A Comprehensive Stress Test of Truncated Hilbert Space Bases against Green's function Monte Carlo in U(1) Lattice Gauge Theory

TL;DR

This paper compares various Hilbert space truncation schemes for U(1) lattice gauge theories using tensor network states, demonstrating that a plaquette-based basis outperforms others in accuracy and efficiency, and highlights Green's function Monte Carlo as a verification tool.

Contribution

It introduces and validates a plaquette state basis for U(1) LGTs that improves accuracy and efficiency over existing truncation schemes, and explores its application in higher dimensions.

Findings

Plaquette basis outperforms other truncation schemes in 2D.

Accurate results achieved with minimal basis states across coupling strengths.

Green's function Monte Carlo effectively verifies tensor network results.

Abstract

A representation of Lattice Gauge Theories (LGT) suitable for simulations with tensor network state methods or with quantum computers requires a truncation of the Hilbert space to a finite dimensional approximation. In particular for U(1) LGTs, several such truncation schemes are known, which we compare with each other using tensor network states. We show that a functional basis obtained from single plaquette Hamiltonians -- which we call plaquette state basis -- outperforms the other schemes in two spatial dimensions for plaquette, ground state energy and mass gap, as it is delivering accurate results for a wide range of coupling strengths with a minimal number of basis states. We also show that this functional basis can be efficiently used in three spatial dimensions. Green's function Monte Carlo appears to be a highly useful tool to verify tensor network states results, which deserves further investigation in the future.