Realistic scheme for quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical matter in $(2+1)$D

Abstract

Gauge fields coupled to dynamical matter are ubiquitous in many disciplines of physics, ranging from particle to condensed matter physics, but their implementation in large-scale quantum simulators remains challenging. Here we propose a realistic scheme for Rydberg atom array experiments in which a ${\mathbb{Z}}_2$ gauge structure with dynamical charges emerges on experimentally relevant timescales from only local two-body interactions and one-body terms in two spatial dimensions. The scheme enables the experimental study of a variety of models, including $(2+1)$D ${\mathbb{Z}}_2$ lattice gauge theories coupled to different types of dynamical matter and quantum dimer models on the honeycomb lattice, for which we derive effective Hamiltonians. We discuss ground-state phase diagrams of the experimentally most relevant effective ${\mathbb{Z}}_2$ lattice gauge theories with dynamical matter featuring various confined and deconfined, quantum spin liquid phases. Further, we present selected probes with immediate experimental relevance, including signatures of disorder-free localization and a thermal deconfinement transition of two charges.

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• High-fidelity detection of large-scale atom arrays in an optical lattice
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• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Spin exchange-enabled quantum simulator for large-scale non-Abelian gauge theories
• False vacuum decay and nucleation dynamics in neutral atom systems
• Confinement in 1+1D ${\mathbb{Z}}_2$ Lattice Gauge Theories at Finite Temperature
• Quantum dimer models with Rydberg gadgets
• Probing Hilbert Space Fragmentation with Strongly Interacting Rydberg Atoms
• Percolation as a confinement order parameter in ${\mathbb{Z}}_2$ lattice gauge theories
• Large-Scale $2+1$D $\mathrm{U}(1)$ Gauge Theory with Dynamical Matter in a Cold-Atom Quantum Simulator
• Scalable, ab initio protocol for quantum simulating SU($N$)$\times$U(1) Lattice Gauge Theories
• Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians
• Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to ${\mathbb{D}}_8$
• Interplay between lattice gauge theory and subsystem codes
• Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
• Quantum Simulation with Gauge Fixing: from Ising Lattice Gauge Theory to Dynamical Flux Model
• Percolation renormalization group analysis of confinement in ${\mathbb{Z}}_2$ lattice gauge theories
• Spontaneous symmetry breaking in a $SO(3)$ non-Abelian lattice gauge theory in $2+1$D with quantum algorithms
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• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
• Topological order in symmetric blockade structures
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
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• Sign-problem-free effective models of triangular lattice quantum antiferromagnets
• Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection
• Quantum circuit for ${\mathbb{Z}}_3$ lattice gauge theory at nonzero baryon density
• Disorder-Free Localization and Fragmentation in a Non-Abelian Lattice Gauge Theory
• Partial confinement in a quantum-link simulator
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Gapless deconfined phase in a ${\mathbb{Z}}_N$ symmetric Hamiltonian created in a cold-atom setup
• Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder
• Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions