https://doi.org/10.1140/epjc/s10052-026-15753-6
Regular Article - Theoretical Physics
A comprehensive stress test of truncated Hilbert space bases against Green’s function Monte Carlo in U(1) lattice Gauge theory
1
Helmholtz-Institut für Strahlen- und Kernphysik, University of Bonn, Nussallee 14-16, 53115, Bonn, Germany
2
Bethe Center for Theoretical Physics, University of Bonn, Nussallee 12, 53115, Bonn, Germany
3
Northeastern University - London, Devon House, St Katharine Docks, E1W 1LP, London, UK
4
Khoury College of Computer Sciences, Northeastern University, #202, West Village Residence Complex H, 440 Huntington Ave, 02115, Boston, MA, USA
5
Computation-Based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, 2121, Nicosia, Cyprus
6
Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738, Zeuthen, Germany
7
Institute for Theoretical Physics, Albert Einstein Center for Fundamental Physics, University of Bern, CH-3012, Bern, Switzerland
a
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Received:
27
January
2026
Accepted:
24
April
2026
Published online:
13
June
2026
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.
© The Author(s) 2026
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