Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks

Abstract

We numerically simulate a non-Abelian lattice gauge theory in two spatial dimensions, with tensor networks (TN), up to intermediate sizes (>30 matter sites) well beyond exact diagonalization. We focus on the SU(2) Yang-Mills model in Hamiltonian formulation, with dynamical matter and minimally truncated gauge field (hardcore gluon). Thanks to the TN sign-problem-free approach, we characterize the phase diagram of the model at zero and finite baryon number as a function of the quark bare mass and color charge. At intermediate system sizes, we detect a liquid phase of quark-pair bound-state quasiparticles (baryons), whose mass is finite towards the continuum limit. Interesting phenomena arise at the transition boundary where color-electric and color-magnetic terms are maximally frustrated: For low quark masses, we see traces of potential deconfinement, while for high masses, signatures of a possible topological order.

arXiv comment19 pages, 16 figures, published version

References in corpus (89)

• Anyons in an exactly solved model and beyond
• Area laws for the entanglement entropy - a review
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Color-Flavor Locking and Chiral Symmetry Breaking in High Density QCD
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Tensor networks for complex quantum systems
• Simulating Lattice Gauge Theories within Quantum Technologies
• 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 Link Models: A Discrete Approach to Gauge Theories
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Observation of gauge invariance in a 71-site Bose-Hubbard quantum simulator
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Tensor network decompositions in the presence of a global symmetry
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• Chiral symmetry breaking in continuum QCD
• Fermionic Projected Entangled Pair States
• Simulations of non-Abelian gauge theories with optical lattices
• The mass spectrum of the Schwinger model with Matrix Product States
• Simulating lattice gauge theories on a quantum computer
• Thermalization dynamics of a gauge theory on a quantum simulator
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Mapping local Hamiltonians of fermions to local Hamiltonians of spins
• What limits the simulation of quantum computers?
• QCD as a Quantum Link Model
• 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
• Observation of many-body scarring in a Bose--Hubbard quantum simulator
• Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition
• Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories
• Towards simulating 2D effects in lattice gauge theories on a quantum computer
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• SU(2) hadrons on a quantum computer
• Quantum Simulating Nature's Fundamental Fields
• Towards analog quantum simulations of lattice gauge theories with trapped ions
• Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
• 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
• A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Non-Abelian $SU(2)$ Lattice Gauge Theories in Superconducting Circuits
• Quantum simulation of the Schwinger model: A study of feasibility
• Entanglement renormalization and gauge symmetry
• Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
• Lattice Gauge Tensor Networks
• Thermal evolution of the Schwinger model with Matrix Product Operators
• Quantum simulation of lattice gauge theories using Wilson fermions
• Topological vacuum structure of the Schwinger model with matrix product states
• Real-time simulation of the Schwinger effect with Matrix Product States
• Gauss's Law, Duality, and the Hamiltonian Formulation of U(1) Lattice Gauge Theory
• Hamiltonian simulation of the Schwinger model at finite temperature
• Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• 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
• Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
• Eliminating fermionic matter fields in lattice gauge theories
• Toward scalable simulations of Lattice Gauge Theories on quantum computers
• Entanglement generation in $(1+1)D$ QED scattering processes
• A density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Fermion-qudit quantum processors for simulating lattice gauge theories with matter
• Symmetry-protected topological phases in lattice gauge theories: topological QED${}_2$
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
• 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
• Combining Tensor Networks with Monte Carlo Methods for Lattice Gauge Theories
• Review on Quantum Computing for Lattice Field Theory
• The basis of the physical Hilbert space of lattice gauge theories
• Tensor Network Simulation of compact one-dimensional lattice Quantum Chromodynamics at finite density
• ${\mathbb{Z}}_N$ gauge theories coupled to topological fermions: QED${}_2$ with a quantum-mechanical $\theta$ angle
• SU(2) Gauge Theory in $2+1$ Dimensions on a Plaquette Chain Obeys the Eigenstate Thermalization Hypothesis
• Gauge invariant quantum circuits for $U(1)$ and Yang-Mills lattice gauge theories
• Investigating a (3+1)D Topological $\theta$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations
• Plaquette expectation value and lattice free energy of three-dimensional SU(N) gauge theory
• Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ ${\mathbb{Z}}_2$ demonstration
• Simple Hamiltonian for Quantum Simulation of Strongly Coupled 2+1D SU(2) Lattice Gauge Theory on a Honeycomb Lattice
• Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Dynamical quantum phase transitions of the Schwinger model: real-time dynamics on IBM Quantum
• Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group
• Anomalous dimensions on the lattice
• Quantum simulator of link models using spinor dipolar ultracold atoms
• Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks
• A quantum information perspective on meson melting
• Confinement-Deconfinement transition in $SU(2)+$Higgs Theory

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• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
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• Gapless deconfined phase in a ${\mathbb{Z}}_N$ symmetric Hamiltonian created in a cold-atom setup
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