Program

• See also the indico webpage

• Chair: Prof. Gert Aarts
• Dr. Lukas Rammelmuller, "Approaching imbalanced ultracold Fermi gases via complex Langevin"

Experiments with ultracold Fermi gases continue to provide us with a plethora of insight into the dynamics of strongly correlated systems. However, the theoretical description of such systems is challenging as analytic solutions are not available for general cases. On the numerical side progress is slowed down by the infamous sign-problem that causes Monte Carlo approaches to be exponentially expensive for increasing system sizes. To address this issue in a non-relativistic setting, we can learn from methodological advances made by the high-energy community. Specifically, we adapt the so-called complex Langevin (CL) approach to ultracold quantum gases which turns out to be a valuable tool in this context. In this talk, I will report on recent progress that has been made with the CL method in the regime of strongly interacting Fermi gases. In particular, I will focus on recent results for the unitary Fermi gas in the presence of a finite spin-asymmetry and discuss equations of state of various quantities. Further, we derive thermodynamic response functions which provide us with valuable information on the structure of the finite-temperature phase diagram.

• Chair: Dr. Alejandro Bermudez
• Dr. Luca Barbiero, "Engineering Z_2 lattice gauge theories with a strongly interacting atomic mixture"

Artificial magnetic fields and spin-orbit couplings have been recently generated in ultracold gases in view of realizing topological states of matter and frustrated magnetism in a highly controllable environment. Despite being dynamically tunable, such artificial gauge fi elds are genuinely classical and exhibit no back-action from the neutral particles. I will show that going beyond this paradigm is possible, and will demonstrate how quantized dynamical gauge fi elds can be created in mixtures of ultracold atoms in optical lattices. This can be achieved by employing a protocol by which atoms of one species carry a magnetic flux felt by an other species, hence realizing an instance of flux-attachment. This is obtained by combining coherent lattice modulation techniques with strong Hubbard interactions. I will also demonstrate how this setting can be arranged so as to implement lattice models displaying a local Z2 gauge symmetry, both in one and two dimensions. In conclusion I'll also provide a detailed analysis of a ladder toy model, which features a global Z2 symmetry, and reveal the phase transitions that occur both in the matter and gauge sectors.

• Dr. Monika Aidelsburger, "From Static to Dynamical Gauge Fields with Ultracold Atoms"

Recently, the realization of paradigmatic topological condensed matter models has been achieved with ultracold atoms in optical lattices, in particular the Hofstadter and the Haldane model. I will introduce one of the most common experimental methods used to generate topological band structures in ultracold atoms, i.e., Floquet engineering, and report on recent results as well as challenges regarding its application to many-body systems. The basic idea of the method is to periodically modulate the system's parameters to emulate the properties of a non-trivial static system. Floquet engineering has further been proposed to engineer density-dependent gauge fields or even complete gauge theories, which require an interaction between matter and gauge fields. One example is the realization of Z₂ lattice gauge theories, which play an important role in condensed matter physics and quantum computation. Recently, we have implemented such a model with a two-component mixture of ultracold bosons in a double-well potential - the basic building block of Z₂ lattice gauge theories.

• Chair: t.b.a.
• Prof. Sandro Stringari, "Decay of the sine-Gordon domain wall into confined vortex pairs: the case of a Rabi coupled bosonic mixture"

Sine-Gordon domain walls built with Rabi coupled Bose-Einstein condnsates can decay into vortex paires through two different mechanisms. For large values of the Rabi coupling the mixture undergoes a dynamic snake instability, caused by the negative value of the effective mass, and results in the fragmentation of the wall into smaller domain walls confining vortex pairs. For small values of $\Omega$ the instability has instead an energetic nature and is associated with the formation of confined vortex-antivortex pairs. Numerical predictions are given by solving the time dependent Gross-Pitaevskii equation in experimentally available configurations of sodium atomic gases.

• Dr. Erez Zohar , "Quantum Simulation and Fermionic PEPS Methods for Lattice Gauge Theories"

I will discuss the application of quantum simulation and tensor network methods for the study of lattice gauge theories, focusing on the work that has been carried out at MPQ: first, I will briefly talk about quantum simulation of lattice gauge theories with ultracold atoms in optical lattices - suggesting to observe non-perturbative elementary particle physics in atomic simulators; second, I will introduce gauged Gaussian fermionic PEPS - a particular tensor network construction of gauge invariant states, involving dynamical gauge fields and fermionic matter, allowing one to use the efficient tensor network toolbox for the study of gauge theories, and extend it, thanks to the presence of gauge fields, to numerical studies that combine Monte-Carlo in (2+1)-d and more

• Dr. Chris Self , "Topological bulk currents in topological insulators"

Topological insulators have symmetry protected edge states that support robust currents on physical edges of the system. We provide evidence that such topological phases also support bulk currents that are activated by local potential gradients even if they do not cause a phase transition. We perform calculations using the Haldane model as a lattice realisation of a topological insulator. I will begin with an outline of the Haldane model and the method we use to calculate currents. Following this I will show the behaviour we find for both the edge and bulk currents. Specifically, edge currents respond to a uniform chemical potential $\mu$ as $I_{edge} = e^2 \nu \mu / h$, where $\nu$ in the Chern number of the topological phase. Similarly, a small potential gradient $\nabla V$ induces a perpendicular bulk current $I_{bulk} = e^2 \nu a_0 | \nabla V | / h$, where $a_0$ is the lattice spacing. We demonstrate that bulk currents are topologically protected, like edge currents, and are not disturbed by noise such as temperature or local disorder. The resilience and the tuning of bulk currents with local potentials makes them an appealing medium for technological applications.

• Chair: t.b.a.
• Prof. Joaquin Drut, "Scale anomalies in low-dimensional fermions".

Nonrelativistic fermions in 2D with attractive pairwise interactions display a scale anomaly that is well-known. I will present the results of our Monte Carlo calculations for that system in few- and many-body regimes, in the ground state and at finite temperature. A less-known example of a scale anomaly, more recently studied by several groups, is the case of nonrelativistic fermions in 1D with attractive three-body interactions. I will discuss our recent work on that system and present some results on the few-body regime including the possibility of multicomponent fermions.

• Chair: t.b.a.
• Dr. Fabian Grudst , "Meson formation in strongly correlated quantum matter: A high-energy perspective"

Quantum gas microscopy provides a new perspective on strongly correlated quantum matter. Instantaneous projective measurements can reveal quantum fluctuations on all time scales, which allows access to high-energy properties. In this talk I show how these unique capabilities can be used to search for universal constituents of strongly correlated quantum matter, analogous to the search of elementary particles in high-energy physics. Specifically, I will focus on spinons and chargons in the doped Fermi-Hubbard or t-J model, which can form mesonic bound states in two dimensions. Analogies with Z2 lattice gauge theories will briefly be discussed.

• Prof. Yannick Meurice, " Lattice Gauge Theory with Cold Atoms and Quantum Computers"

We review tensorial formulations of lattice gauge/spin theories and algorithmic aspects of their coarse graining. We discuss truncations and show that they preserve the symmetries of the original lattice models (arXiv:1903.01918).We show that tensor reformulations fit the needs of quantum computation. We discuss concrete proposals of quantum simulation experiments with cold atoms for the Abelian Higgs model and other simple models in 1+1 dimensions. We discuss methods to measure the second order Renyi entanglement entropy with cold atoms. We report recent calculations for real time scattering for the quantum Ising model (arXiv:1901.05944) and discuss the errors associated with the Trotter step size and gate errors for existing or near term quantum computers (such as IBM or trapped ions devices).

• Dr. Luca Tagliacozzo, "Universal and robust phenomena in and out of equilibrium"

Universal and robust phenomena in and out of equilibrium. We need to understand which physical phenomena are robust when simulated with approximated classical and quantum algorithms. Here I will review some of the results we obtained in this direction for the simulation of lattice systems with tensor networks techniques (classical simulations). I will mainly focus on 1D and 2D quantum criticality and on the out-of-equilibrium evolution of 1D quantum systems.

• Chair: t.b.a.
• Dr. Mari Carmen Bañuls, "Using TNS to solve gauge field theories on the lattice: the (1+1)-dimensional testbed"

Tensor Network States are ansatzes for the efficient description of the state of a quantum many-body system. They can be used to study static and dynamic properties of strongly correlated states. In this talk I will present some recent work on the application of these techniques to study Lattice Gauge Theories. In particular, using the Schwinger model as a testbench, we have shown that these ansatzes are suitable to approximate low energy states precisely enough to allow for accurate finite size and continuum limit extrapolations of ground state properties, mass gaps and temperature dependent quantities. Beyond this case the feasibility of the method has already been tested also for non-Abelian models, out-of-equilibrium scenarios, and non-vanishing chemical potential, the latter two cases that offer difficulties to standard Montecarlo techniques.

• Dr. Titas Chanda, “Pair-production and real-time confinement in 1+1 discretized scalar QED"

At high energies, pairs of particle and anti-particle are created from energetically favorable photons due to relativistic physics. Moreover, due to local (Abelian or non-Abelian) gauge symmetries present in high-energy physics, we have celebrated “confinement” phenomenon in the non-perturbative limits, which is responsible for binding elementary quarks into baryons. We consider discretized version of 1+1 scalar (bosonic) QED on a one-dimensional lattice, which can be simulated by ultra-cold atomic systems. The model obeys local U(1) Abelian gauge invariance. By employing one-dimensional tensor network algorithms, we show signatures of pair-production in the time-evolution of the system after a local or global quench, where particles and anti-particles get created and fly away in opposite directions. Moreover, due to confinement, attraction between particles and anti-particle increases with distance as they fly away from each other, which strongly hinders the spreading of information in the dynamics, and results in bending of light-cone.

• Dr. Emanuele Tirrito , "Creutz-Hubbard ladder and its connection to high-energy physics."

Understanding the robustness of topological phases of matter in the presence of strong interacions is a difficult challenge of modern theoretical physics. In this talk, I will describe the imbalanced Creutz-Hubbard ladder, a paradigmatic topological-insulator model that can be realized in a synthetic ladder made of two intenal states of ultracold fermionic atoms in a one-dimensional optical lattice. I will discuss its phase diagram, and the interesting connections to high-energy physics Gross-Neveu model, which were put forth in the context of quantum chromidynamics, and open an interesting dialogue between both disciplines. Moreover I will discuss the large- N study, both in the Hamiltonian and Euclidean formalisms, we have developed to understand the Gross-Neveu phase diagram and their numerical benchmark via Matrix Product State methods.

• Chair: t.b.a.
• Dr. Christof Witenberg , "Ultracold topological matter via Floquet driving".

Ultracold atoms in optical lattices constitute a versatile platform to study the fascinating phenomena of gauge fields and topological matter. Periodic driving can induce topological band structures with non-trivial Chern number of the effective Floquet Hamiltonian and paradigmatic models, such as the Haldane model on the honeycomb latticce, can be directly engineered. In this talk, I will report on recent experiments, in which we realized new approaches for measuring the Chern number in this system and map out the Haldane phase diagram.

• Chair: t.b.a.
• Dr. Alessio Celi, “2D U(1) gauge theories in configurable Rydberg arrays”

Understanding strongly coupled gauge theories is a fundamental challenge of physics, with dramatic implications both for high energy and condensed matter. Doing it with a quantum simulator is a formidable test for quantum simulation. Here we show that by exploiting electromagnetic duality, we can create the Rokhsar-Kivelson Hamiltonian –a 2D U(1) lattice gauge theory that describes quantum dimers- in running Rydberg experiments by exploiting Rydberg blockade in a novel fashion. Quantum phases like resonating valence bonds and their dynamical properties become immediately accessible to Rydberg experiments, with dramatic implications for atomic, condensed matter, and high energy physics.

• Dr. David Schaich, "Supersymmetric lattice field theories: Classical simulations and quantum opportunities"

I will motivate, review and propose lattice investigations of supersymmetric systems, which play prominent roles in modern theoretical physics---as a tool to improve our understanding of quantum field theory, as an ingredient in many models of new high-energy physics, and as a means to study quantum gravity via holographic duality. Classical simulations of certain supersymmetric lattice field theories have made significant progress in recent years. After an overview of the classical state of the art, with a focus on lower-dimensional systems, I will discuss opportunities for future quantum simulations to address current challenges, in particular by evading sign problems.

• Chair: t.b.a.
• Dr. João Pinto Barros, "2-d CP(N-1) models and merons as the relevant topological charge carriers in CP(1)"

2-d CP(N-1) models share several relevant features with QCD. These include asymptotic freedom, nonperturbatively generated mass gap and nontrivial topological charge, which make 2-d CP(N-1) models interesting from the theoretical point of view. By other side, they also arise as effective low-energy theories of certain SU(N) quantum spin ladders. This feature can, in principle, be explored for quantum simulations and even be used to address their continuum limit. After an overview of 2-d CP(N-1) models, we will focus on the particular case of CP(1), which is equivalent to the 2-d O(3) model and can be efficiently simulated using a Wolff cluster algorithm. By an analytic rewriting of the partition function, we identify a particular type of Wolff clusters with half-integer charge – merons – as the relevant topological charge carriers. In contrast to semiclassical instantons, merons are uniquely identified in the fully nonperturbative functional integral. While instantons are smooth 2-d objects, merons are physical objects with a fractal dimension D=1.88(1), which also exist in the continuum limit. In particular, we show that the logarithmic divergence of the topological susceptibility of CP(1) is entirely physical, originating from small merons. Our study raises hopes that a solid field theoretical identification of the relevant topological degrees of freedom may also be achievable in higher CP(N-1) models and in non-Abelian gauge theories in general.

• Dr. Javier Molina, "Entanglement Renormalization for Interacting Field Theories"

In this talk, I will present a general method to build the entanglement renormalization (cMERA) for interacting quantum field theories. This improves upon the well-known Gaussian formalism used in free theories. Thus, we provide a class of variational, non-Gaussian, and scale-dependent wavefunctionals (NG-cMERA), for which expectation values of local operators in interacting Quantum Field Theories can be efficiently calculated analytically and in a closed form. The scalar field theory with quartic interaction is used to show how the non-perturbative effects far beyond the Gaussian approximation are obtained by considering the energy functional and the correlation functions of the theory.

• Dr. Xhek Turkeshi, "Identifying parent Hamiltonians via entanglement: from field theory ansaetze to lattice models"

Variational wave functions have been a successful approach to strongly correlated systems and novel phases of matter. A natural question, motivated also by the recent experimental advances, is to find parent Hamiltonians that have a desired input state as the ground state. In this talk we present an algorithm for parent Hamiltonian reconstruction relying on a field theory result concerning the entanglement content of the ground state.

• Chair: t.b.a.
• Dr. Leonardo Mazza, "Detecting non-Abelian anyons in cold gases"

Fractional statistics is forbidden in real 4-dimensional space time but possible in systems with two spatial dimensions. In this talk I will discuss how to use cold-atom experiments as a quantum simulator for a two-dimensional world with anyons. We present a method for characterizing non-Abelian anyons that is based only on static measurements and that does not rely on any form of interference or time evolution. For geometries where the anyonic statistics can be revealed by rigid rotations of the anyons, we link this property to the angular momentum of the initial state. We test our method on the paradigmatic example of the Moore-Read state, that is known to support excitations with non-Abelian statistics of Ising type. As an example, we reveal the presence of different fusion channels for two such excitations, a defining feature of non-Abelian anyons. This is obtained by measuring density-profile properties, like the mean square radius of the system or the depletion generated by the anyons. This study paves the way to novel methods for characterizing non-Abelian anyons, both in the experimental and theoretical domains. Reference: Macaluso, Comparin, Mazza and Carusotto, arXiv:1903.03011 (2019)

• Chair: t.b.a.
• Dr. Philipp Hauke, “Reliable quantum simulation of gauge theories: near-future target phenomena and robustness against Trotter errors“

With the advent of first quantum-simulation experiments of lattice gauge theories, an exciting perspective for solving quantum many-body models has moved within grasp. Here, I will outline future steps towards quantum simulations of gauge theories of practical relevance. In particular, I will discuss physical phenomena that may be accessed with near-future quantum simulators which are restricted to rather small lattices and coherence times. Such robust first targets include the Schwinger mechanism of quantum electrodynamics and a novel dynamical topological transition. Moreover, I will highlight the major challenge of certifying the reliability of the quantum simulation. In particular, I will discuss how quantum chaos makes Trotter errors, which are inherent to any digital quantum simulation, much more benign than previously assumed. These advances open the door towards reliable quantum simulations of relevant physical phenomena.

• Dr. Torsten Zache, "Simulating gauge theories: microscopic vs. universal approaches"

Analog quantum simulators and digital quantum computers have the exciting prospect to access physical phenomena that lie beyond the reach of classical simulations. In the context of gauge theories, the microscopic implementation of simple toy models has been achieved recently. However, it is necessary to identify physically relevant settings that can be probed with current experimental limitations. At the same time, universal aspects of gauge theories may also be studied with seemingly unrelated physical systems. This becomes possible in the many-body limit described by effective quantum field theories. In this talk, I will report on our recent progress of these two complementary approaches. In quantum electrodynamics in one and two spatial dimensions, we have identified dynamical topological transitions and anomalous parity violating dynamics, respectively. Both constitute ideal targets for future experiments. On the other hand, we study emergent universal real-time dynamics as described by so-called non-thermal fixed points. This is facilitated by recent experimental achievements in measuring higher-order correlation functions, which will allow for extracting the effective couplings of quantum many-body systems in the near future.

• Dr. Giandomenico Palumbo, "Tensor gauge fields in topological phases of matter"

The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter physics, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector potential defined in momentum space. Inspired by string theory, where tensor (Kalb-Ramond) gauge fields play a crucial role in bosonic strings, in this talk I introduce and explore generalized Berry connections, named "tensor Berry connections", which behave like Kalb-Ramond fields in the momentum space of topological systems. My approach consists in a general construction of effective gauge fields, which I ultimately relate to the components of Bloch states. I apply this formalism to various models of topological matter, and I investigate the topological invariants that result from generalized Berry connections. I introduce the 2D Zak phase of a tensor Berry connection, which I then relate to the more conventional first Chern number; I also reinterpret the winding number characterizing 3D chiral topological insulators to a Dixmier-Douady invariant, which is associated with the curvature of a tensor connection. Besides, my approach identifies the Berry connection of tensor monopoles, which are found in 4D Weyl-type cold-atom systems. These results shed light on the emergence of gauge fields in condensed-matter physics, with direct consequences on the search for novel topological states in solid-state and quantum-engineered systems

• Chair: t.b.a.
• Prof. Fred Jendrzejewski , "Dynamical gauge fields in atomic mixtures"

Mixtures of ultracold atomic gases are a versatile platform for the investigation of a wide variety of fundamental questions in physics. In this talk, we will discuss first discuss their realization as done in our lab. We will then present our approach to the quantum simulation of dynamical gauge fields.

• Dr. Daniel Gonzalez-Cuadra, "The Z2 Bose-Hubbard model: from symmetry breaking to symmetry protection"

In this talk, I will present a one-dimensional model of interacting bosons coupled to a dynamical Z2 field, the Z2 Bose-Hubbard model. Here, the field plays a similar role to a dynamical lattice structure in solid-state physics. In particular, it allows the system to undergo a bosonic Peierls transition for sufficiently strong interactions, where translational symmetry is spontaneously broken [1]. I will show how, for commensurate densities, the resulting phase is an interaction-induced symmetry-breaking topological insulator, where the topological properties coexist with the presence of long-range order [2]. This particular interplay between symmetry breaking and symmetry protection gives rise to interesting static and dynamical effects, such as constrained topological transitions and a self-adjusted fractional pumping [3]. This model, that can be implemented using atomic systems, constitutes an interesting playground to study novel strongly-correlated topological phenomena.

[1] D. González-Cuadra et al., Phys. Rev. Lett. 121, 090402 (2018) [2] D. González-Cuadra et al., Phys. Rev. B 99, 045139 (2019) [3] D. González-Cuadra et al., arXiv:1903.01911 (2019) (accepted in Nat. Commun.)

• Dr. Judah F Unmuth-Yockey "Rotor formulation of 3d U(1) gauge theory and amenability to quantum simulation".

Quantum simulation aims to simulate physically interesting models using quantum systems. In order to understand the practical and subtle nature of quantum simulation one attempts to gradually and systematically quantum simulate increasingly difficult models, eventually working towards the standard model. Here, using spin-gauge duality for a 3d model, we show that 3d u(1) gauge theory can be cast as a spin model with only local interactions. This makes it more tractable, since the initial gauge freedom is completely absent in the spin model. In addition we include ideas to quantum simulate this model with ultra cold atoms on an optical lattice.

• Chair: t.b.a.
• Dr. Enrique Rico, "Lattice gauge theories with superconducting circuits"

We will describe the quantum link formalism for gauge theories and we will show how these models can be implemented within quantum technologies.We will discuss in some detail several approaches to fix the Gauss law condition for gauge invariant models (energy penalty, exact implementation, encoding). Finally, we will show the tools from superconducting circuits to implement these ideas

• Chair: t.b.a.
• Prof. Ignacio Cirac, "Tensor Network and Quantum Information Theory: Applications in Condensed Matter and High Energy Physics "

Certain Quantum Many-body states can be efficiently described in terms of tensor networks.Those include Matrix Product States (MPS), Projected Entangled-Pair Etates (PEPS), or the Multi-scale Entanglement Renormalization Ansatz (MERA). They play an important role in quantum computing, error correction, or the description of topological order in condensed matter physics, and are widely used in computational physics. In this talk, I will briefly review one of the basic results in the theory of tensor networks and explain some of their applications to high-energy physics models.

• Dr. Patrick Emonts , " Combining Tensor Networks and Monte Carlo for Lattice Gauge Theories"

By combining Monte Carlo sampling and Tensor Networks, specifically Gauged Gaussian Projected Entangled Pair States (GGPEPS), we show an efficient way to compute expectation values for lattice gauge theories including fermionic matter in arbitrary spatial dimensions. The method can be applied to arbitrary gauge groups, in the talk, however, we will focus on the U(1) gauge group. In particular, we will have a detailed look at the calculation of observables like Wilson loops and mesonic strings.