Bilinear correlations in Fluctuating Gaussian States with anti-unitary symmetries

@misc{zhang2026bilinear,
  title = {{Bilinear correlations in Fluctuating Gaussian States with anti-unitary symmetries}},
  author = {Xu Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01724},
  eprint = {2609.01724},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01724},
}

TY  - UNPB
TI  - Bilinear correlations in Fluctuating Gaussian States with anti-unitary symmetries
AU  - Xu Zhang
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01724
UR  - https://arxiv.org/abs/2609.01724
AB  - We study bilinear order-parameter correlations in a general class of sign problem-free systems that are described by what we call Fluctuating Gaussian States (FGS) with anti-unitary symmetries, where the weight of each Gaussian measurement in the space-time path integral is positive-definite. Supported by Monte Carlo simulations on fluctuating Gaussian fermionic and bosonic examples, we argue that such systems generally exhibit two types of broken-symmetry phases: a \emph{saddle point phase} and a \emph{non-local contraction phase}, with the competition between the two determined by the stability of the fluctuation saddle point of FGS. Due to the Fermi liquid instability in fermionic FGS with anti-unitary symmetries, we also discuss the possibility of representing fermionic FGS with a particular Projected Entangled-Pair State (PEPS) ansatz, which we argue a certain construction provides an efficient description for the saddle point phase, but not for the non-local contraction phase. Finally, we discuss the potential implication of our result in non-equilibrium systems and stabilizing a target bilinear order.
ER  -