Erez Zohar

Cold-Atom Quantum Simulator for SU(2) Yang-Mills Lattice Gauge Theory

Non-Abelian gauge theories play an important role in the standard model of particle physics, and unfold a partially unexplored world of exciting physical phenomena. In this Letter, we suggest a realization of a non-Abelian lattice gauge theory-SU(2) Yang-Mills in (1 + 1) dimensions, using ultracold atoms. Remarkably, and in contrast to previous proposals, in our model gauge invariance is a direct consequence of angular momentum conservation and thus is fundamental and robust. Our proposal may serve as well as a starting point for higher-dimensional realizations.

Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices.

Can high-energy physics be simulated by low-energy, non-relativistic, many-body systems such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure an atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective low-energy symmetry, or as an exact symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to a new type of (table-top) experiments which will be used to study various QCD (quantum chromodynamics) phenomena, such as the confinement of dynamical quarks, phase transitions and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing the quantum simulation of Abelian and non-Abelian lattice gauge theories in 1  +  1 and 2  +  1 dimensions using ultracold atoms in optical lattices.

Simulating Compact Quantum Electrodynamics with Ultracold Atoms: Probing Confinement and Nonperturbative Effects

Recently, there has been much interest in simulating quantum field theory effects of matter and gauge fields. In a recent work, a method for simulating compact quantum electrodynamics (CQED) using Bose-Einstein condensates has been suggested. We suggest an alternative approach, which relies on single atoms in an optical lattice, carrying 2l + 1 internal levels, which converges rapidly to CQED as l increases. That enables the simulation of CQED in 2 + 1 dimensions in both the weak and the strong coupling regimes, hence, allowing us to probe confinement as well as other nonperturbative effects of the theory. We provide an explicit construction for the case l = 1 which is sufficient for simulating the effect of confinement between two external static charges.

Quantum simulations of gauge theories with ultracold atoms: Local gauge invariance from angular-momentum conservation

Quantum simulations of High Energy Physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge and Lorentz invariance. In this paper we discuss these special requirements, and present a new method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows to include local gauge invariance as a fundamental symmetry of the atomic Hamiltonian, arising from natural atomic interactions and conservation laws (and not as a property of a low energy sector). This allows us to implement elementary gauge invariant interactions for three lattice gauge theories: compact QED (U(1)), SU(N) and Z_N, which can be used to build quantum simulators in 1+1 dimensions. We also present a new loop method, which uses the elementary interactions as building blocks in the effective construction of quantum simulations for d+1 dimensional lattice gauge theories (d>1), without having to use Gausss law as a constraint, as in previous proposals. We discuss in detail the quantum simulation of 2+1 dimensional compact QED and provide a numerical proof of principle. The simplicity of the already gauge invariant elementary interactions of this model suggests it may be useful for future experimental realizations.

Simulating (2+1)-dimensional lattice QED with dynamical matter using ultracold atoms.

We suggest a method to simulate compact quantum electrodynamics using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows us to test the dynamical effects of confinement as well as the deformations and breaking of two-dimensional flux loops, and to observe the Wilson-loop area law.

Non-Abelian string breaking phenomena with matrix product states

A bstractUsing matrix product states, we explore numerically the phenomenology of string breaking in a non-Abelian lattice gauge theory, namely 1+1 dimensional SU(2). The technique allows us to study the static potential between external heavy charges, as traditionally explored by Monte Carlo simulations, but also to simulate the real-time dynamics of both static and dynamical fermions, as the latter are fully included in the formalism. We propose a number of observables that are sensitive to the presence or breaking of the flux string, and use them to detect and characterize the phenomenon in each of these setups.

Formulation of lattice gauge theories for quantum simulations

We examine the Kogut-Susskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We consider both discrete and continuous gauge groups and adopt a realistic multi-component Fock space for the definition of matter degrees of freedom. In particular, we express the Hamiltonian of the gauge theory and the Gauss law in terms of Fock operators. The gauge fields are described in two different bases, based on either group elements or group representations. This formulation allows for a natural scheme to achieve a consistent truncation of the Hilbert space for continuous groups, and provides helpful tools to study the connections of gauge theories with topological quantum double and string-net models for discrete groups. Several examples, including the case of the discrete

Fermionic Projected Entangled Pair States and Local U(1) Gauge Theories

D_3

Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study

gauge group, are presented.

Building Projected Entangled Pair States with a Local Gauge Symmetry

Tensor networks, and in particular Projected Entangled Pair States (PEPS), are a powerful tool for the study of quantum many body physics, thanks to both their built-in ability of classifying and studying symmetries, and the efficient numerical calculations they allow. In this work, we introduce a way to extend the set of symmetric PEPS in order to include local gauge invariance and investigate lattice gauge theories with fermionic matter. To this purpose, we provide as a case study and first example, the construction of a fermionic PEPS, based on Gaussian schemes, invariant under both global and local U(1) gauge transformations. The obtained states correspond to a truncated U(1) lattice gauge theory in 2 + 1 dimensions, involving both the gauge field and fermionic matter. For the global symmetry (pure fermionic) case, these PEPS can be studied in terms of spinless fermions subject to a p-wave superconducting pairing. For the local symmetry (fermions and gauge fields) case, we find confined and deconfined phases in the pure gauge limit, and we discuss the screening properties of the phases arising in the presence of dynamical matter.