Bilinear correlations in Fluctuating Gaussian States with anti-unitary symmetries

Quantum Physics arXiv:2609.01724 (quant-ph) [Submitted on 1 Sep 2026] Title:Bilinear correlations in Fluctuating Gaussian States with anti-unitary symmetries Authors:Xu Zhang View a PDF of the paper titled Bilinear correlations in Fluctuating Gaussian States with anti-unitary symmetries, by Xu Zhang View PDF HTML (experimental) 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. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2609.01724 [quant-ph] (or arXiv:2609.01724v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.01724 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Xu Zhang [view email] [v1] Tue, 1 Sep 2026 18:00:49 UTC (2,505 KB) Full-text links: Access Paper: View a PDF of the paper titled Bilinear correlations in Fluctuating Gaussian States with anti-unitary symmetries, by Xu ZhangView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)