Sign problem and criticality in world-line quantum Monte Carlo methods

@misc{mondaini2026sign,
  title = {{Sign problem and criticality in world-line quantum Monte Carlo methods}},
  author = {Rubem Mondaini and Richard T. Scalettar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38740},
  eprint = {2609.38740},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38740},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Sign problem and criticality in world-line quantum Monte Carlo methods
AU  - Rubem Mondaini
AU  - Richard T. Scalettar
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.38740
UR  - https://arxiv.org/abs/2609.38740
AB  - 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.
ER  -