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This study addresses a critical bottleneck in quantum simulation by identifying specific Gauss law sectors within U(1) quantum link models that are free from the fermion sign problem. By mapping these sectors to solvable quantum dimer and loop models, the research provides a pathway to efficiently simulate strongly correlated systems using Monte Carlo methods where traditional approaches fail. The findings offer significant theoretical advances for lattice gauge theory and could inform the development of more robust algorithms for future quantum computers tackling condensed matter problems.
Sign-problem landscape of dimer, loop, and ground state sectors of a U(1) quantum link model
arXiv:2512.14833v2 Announce Type: replace-cross Abstract: The fermion sign problem poses a formidable challenge to the use of Monte Carlo methods for lattice gauge theories with dynamical fermionic matter fields. A meron cluster algorithm recently formulated for gauge fields represented as spin-$\frac{1}{2}$ quantum links coupled to a single flavour of staggered fermions samples only two of the exponentially many Gauss law (GL) sectors at low temperatures, allowing the simulation of those two GL sectors at zero temperature in polynomial time. In this article, we analytically identify GL sectors which can be simulated without encountering the fermion sign problem in arbitrary spatial dimensions. Using large-scale exact diagonalization and cluster Monte Carlo methods, we explore the nature of phases in the GL sectors dominating at zero temperature. The ground state lives in a superselection sector free of the sign problem, and maps to the quantum dimer model with mobile monomers. The usual zero-charge GL sector suffers from the fermion sign problem, and maps to the fully packed loop model with mobile monomers. The role of the magnetic energy in causing transitions between GL sectors is outlined. We expect our results to be valid for truncated Kogut-Susskind gauge theories, beyond quantum link models.
Abstract:The fermion sign problem poses a formidable challenge to the use of Monte Carlo methods for lattice gauge theories with dynamical fermionic matter fields. A meron cluster algorithm recently formulated for gauge fields represented as spin-$\frac{1}{2}$ quantum links coupled to a single flavour of staggered fermions samples only two of the exponentially many Gauss law (GL) sectors at low temperatures, allowing the simulation of those two GL sectors at zero temperature in polynomial time. In this article, we analytically identify GL sectors which can be simulated without encountering the fermion sign problem in arbitrary spatial dimensions. Using large-scale exact diagonalization and cluster Monte Carlo methods, we explore the nature of phases in the GL sectors dominating at zero temperature. The ground state lives in a superselection sector free of the sign problem, and maps to the quantum dimer model with mobile monomers. The usual zero-charge GL sector suffers from the fermion sign problem, and maps to the fully packed loop model with mobile monomers. The role of the magnetic energy in causing transitions between GL sectors is outlined. We expect our results to be valid for truncated Kogut-Susskind gauge theories, beyond quantum link models.
5 pages, 7 figures, 9 pages of supplementary material. Published in Phys. Rev. Lett. 137, 090404
High Energy Physics - Lattice (hep-lat); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
arXiv:2512.14833 [hep-lat]
(or arXiv:2512.14833v2 [hep-lat] for this version)
Phys. Rev. Lett. 137, 090404 (2026)
https://doi.org/10.1103/8zg2-cxc1 DOI(s) linking to related resources
Full text under the publisher's open licence · 249 words
