Phase Transitions in $Z_n$ Gauge Models: Towards Quantum Simulations of the Schwinger-Weyl QED

Abstract

We study the ground-state properties of a class of ${\mathbb{Z}}_n$ lattice gauge theories in 1 + 1 dimensions, in which the gauge fields are coupled to spinless fermionic matter. These models, stemming from discrete representations of the Weyl commutator for the $\mathrm{U}(1)$ group, preserve the unitary character of the minimal coupling, and have therefore the property of formally approximating lattice quantum electrodynamics in one spatial dimension in the large-$n$ limit. The numerical study of such approximated theories is important to determine their effectiveness in reproducing the main features and phenomenology of the target theory, in view of implementations of cold-atom quantum simulators of QED. In this paper we study the cases $n=2÷8$ by means of a DMRG code that exactly implements Gauss' law. We perform a careful scaling analysis, and show that, in absence of a background field, all ${\mathbb{Z}}_n$ models exhibit a phase transition which falls in the Ising universality class, with spontaneous symmetry breaking of the $CP$ symmetry. We then perform the large-$n$ limit and find that the asymptotic values of the critical parameters approach the ones obtained for the known phase transition the zero-charge sector of the massive Schwinger model, which occurs at negative mass.

15 pages, 18 figures

References in corpus (19)

• Many-Body Physics with Ultracold Gases
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• A one-dimensional liquid of fermions with tunable spin
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Optical Abelian Lattice Gauge Theories
• Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
• Quantum simulation of the Schwinger model: A study of feasibility
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Implementing quantum electrodynamics with ultracold atomic systems
• Real-time simulation of the Schwinger effect with Matrix Product States
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Confinement and string breaking for QED${}_2$ in the Hamiltonian picture
• Investigation of Quantum Phase Transitions using Multi-target DMRG Methods

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