Year: 2026
Type: preprint
Abstract: Discussions of the sign problem usually focus on its role as the primary limitation of the applicability of quantum Monte Carlo methods for reliably solving quantum many-body models. Its behavior as a function of spatial lattice size, doping, temperature, and interaction strengths has been carefully characterized within the determinant quantum Monte Carlo algorithm. Here, we consider the much less well-explored question of the temperature- and size-dependence of the sign problem in the world-line quantum Monte Carlo method. We review how, in this algorithm, even sampling the partition function of free fermions yields a sign problem, which we connect to non-analytic behavior in the corresponding reference model, hard-core bosons on a lattice. The latter exhibits a finite-temperature Kosterlitz-Thouless phase transition in 2D, and we show how this non-analytic behavior is imprinted on the average sign of the weights for the corresponding free fermion 2D tight-binding model. Our results thus show how phase-transition information can remain encoded in the sign problem even after direct sign sampling becomes impractical.
Source: arXiv (Cornell University)
Authors: Mondaini, Rubem, Scalettar, Richard T.
Institutions: University of Houston, University of California, Davis
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
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OpenAlex ID: W7215114934