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Exact solutions of hidden free fermion models
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.14134
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- Topics
Abstract
Hidden-free-fermion (HFF) Hamiltonians exhibit free-fermion spectra despite lacking an explicit quadratic representation, yet their algebraic provenance and periodic-boundary behavior remain open questions. Here we establish that a broad class of HFF models arises from distinct Lax operator realizations of a twisted multistate Perk--Schultz \(R\) matrix. Its reflected degeneration generates a closed finite hierarchy of mutually commuting transfer matrices, whose functional relations determine the complete many-body spectrum. As a decisive example, we solve the inhomogeneous free-fermions-in-disguise (FFD) chain, which exhibits HFF, nested HFF, or interacting spectra, depending on its coupling. The homogeneous FFD chain with both one-wrap and periodic boundary conditions exhibits an emergent cubic finite-size gap while retaining the exact \(z=3/2\) bulk behavior. The construction extends to higher-state and face-type realizations, providing a common algebraic framework for coupling-dependent spectral organization and multiscale behavior in interacting quantum systems.
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