Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks

Abstract

Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative effects are still debated, especially at finite charge density, mostly due to the sign-problem affecting Monte Carlo numerical simulations. Here, we report the Tensor Network simulation of a three dimensional lattice gauge theory in the Hamiltonian formulation including dynamical matter: Using this sign-problem-free method, we simulate the ground states of a compact Quantum Electrodynamics at zero and finite charge densities, and address fundamental questions such as the characterization of collective phases of the model, the presence of a confining phase at large gauge coupling, and the study of charge-screening effects.

arXiv comment16 pages, 9 Figures

References in corpus (80)

• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum Spin Liquid States
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Entanglement renormalization
• Unifying time evolution and optimization with matrix product states
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Matrix product states represent ground states faithfully
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Criticality, the area law, and the computational power of PEPS
• Classical simulation of quantum many-body systems with a tree tensor network
• QCD and strongly coupled gauge theories: challenges and perspectives
• Quantum Algorithms for Quantum Field Theories
• Simulating Lattice Gauge Theories within Quantum Technologies
• Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers
• Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Quantum Link Models: A Discrete Approach to Gauge Theories
• 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
• Lattice gauge theories simulations in the quantum information era
• Matrix-product-groundstates for one-dimensional spin-1 quantum antiferromagnets
• Realizing a scalable building block of a U(1) gauge theory with cold atomic mixtures
• Fermionic Projected Entangled Pair States
• The mass spectrum of the Schwinger model with Matrix Product States
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• QCD as a Quantum Link Model
• Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
• Optical Abelian Lattice Gauge Theories
• Density Matrix Renormalisation Group Approach to the Massive Schwinger Model
• Matrix product states for gauge field theories
• Fermionic multi-scale entanglement renormalization ansatz
• Entanglement renormalization in two spatial dimensions
• Towards simulating 2D effects in lattice gauge theories on a quantum computer
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Real Time Dynamics and Confinement in the ${\mathbb{Z}}_n$ Schwinger-Weyl lattice model for 1+1 QED
• A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Non-Abelian string breaking phenomena with Matrix Product States
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Entanglement renormalization and gauge symmetry
• Lattice Gauge Tensor Networks
• Thermal evolution of the Schwinger model with Matrix Product Operators
• Topological vacuum structure of the Schwinger model with matrix product states
• Real-time simulation of the Schwinger effect with Matrix Product States
• Implementing quantum electrodynamics with ultracold atomic systems
• Real-Space Parallel Density Matrix Renormalization Group
• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
• 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
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Phase Transitions in $Z_n$ Gauge Models: Towards Quantum Simulations of the Schwinger-Weyl QED
• Permanent confinement in the compact QED3 with fermionic matter
• Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
• Removing Staggered Fermionic Matter in $U(N)$ and $SU(N)$ Lattice Gauge Theories
• Eliminating fermionic matter fields in lattice gauge theories
• Toward scalable simulations of Lattice Gauge Theories on quantum computers
• Quark Confinement: The Hard Problem of Hadron Physics
• 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
• D-Theory: Field Quantization by Dimensional Reduction of Discrete Variables
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Fermionic Projected Entangled Pair States and Local U(1) Gauge Theories
• Critical properties of homogeneous binary trees
• Symmetry-protected topological phases in lattice gauge theories: topological QED${}_2$
• Contracting projected entangled pair states is average-case hard
• Two-dimensional quantum-link lattice Quantum Electrodynamics at finite density
• Combining Tensor Networks with Monte Carlo Methods for Lattice Gauge Theories
• Tensor Network Simulation of compact one-dimensional lattice Quantum Chromodynamics at finite density
• Variational Monte Carlo simulation with tensor networks of a pure ${\mathbb{Z}}_3$ gauge theory in (2+1)d
• Existence of Confinement Phase in Quantum Electrodynamics
• The area law and real-space renormalization
• Real-time dynamics in 2+1d compact QED using complex periodic Gaussian states
• Classification of Matrix Product States with a Local (Gauge) Symmetry
• Compact quantum electrodynamics in 2+1 dimensions and spinon deconfinement: a renormalization group analysis

Cited by in corpus (57)

• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Towards simulating 2D effects in lattice gauge theories on a quantum computer
• Tensor Network Algorithms: a Route Map
• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Provably accurate simulation of gauge theories and bosonic systems
• Entanglement generation in $(1+1)D$ QED scattering processes
• Simulating 2D lattice gauge theories on a qudit quantum computer
• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States
• Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
• Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories
• Investigating a (3+1)D Topological $\theta$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations
• Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks
• Computing the Mass Shift of Wilson and Staggered Fermions in the Lattice Schwinger Model with Matrix Product States
• Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ ${\mathbb{Z}}_2$ demonstration
• 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
• Real-time scattering in the lattice Schwinger model
• Dynamical quantum phase transitions of the Schwinger model: real-time dynamics on IBM Quantum
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Exploring the CP-violating Dashen phase in the Schwinger model with tensor networks
• Phase structure of the CP(1) model in the presence of a topological $\theta$-term
• Lattice physics approaches for neural networks
• A relativistic discrete spacetime formulation of 3+1 QED
• Loop-Free Tensor Networks for High-Energy Physics
• Neural activity in quarks language: Lattice Field Theory for a network of real neurons
• A variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: a study of (2+1)-dimensional compact QED with dynamical fermions at finite density
• Efficient Quantum Simulation of QCD Jets on the Light Front
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term
• Confinement in 1+1D ${\mathbb{Z}}_2$ Lattice Gauge Theories at Finite Temperature
• Casimir boundaries, monopoles, and deconfinement transition in 3+1 dimensional compact electrodynamics
• Studying the phase diagram of the three-flavor Schwinger model in the presence of a chemical potential with measurement- and gate-based quantum computing
• Entanglement and confinement in lattice gauge theory tensor networks
• Fermionic wave packet scattering: a quantum computing approach
• Synthetic ${\mathbb{Z}}_2$ gauge theories based on parametric excitations of trapped ions
• Large-Scale $2+1$D $\mathrm{U}(1)$ Gauge Theory with Dynamical Matter in a Cold-Atom Quantum Simulator
• Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories
• Partonic distribution functions and amplitudes using tensor network methods
• Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks
• Parton Distribution Functions in the Schwinger model from Tensor Network States
• Exploring Bosonic and Fermionic Link Models on $(3+1)-$d tubes
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• On the question of quark confinement in the Abelian U(1) QED gauge interaction
• Dynamics of quarks and gauge fields in the lowest-energy states in QCD and QED
• Single-layer tensor network approach for three-dimensional quantum systems
• Internal structure of gauge-invariant Projected Entangled Pair States
• Derivation of the deformed Heisenberg algebra from discrete spacetime
• Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory
• Fermion Discretization Effects in the Two-Flavor Lattice Schwinger Model: A Study with Matrix Product States
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Geometric fragmentation and anomalous thermalization in cubic dimer model
• Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder
• Algorithmic Aspects of Gauged Gaussian Fermionic PEPS: Gauge Fixing and Translation Invariance
• Gapless deconfined phase in a ${\mathbb{Z}}_N$ symmetric Hamiltonian created in a cold-atom setup
• Scaling and Luescher Term in a non-Abelian (2+1)d SU$(2)$ Quantum Link Model