Optical Abelian Lattice Gauge Theories

Abstract

We discuss a general framework for the realization of a family of abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable to quantum simulations. Within this class, we study in detail the phases of a U(1)-invariant lattice gauge theory in 2+1 dimensions originally proposed by Orland. By using exact diagonalization, we extract the low-energy states for small lattices, up to 4x4. We confirm that the model has two phases, with the confined entangled one characterized by strings wrapping around the whole lattice. We explain how to study larger lattices by using either tensor network techniques or digital quantum simulations with Rydberg atoms loaded in optical lattices where we discuss in detail a protocol for the preparation of the ground state. We also comment on the relation between standard compact U(1) LGT and the model considered.

arXiv commentv2 27 pages, 11 figures, extended discussion of the experimental set-up and of observables' measurement, similar to published version

References in corpus (37)

• Many-Body Physics with Ultracold Gases
• Fault-tolerant quantum computation by anyons
• Quantum information with Rydberg atoms
• Efficient classical simulation of slightly entangled quantum computations
• Artificial gauge potentials for neutral atoms
• Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles
• Fast quantum gates for neutral atoms
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• String-net condensation: A physical mechanism for topological phases
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Synthetic magnetic fields for ultracold neutral atoms
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• An Open-System Quantum Simulator with Trapped Ions
• A Rydberg Quantum Simulator
• Light-cone-like spreading of correlations in a quantum many-body system
• Preparation of Entangled States by Quantum Markov Processes
• Quantum simulation of frustrated magnetism in triangular optical lattices
• Optimal control technique for Many Body Quantum Systems dynamics
• Chopped random-basis quantum optimization
• Dynamical density-matrix renormalization-group method
• Quantum simulation of an extra dimension
• Quantum Link Models: A Discrete Approach to Gauge Theories
• Can One Trust Quantum Simulators?
• Mesoscopic Rydberg Gate based on Electromagnetically Induced Transparency
• Three-body interactions with cold polar molecules
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
• QCD as a Quantum Link Model
• Atomic quantum simulator for lattice gauge theories and ring exchange models
• Variational quantum Monte Carlo simulations with tensor-network states
• Confinement and lattice QED electric flux-tubes simulated with ultracold atoms
• An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Entanglement renormalization and gauge symmetry
• Monte Carlo simulation with Tensor Network States
• Non-perturbative gadget for topological quantum codes
• Random percolation as a gauge theory

Cited by in corpus (165)

• Quantum Simulation
• Light-induced gauge fields for ultracold atoms
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Simulating Lattice Gauge Theories within Quantum Technologies
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Floquet approach to ${\mathbb{Z}}_2$ lattice gauge theories with ultracold atoms in optical lattices
• Quantum Simulation for High Energy Physics
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• Lattice gauge theories simulations in the quantum information era
• Simulations of non-Abelian gauge theories with optical lattices
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• Tailoring quantum gases by Floquet engineering
• Constrained dynamics via the Zeno effect in quantum simulation: Implementing non-Abelian lattice gauge theories with cold atoms
• Review on novel methods for lattice gauge theories
• Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• U(1) Wilson lattice gauge theories in digital quantum simulators
• Quantum simulation of a lattice Schwinger model in a chain of trapped ions
• Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
• Digital lattice gauge theories
• Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms
• Superconducting Circuits for Quantum Simulation of Dynamical Gauge Fields
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• Quantum computers as universal quantum simulators: state-of-art and perspectives
• Real Time Dynamics and Confinement in the ${\mathbb{Z}}_n$ Schwinger-Weyl lattice model for 1+1 QED
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Quantum Spin Ice and dimer models with Rydberg atoms
• Towards Quantum Simulating QCD
• A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Non-Abelian $SU(2)$ Lattice Gauge Theories in Superconducting Circuits
• Gauge-invariant implementation of the Abelian Higgs model on optical lattices
• Quantum simulation of the Schwinger model: A study of feasibility
• Emerging 2D Gauge theories in Rydberg configurable arrays
• Digital quantum simulation of lattice gauge theories in three spatial dimensions
• Non-Abelian string breaking phenomena with Matrix Product States
• Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
• Real-time dynamics of string breaking
• Lattice Gauge Tensor Networks
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Quantum simulation of the universal features of the Polyakov loop
• Quantum simulation of lattice gauge theories using Wilson fermions
• Schwinger pair production with ultracold atoms
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (I) Axial Gauge
• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Oracles for Gauss's law on digital quantum computers
• Quantum Simulation of the Abelian-Higgs Lattice Gauge Theory with Ultracold Atoms
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Phase Transitions in $Z_n$ Gauge Models: Towards Quantum Simulations of the Schwinger-Weyl QED
• Removing Staggered Fermionic Matter in $U(N)$ and $SU(N)$ Lattice Gauge Theories
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (II) Single-Baryon $\beta$-Decay in Real Time
• Preparation of the SU(3) Lattice Yang-Mills Vacuum with Variational Quantum Methods
• A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations
• Dynamical quantum phase transitions in $U(1)$ quantum link models
• Scattering of mesons in quantum simulators
• Quantum simulation of non-trivial topology
• Meissner-like effect for synthetic gauge field in multimode cavity QED
• Basic Elements for Simulations of Standard Model Physics with Quantum Annealers: Multigrid and Clock States
• Real time dynamics and proposal for feasible experiments of lattice gauge-Higgs model simulated by cold atoms
• The (2+1)-d U(1) Quantum Link Model Masquerading as Deconfined Criticality
• Fermion-qudit quantum processors for simulating lattice gauge theories with matter
• Toolbox for Abelian lattice gauge theories with synthetic matter
• Atomic Quantum Simulation of Lattice Gauge-Higgs Model: Higgs Couplings and Emergence of Exact Local Gauge Symmetry
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
• Two-dimensional quantum-link lattice Quantum Electrodynamics at finite density
• ${\mathbb{Z}}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation
• Interaction-Dependent Photon-Assisted Tunneling in Optical Lattices: A Quantum Simulator of Strongly-Correlated Electrons and Dynamical Gauge Fields
• Interfaces, Strings, and a Soft Mode in the Square Lattice Quantum Dimer Model
• Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks
• Gross-Neveu-Wilson model and correlated symmetry-protected topological phases
• Phase Diagram and Conformal String Excitations of Square Ice using Gauge Invariant Matrix Product States
• Hexagonal Plaquette Spin-spin Interactions and Quantum Magnetism in a Two-dimensional Ion Crystal
• Progress towards quantum simulating the classical O(2) model
• Tensor Network Simulation of compact one-dimensional lattice Quantum Chromodynamics at finite density
• CP(N-1) Quantum Field Theories with Alkaline-Earth Atoms in Optical Lattices
• Interrelated Thermalization and Quantum Criticality in a Lattice Gauge Simulator
• Photon-mediated Stroboscopic Quantum Simulation of a ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate
• ${\mathbb{Z}}_N$ gauge theories coupled to topological fermions: QED${}_2$ with a quantum-mechanical $\theta$ angle
• Unruh effect for interacting particles with ultracold atoms
• Real-time simulation of (2+1)-dimensional lattice gauge theory on qubits
• An Algorithm for Quantum Computation of Particle Decays
• Towards the continuum limit of a $(1+1)$d quantum link Schwinger model
• Gauge invariant quantum circuits for $U(1)$ and Yang-Mills lattice gauge theories
• Two-dimensional ${\mathbb{Z}}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order
• Robust topological order in fermionic ${\mathbb{Z}}_2$ gauge theories: from Aharonov-Bohm instability to soliton-induced deconfinement
• Loops and Strings in a Superconducting Lattice Gauge Simulator
• From the Jaynes-Cummings model to non-Abelian gauge theories: a guided tour for the quantum engineer
• Different lattice geometries with synthetic dimension
• Engineering a U(1) lattice gauge theory in classical electric circuits
• Synthetic dimensions for topological and quantum phases: Perspective
• Quantum Simulation of Abelian Lattice Gauge Theories via State-Dependent Hopping
• Lattice Gauge Theories and Spin Models
• Variational quantum simulation of U(1) lattice gauge theories with qudit systems
• Order-by-disorder and quantum Coulomb phase in quantum square ice
• Towards overcoming the Monte Carlo sign problem with tensor networks
• Theoretical methods to design and test quantum simulators for the compact Abelian Higgs model
• Quantum sensors for the generating functional of interacting quantum field theories
• Digital quantum simulation of a (1+1)D SU(2) lattice gauge theory with ion qudits
• Simulating Effective QED on Quantum Computers
• Real-time dynamics in 2+1d compact QED using complex periodic Gaussian states
• Selected topics of quantum computing for nuclear physics
• Glassy Dynamics from Quark Confinement: Atomic Quantum Simulation of Gauge-Higgs Model on Lattice
• Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition and Free Theory
• Schwinger pair production and string breaking in non-Abelian gauge theory from real-time lattice improved Hamiltonians
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Variational classical networks for dynamics in interacting quantum matter
• Probing the conformal Calabrese-Cardy scaling with cold atoms
• Different models of gravitating Dirac fermions in optical lattices
• Atomic quantum simulation of a three-dimensional U(1) gauge-Higgs model
• Topological Wilson-loop area law manifested using a superposition of loops
• Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories
• The Heisenberg XX spin chain and low-energy QCD
• Phase structure of the CP(1) model in the presence of a topological $\theta$-term
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
• Quantum optics and frontiers of physics: The third quantum revolution
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory
• Local Manipulation and Measurement of Nonlocal Many-Body Operators in Lattice Gauge Theory Quantum Simulators
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Semimetal-superfluid quantum phase transitions in 2D and 3D lattices with Dirac points
• Quantum magnetism of ultracold atoms with a dynamical pseudospin degree of freedom
• Synthetic ${\mathbb{Z}}_2$ gauge theories based on parametric excitations of trapped ions
• Spin liquid phases of alkaline-earth-metal atoms at finite temperature
• Real-time dynamics of open quantum spin systems driven by dissipative processes
• Multiparticle interactions for ultracold atoms in optical tweezers: Cyclic ring-exchange terms
• Topological phases of lattice bosons with a dynamical gauge field
• SU(3) Quantum Spin Ladders as a Regularization of the CP(2) Model at Non-Zero Density: From Classical to Quantum Simulation
• Large-Scale $2+1$D $\mathrm{U}(1)$ Gauge Theory with Dynamical Matter in a Cold-Atom Quantum Simulator
• Real-Time Simulation of Large Open Quantum Spin Systems driven by Measurements
• A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms
• Spontaneous quantum Hall effect in an atomic spinor Bose-Fermi mixture
• Many-Body Localization from Dynamical Gauge Fields
• Simulation of two-flavors symmetry-locking phases in ultracold fermionic mixtures
• Quantum Simulation of Two-Dimensional $\mathrm{U}(1)$ Gauge Theory in Rydberg and Rydberg-Dressed Atom Arrays
• Chern-Simons theory encoded on a spin chain
• Discrete Abelian lattice gauge theories on a ladder and their dualities with quantum clock models
• Collective modes in a Dirac insulator with short range interactions
• One-dimensional s-p superlattice
• SU($N$) Toric Code and Nonabelian Anyons
• Gauge-Symmetry Protection Using Single-Body Terms
• The rotor Jackiw-Rebbi model: a cold-atom approach to chiral symmetry restoration and quark confinement
• Real-Time Evolution of Strongly Coupled Fermions driven by Dissipation
• Phase diagram and non-Abelian symmetry locking for fermionic mixtures with unequal interactions
• Determination of Chern numbers with a phase retrieval algorithm
• Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach
• A single-particle framework for unitary lattice gauge theory in discrete time
• Cold atoms meet lattice gauge theory
• Digital quantum simulation and Pseudoquantum Simulation of ${\mathbb{Z}}_2$ Gauge Higgs Model
• Magic of discrete lattice gauge theories
• Gauge transformations and Galilean covariance in nonlinear gauge-coupled quantum fluids
• Hybrid rank-1 and rank-2 U(1) lattice gauge theory, the F3 model, and its effective field theory
• Engineering an Effective Three-spin Hamiltonian in Trapped-ion Systems for Applications in Quantum Simulation
• Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder
• Shearing approach to gauge-invariant Trotterization
• Gapless deconfined phase in a ${\mathbb{Z}}_N$ symmetric Hamiltonian created in a cold-atom setup
• Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d