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arXiv · 2510.27611

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

Timo Jakobs·Marco Garofalo·Tobias Hartung·Karl Jansen·Paul Ludwig·Johann Ostmeyer·Simone Romiti·Carsten Urbach
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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.

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Timo Jakobs, Marco Garofalo, Tobias Hartung, Karl Jansen, Paul Ludwig, Johann Ostmeyer, Simone Romiti, Carsten Urbach. 2025-10-31. A Comprehensive Stress Test of Truncated Hilbert Space Bases against Green's function Monte Carlo in U(1) Lattice Gauge Theory. https://doi.org/10.1140/epjc%2Fs10052-026-15753-6

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