Bilinear correlations in Fluctuating Gaussian States with anti-unitary symmetries

• URL: http://arxiv.org/abs/2609.01724v1
• Date: Tue, 01 Sep 2026 18:00:49 GMT
• Title: Bilinear correlations in Fluctuating Gaussian States with anti-unitary symmetries
• Abstract summary: We study bilinear order- parameter correlations in a general class of sign problem-free systems.<n> Supported by Monte Carlo simulations, we argue that such systems exhibit two types of broken-symmetry phases.<n>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.
• Score: 4.626673284373866
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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