
Biao Lian (Princeton), "Hofstadter butterfly: a momentum space method, and topological effects"
In the first part, I will present a generic open momentum space method for calculating the Hofstadter butterfly, which simply substitutes the quasi-momentum by the Landau level (LL) operators. By taking a LL cutoff (and a reciprocal lattice cutoff for continuum models), one obtains the Hofstadter butterfly with in-gap spectral flows. The spectral flows can be understood as edge states on a momentum space boundary and can be removed, from which one can determine the two topological numbers (t, s) of the Diophantine equation. t is the Chern number, while s can be understood as a dual Chern number, which we prove corresponds to a quantized Lorentz susceptibility. In the second part, I will show that topological bands quite generically exhibit connected Hofstadter butterflies in a magnetic field. In particular, I will discuss the Hofstadter spectra of Chern bands and the fragile topological bands, which have been experimentally observed in Moire systems.
Host: Dominic Else
The realization of programmable quantum many-body systems capable of coherently controlling hundreds of individual particles is one of the frontiers of quantum science and engineering. Such systems provide unique insights into correlated quantum states of matter and enable new approaches to quantum information processing. Our experimental platform at Harvard consists of defect-free 2D arrays of over 200 laser-cooled neutral atoms trapped in optical tweezers and with long-range van der Waals interactions between highly-excited Rydberg states. Using this platform, we realize a tunable Ising-type quantum spin model with several distinct phases that arise from the interplay between interactions and driving fields. We map out the phase diagram using single-site-resolved state readout, demonstrate high-fidelity preparation of antiferromagnetic Néel-ordered states, identify a quantum phase transition in the (2+1)D Ising universality class, and use non-equilibrium dynamics to probe the nature of a novel phase stabilized by quantum fluctuations.
Host: Dominic Else
Sid Morampudi (MIT), "Universal entanglement of typical states in constrained systems"
Constraints play an important role in the structure of a wide variety of quantum systems ranging from gauge theories to atomic systems. Their impact on dynamics and entanglement thermalization are just beginning to be unravelled. In this talk, I will show that the entanglement spectrum of random wave functions split into various universal “entanglement phases” depending on the constraint structure of the system. The simplest class of constraints already reveals a non-trivial phase diagram revealing an unusual critical point and violations of Page’s inequality. The results point to a novel structure in the entanglement of infinite temperature eigenstates of thermalizing constrained systems.
Host: Ruben Verresen
Inspired by twisted bilayer graphene, I will consider a model of n pairs of tunnel-coupled opposite Chern bands in the presence of strong repulsive interaction with U(n) symmetry. For n=2, I will show that this model develops SU(2)-singlet charge 2e superconductivity in the vicinity of half-filling due to skyrmion pairing. I will show how the properties of this superconductor can be derived within a large N analysis of the non-compact CP1 model. In this setting the superconductor to insulator transition tuned by bandwidth, is the well known deconfined quantum critical point, believed to exhibit an emergent SO(5) symmetry. I will generalize this problem to n=4 and beyond, presenting a parton field theory to study the unusual superconducting phases as well as phase transitions in these models and argue that this setup can be home to exotic deconfined quantum critical points beyond the well-studied SO(5) theory.
Host: Dominic Else
In this talk I will describe a proposed class of bosonic systems whose low-energy excitations are located on the surface of a sphere in momentum space. In some aspects these phases can be regarded as bosonic analogues of Fermi liquids. Unlike Fermi liquids however they lack quasiparticles, possess different RG flows, and have correlation functions controlled by continuously varying exponents. This is ongoing work with T. Senthil and A. Vishwanath.
Host: Ruben Verresen
Yijian Zou (Perimeter Institute), "Extracting universal data of critical quantum spin chains from periodic uniform matrix product states"
We explain how periodic uniform matrix product states (puMPS) can be used to extract universal data of critical quantum spin chains. We show that puMPS and puMPS Bloch states accurately capture the ground state and low-energy excited states of critical quantum spin chains up to several hundreds of spins. This enables us to extract (i) scaling dimensions, conformal spins of scaling operators, (ii) spectral renormalization group flows between CFTs, (iii) lattice realizations of scaling operators, and operator product expansion coefficients, (iv) emergent symmetries such as superconformal symmetry, and (v) universal tripartite entanglement of the ground state, including entanglement of purification and reflected entropy. We give examples how each of these is achieved and discuss potential applications to open problems.
Host: Ruben Verresen
Han Ma (Perimeter Institute), "Constraints on beta functions in field theories"
Renormalization group allows a systematical understanding of the physical phenomena at different energy scales. The beta functions describe how couplings run as a function of energy scales. In general, all couplings allowed by symmetry and locality are generated under the renormalization group flow, and the exact renormalization group flow takes place in the infinite dimensional space of couplings.
In this talk, I will show that the renormalization group flow is highly constrained so that the beta functions defined in a measure zero subspace of couplings completely determine the beta functions in the entire space of couplings. I will also give a quantum renormalization group-based algorithm for reconstructing the full beta functions from the beta functions defined in the subspace.
Host: Dominic Else
Shreya Vardhan (MIT), "A universal approximation for entanglement entropies of equilibrated pure states"
When a pure state in a non-integrable quantum many-body system is evolved to late times, we expect it to thermalize—that is, we expect its macroscopic properties to resemble those of an equilibrium density matrix. However, the entanglement entropies of such a state must obey certain constraints coming from unitarity, which are not obeyed by an equilibrium density matrix. In this talk, I will explain an approximation method that leads to a simple universal expression for the entanglement entropies of an equilibrated pure state in any quantum many-body system. This expression is independent of the details of the initial state and hence reflects thermalization, while also being manifestly consistent with unitarity. I will also discuss how this method can be applied to equilibrated pure states in gravitational systems, such as those involving black holes, where it can be used to address the information loss paradox of Hawking.
Host: Ruben Verresen
Ya-Hui Zhang (Harvard), "Fractional Fermi Liquid from doping spin-triplet doublons and possible realization in Nickelate"
In this talk I will propose and study a new kind of t-J model. I will consider an unusual case for hole doping a spin 1/2 Mott insulator formed by d^9 state: the spin-triplet doublon (d^8 state ) has lower energy than the spin singlet doublon. This scenario can be potentially realized in transition metal oxide with large Hund’s coupling between the two e_g orbitals and with oxygen band far away from fermi energy, for example, in certain nickelate in which we dope S=1 Ni^{2+} into Mott insulator formed by S=1/2 Ni^{1+}. The low energy model is an unconventional t-J model with two spin 1/2 singly occupied states and three spin-triplet doublon states per site. We simulate the 1D version of this model by DMRG and find clear evidence of a 1D analog of fractional Fermi liquid (FL*) phase: a small pocket coexists with the spin liquid inherited from the Mott insulator, with a total central charge c=3. I will provide a theoretical description based on a three-fermion parton mean field theory with U(2) gauge structure. The theory can be easily generalized to high dimension and I will conjecture that a metal with small Fermi surface is a generic fate of this unusual t-J model. If time allowed, I will also show numerical evidence of a continuous quantum critical point in 1D between this FL* phase and the conventional phase with large Fermi surface. Across the transition there is a jump of total Fermi surface volume (or carrier density) by 1/2 .
Host: Dominic Else
We study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs. The resulting model has a new parameter, k, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse limit corresponding to the thermodynamic limit at fixed k. We argue that this sparse SYK model recovers the interesting global physics of ordinary SYK even when k is of order unity. In particular, at low temperature the model exhibits a gravitational sector which is maximally chaotic. Our argument proceeds by constructing a path integral for the sparse model which reproduces the conventional SYK path integral plus gapped fluctuations. The sparsity of the model permits larger scale numerical calculations than previously possible, the results of which are consistent with the path integral analysis. Additionally, we show that the sparsity of the model considerably reduces the cost of quantum simulation algorithms. This makes the sparse SYK model the most efficient currently known route to simulate a holographic model of quantum gravity. We also define and study a sparse supersymmetric SYK model, with similar conclusions to the non-supersymmetric case. Looking forward, we argue that the class of models considered here constitute an interesting and relatively unexplored sparse frontier in quantum many-body physics.
Host: Dominic Else
Tarun Grover (UCSD), "Mixed-state entanglement as a diagnostic for quasiparticles and finite-T topological order"
Quantum entanglement of pure states has led to new insights into a wide variety of topics. Entanglement of mixed states is however less well understood. In this talk I will focus on a few themes where mixed-state entanglement leads to new insights that are difficult to obtain otherwise. I will mainly focus on two topics: (i) Characterizing finite-temperature topological order (ii) Detecting presence of quasiparticles. Time permitting, I will also discuss characterizing multi-component systems such as quantum disentangled liquids, and a class of gapless topological phases.
Host: Ruben Verresen
Many of the most mysterious phenomena in condensed matter physics involve systems near quantum phase transitions where the interplay of quenched disorder and strong interactions likely plays an essential role. Examples include the appearance of "anomalous" 2d metallic phases and the sharing of critical exponents between seemingly different quantum Hall plateau transitions. However, few organizing principles have been developed for understanding quantum critical systems with interactions and disorder, and analytically tractable models have proven rare. In this talk, I will describe some of the first examples of quantum critical theories in 2d characterized by finite disorder and interaction strengths, focusing on the particular example of quenched disorder in a theory of scalar bosons at their Wilson-Fisher fixed point. We will see that dirty-interacting quantum critical points generally exhibit universal features not found together in systems with interactions or disorder alone, such as vanishing compressibility, finite DC conductivities, and novel critical exponents.
Host: Ruben Verresen
Tyler D. Ellison (University of Washington), "Disentangling interacting fermionic symmetry-protected topological phases of matter"
Symmetry-protected topological (SPT) phases of matter are described by short-range entangled states, where, by definition, the entanglement can be (approximately) generated by a finite-depth quantum circuit (FDQC). For each bosonic SPT phase within the group cohomology classification, there is a well-establised fixed-point state that can be prepared by a FDQC built expressly in terms of the corresponding cohomology data. In this talk, I will describe a generalization to a class of (3+1)D intrinsically interacting fermionic SPT phases known as the supercohomology phases. In particular, I will introduce a FDQC, constructed directly from the associated supercohomology data, that both prepares a representative state from an unentangled state and can be used to define an exactly solvable Hamiltonian within the supercohomology phase. The derivation of the FDQC utilizes a series of exact lattice dualities that relate bosonic SPT phases with a certain 2-group symmetry to supercohomology phases. A primary feature of this approach is that the “symmetry fractionalization” on fermion parity flux loops, characteristic of supercohomology phases, is immediate. Time permitting, I will comment on the construction of topologically ordered boundaries of supercohomology phases and generalizations to fermionic SPT phases outside of the supercohomology classification.
This work was done in collaboration with Yu-An Chen and Nathanan Tantivasadakarn and is based on arXiv:2008.05652.
Host: Ruben Verresen
Out-of-time-order correlators (OTOCs) describe quantum chaos in a way comparable to classical chaos, at least for systems with a large parameter N, where the early-time OTOCs are characterized by a Lyapunov exponent, whose inverse defines a time scale known as Lyapunov time. In this talk, I will discuss another time scale called branching time and derive a bound on it for SYK-like models. It turns out that the branching time plays significantly different roles in the strong and weak coupling limits, suggesting two different mechanisms for scrambling. This talk is based on [1812.00120] with Alexei Kitaev and work in progress with Alexei Kitaev and Pengfei Zhang.
Host: Dominic Else
Tibor Rakovszky (TUM/Stanford), "Dissipation-assisted operator evolution method for capturing hydrodynamic transport"
We introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. DAOE is based on evolving observables in the Heisenberg picture, and applying an artificial dissipation that reduces the weight on non-local operators. We represent the observable as a matrix product operator, and show that the dissipation leads to a decay of operator entanglement, allowing us to capture the dynamics up to long times. We test this scheme by calculating spin and energy diffusion constants in a variety of physical models. By gradually weakening the dissipation, we are able to consistently extrapolate our results to the case of zero dissipation, thus estimating the physical diffusion constant with high precision.
Host: Ruben Verresen
Max Metlitski (MIT), "Boundary criticality of the O(N) model in d = 3 critically revisited"
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 O(3) symmetry.
Host: Ruben Verresen
Topology in quantum matter is typically associated with gapped phases. For example, in symmetry protected topological (SPT) phases, the bulk energy gap localizes edge modes near the boundary. In this talk, I introduce a new mechanism that leads to topological phases which are not only gapless but where the absence of a gap is essential. These `intrinsically gapless SPT phases' have no gapped counterpart and are hence also distinct from recently discovered examples of gapless SPT phases. The essential ingredient of these phases is that on-site symmetries act in an anomalous fashion at low energies. Intrinsically gapless SPT phases are found to display several unique properties including (i) protected edge modes that are impossible to realize in a gapped system with the same symmetries, (ii) string order parameters that are likewise forbidden in gapped phases, and (iii) constraints on the phase diagram obtained upon perturbing the phase. The predictions of the general theory are verified in a specific realization protected by Z_4 symmetry, the one dimensional Ising-Hubbard chain, using both numerical simulations and effective field theory. Time permitting, I will discuss extensions to higher dimensions and possible experimental realizations.
Host: Dominic Else
Dominic Else (MIT), "Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals"
A well-known property of Fermi liquids is that have they have a Fermi surface in momentum space whose volume enclosed is determined by the microscopic electron density according to Luttinger's theorem. The situation for metallic states not described by Fermi liquid theory -- so-called "non-Fermi liquids" -- has so far been far less clear. Do these systems necessarily have Fermi surfaces? What exactly do we even mean by a Fermi surface in systems without quasiparticles? If there is a Fermi surface, does it obey Luttinger's theorem?
In this talk, I will describe a recent work [1] in which powerful non- perturbative methods (involving ideas previously appearing in the theory of symmetry-protected topological phases) are applied to these and other related questions. Our results can be viewed as a vast generalization of both Luttinger's theorem and the Lieb-Schultz-Mattis theorem. Along the way, I will introduce the concept of an "ersatz Fermi liquid". For reasons that I will outline, it is to be expected that most if not all non-Fermi liquids are in fact ersatz Fermi liquids. We show that ersatz Fermi liquids share a number of key properties in common with Fermi liquids, including a well-defined Fermi surface that obeys Luttinger's theorem.
[1] https://arxiv.org/abs/2007.07896
Host: Ruben Verresen