Computing the Mass Shift of Wilson and Staggered Fermions in the Lattice Schwinger Model with Matrix Product States

Abstract

Simulations of lattice gauge theories with tensor networks and quantum computing have so far mainly focused on staggered fermions. In this paper, we use matrix product states to study Wilson fermions in the Hamiltonian formulation and present a novel method to determine the additive mass renormalization. Focusing on the single-flavor Schwinger model as a benchmark model, we investigate the regime of a nonvanishing topological $\theta$-term, which is inaccessible to conventional Monte Carlo methods. We systematically explore the dependence of the mass shift on the volume, the lattice spacing, the $\theta$-parameter, and the Wilson parameter. This allows us to follow lines of constant renormalized mass, and therefore to substantially improve the continuum extrapolation of the mass gap and the electric field density. For small values of the mass, our continuum results agree with the theoretical prediction from mass perturbation theory. Going beyond Wilson fermions, our technique can also be applied to staggered fermions, and we demonstrate that the results of our approach agree with a recent theoretical prediction for the mass shift at sufficiently large volumes.

12 pages, 11 figures

References in corpus (18)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Ab-initio Determination of Light Hadron Masses
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• Finite-density lattice QCD and sign problem: current status and open problems
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Tuning the Topological $\theta$-Angle in Cold-Atom Quantum Simulators of Gauge Theories
• Review on Quantum Computing for Lattice Field Theory
• 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
• Strategies for the Determination of the Running Coupling of $(2+1)$-dimensional QED with Quantum Computing
• Towards overcoming the Monte Carlo sign problem with tensor networks
• DMRG study of the higher-charge Schwinger model and its 't Hooft anomaly
• Strategies for quantum-optimized construction of interpolating operators in classical simulations of lattice quantum field theories
• Schwinger model on an interval: analytic results and DMRG
• Mass Renormalization of the Schwinger Model with Wilson and Staggered Fermions in the Hamiltonian Lattice Formulation
• Lattice QCD: concepts, techniques and some results

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