Topological vacuum structure of the Schwinger model with matrix product states

Abstract

We numerically study the single-flavor Schwinger model with a topological $\theta$-term, which is practically inaccessible by standard lattice Monte Carlo simulations due to the sign problem. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the non-trivial $\theta$-dependence of several lattice and continuum quantities in the Hamiltonian formulation. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermion mass. In the chiral limit, we demonstrate that the continuum model becomes independent of the vacuum angle $\theta$, thus respecting CP invariance, while lattice artifacts still depend on $\theta$. We also confirm that negative masses can be mapped to positive masses by shifting $\theta \to \theta +\pi$ due to the axial anomaly in the continuum, while lattice artifacts non-trivially distort this mapping. This mass regime is particularly interesting for the (3+1)-dimensional QCD analog of the Schwinger model, the sign problem of which requires the development and testing of new numerical techniques beyond the conventional Monte Carlo approach.

arXiv comment15 pages, 10 figures

References in corpus (49)

• The density-matrix renormalization group in the age of matrix product states
• 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
• An Area Law for One Dimensional Quantum Systems
• DMRG and periodic boundary conditions: a quantum information perspective
• QCD and strongly coupled gauge theories: challenges and perspectives
• The Strong CP Problem and Axions
• Fermionic Projected Entangled Pair States
• The mass spectrum of the Schwinger model with Matrix Product States
• Exact chiral symmetry, topological charge and related topics
• Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
• Density Matrix Renormalisation Group Approach to the Massive Schwinger Model
• Matrix product states for gauge field theories
• Fermionic multi-scale entanglement renormalization ansatz
• Series Expansions for the Massive Schwinger Model in Hamiltonian lattice theory
• Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
• Quantum simulation of the Schwinger model: A study of feasibility
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Non-Abelian string breaking phenomena with Matrix Product States
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Unitary circuits for strongly correlated fermions
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Thermal evolution of the Schwinger model with Matrix Product Operators
• Real-time simulation of the Schwinger effect with Matrix Product States
• Chiral condensate in the Schwinger model with Matrix Product Operators
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Hamiltonian simulation of the Schwinger model at finite temperature
• Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
• Phase Transitions in $Z_n$ Gauge Models: Towards Quantum Simulations of the Schwinger-Weyl QED
• Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
• Variational study of U(1) and SU(2) lattice gauge theories with Gaussian states in 1+1 dimensions
• Confinement and string breaking for QED${}_2$ in the Hamiltonian picture
• Massive Schwinger model within mass perturbation theory
• Symmetry-protected topological phases in lattice gauge theories: topological QED${}_2$
• Tensor Networks and their use for Lattice Gauge Theories
• Tensor renormalization group analysis of CP(N-1) model
• 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
• Tensor network simulation of QED on infinite lattices: learning from (1+1)d, and prospects for (2+1)d
• Three-dimensional finite temperature Z${}_2$ gauge theory with tensor network scheme
• Towards overcoming the Monte Carlo sign problem with tensor networks
• Scaling test of fermion actions in the Schwinger model
• Simulation strategies for the massless lattice Schwinger model in the dual formulation
• Normalization of the chiral condensate in the massive Schwinger model
• Matrix product states for Hamiltonian lattice gauge theories
• Thermal evolution of the one-flavour Schwinger model using Matrix Product States
• Quark masses, the Dashen phase, and gauge field topology
• Gaussian states for the variational study of (1+1)-dimensional lattice gauge models
• Renormal-order improvement of the Schwinger mass

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