Progress towards quantum simulating the classical O(2) model

Abstract

We connect explicitly the classical $O(2)$ model in 1+1 dimensions, a model sharing important features with $U(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization group formulation, we take the time continuum limit and check that finite dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a ${}^{87}$Rb and ${}^{41}$K Bose-Bose mixture.

7 pages, 6 figures, uses revtex, new material and one author added, as to appear in Phys. Rev. A

References in corpus (32)

• Many-Body Physics with Ultracold Gases
• Counterflow Superfluidity of Two-Species Ultracold Atoms in a Commensurate Optical Lattice
• Controlled exchange interaction between pairs of neutral atoms in an optical lattice
• Double species condensate with tunable interspecies interactions
• Coarse-graining renormalization by higher-order singular value decomposition
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Worm algorithms for classical statistical models
• Quantum dynamics of impurities in a 1D Bose gas
• Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench
• Phases of the one-dimensional Bose-Hubbard model
• Quantum Link Models: A Discrete Approach to Gauge Theories
• Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• Simulating Compact Quantum Electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects
• Degenerate Bose-Bose mixture in a three-dimensional optical lattice
• Momentum-Resolved Bragg Spectroscopy in Optical Lattices
• Suppression of the critical temperature for superfluidity near the Mott transition: validating a quantum simulator
• Quantum Phases of the Extended Bose-Hubbard Hamiltonian: Possibility of a Supersolid State of Cold Atoms in Optical Lattices
• Commensurate Two-Component Bosons in Optical Lattice: Groundstate Phase Diagram
• Optical Abelian Lattice Gauge Theories
• Sublattice addressing and spin-dependent motion of atoms in a double-well lattice
• Exact blocking formulas for spin and gauge models
• Tensor renormalization group study of classical XY model on the square lattice
• Pair-supersolid phase in a bilayer system of dipolar lattice bosons
• Thermometry with spin-dependent lattices
• Extended Bose Hubbard model of interacting bosonic atoms in optical lattices: from superfluidity to density waves
• Controlling sign problems in spin models using tensor renormalization
• Finite size effects in the presence of a chemical potential: A study in the classical non-linear O(2) sigma-model
• Microwave control of atomic motional states in a spin-dependent optical lattice
• Quantum phase transitions of two-species bosons in square lattice
• Quantum and Thermal Transitions Out of the Pair-Supersolid Phase of Two-Species Bosons in Lattice

Cited by in corpus (31)

• Simulating Lattice Gauge Theories within Quantum Technologies
• Quantum Simulation for High Energy Physics
• Review on novel methods for lattice gauge theories
• Towards analog quantum simulations of lattice gauge theories with trapped ions
• Gauge-invariant implementation of the Abelian Higgs model on optical lattices
• Quantum simulation of the universal features of the Polyakov loop
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Quantum simulation of $(1+1)$-dimensional U(1) gauge-Higgs model on a lattice by cold Bose gases
• Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion
• A gauge-invariant, rotor Hamiltonian from dual variables of 3D U(1) gauge theory
• Gross-Neveu-Wilson model and correlated symmetry-protected topological phases
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• ${\mathbb{Z}}_N$ gauge theories coupled to topological fermions: QED${}_2$ with a quantum-mechanical $\theta$ angle
• The fine structure of the entanglement entropy in the classical XY model
• Tensor renormalization group study of the 3d $O(2)$ model
• The two-dimensional O(3) model at nonzero density: from dual lattice simulations to repulsive bosons
• Estimating the central charge from the Rényi entanglement entropy
• Truncation effects in the charge representation of the O(2) model
• Probing the conformal Calabrese-Cardy scaling with cold atoms
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
• Examples of symmetry-preserving truncations in tensor field theory
• Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories
• Fidelity and entanglement entropy for infinite-order phase transitions
• Spectroscopy with the tensor renormalization group method
• Initial tensor construction and dependence of the tensor renormalization group on initial tensors
• Triad representation for the anisotropic tensor renormalization group in four dimensions
• Quantum simulation of spin-1/2 XYZ model using solid-state spin centers
• Critical behavior of SU(3) lattice gauge theory with 12 light flavors
• Effective action for the Abelian-Higgs model for a gauge-invariant implementation on optical lattices
• Tensor-network study of the 3d $O(2)$ model at non-zero chemical potential and temperature
• The effective U(1)-Higgs theory at strong coupling on optical lattices?