Continuum field theory of matchgate tensor network ensembles

• URL: http://arxiv.org/abs/2603.06202v1
• Date: Fri, 06 Mar 2026 12:15:35 GMT
• Title: Continuum field theory of matchgate tensor network ensembles
• Abstract summary: We develop a continuum description for random ensembles of two-dimensional fermionic matchgate tensor networks.<n>As a diagnostic of the resulting universal physics, we analyze disorder-averaged moments of fermionic two-point functions.<n>We show that disorder drives universal long-distance behavior governed by a nonlinear sigma-model of symmetry class D with a topological term.
• Score: 36.94429692322632
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Tensor networks provide discrete representations of quantum many-body systems, yet their precise connection to continuum field theories remains relatively poorly understood. Invoking a notion of typicality, we develop a continuum description for random ensembles of two-dimensional fermionic matchgate tensor networks with spatially fluctuating parameters. As a diagnostic of the resulting universal physics, we analyze disorder-averaged moments of fermionic two-point functions, both in flat geometry and on a hyperbolic disk, where curvature reshapes their long-distance structure. We show that disorder drives universal long-distance behavior governed by a nonlinear sigma-model of symmetry class D with a topological term, placing random matchgate networks in direct correspondence with the thermal quantum Hall problem. The resulting phase structure includes localized phases, quantum Hall criticality, and a robust thermal metal with diffusive correlations and spontaneous replica-symmetry breaking. Weak non-Gaussian deformations reduce the symmetry to discrete permutations, generate a mass for the Goldstone modes, and suppress long-range correlations. In this way, typicality offers a route from ensembles of discrete tensor networks to continuum quantum field theories.

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