Exact solutions of hidden free fermion models
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.
Related
- Particlelike solutions of the Einstein-Dirac-Higgs equations: ground, excited, and many-fermion states
- Exact SU(N) symmetry resolution of bosonic Hubbard models: general boson-fermion mappings and flat-band singlet-cluster states
- Free Fermion frustration-free models have zero Hall conductance
- Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States
- Discrete WKB approach to density profiles in inhomogeneous two-band free-fermion chains
BibTeX
@misc{zheng2026exact,
title = {{Exact solutions of hidden free fermion models}},
author = {Mingchen Zheng and Balázs Pozsgay and Shu Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14134},
eprint = {2609.14134},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14134},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact solutions of hidden free fermion models
AU - Mingchen Zheng
AU - Balázs Pozsgay
AU - Shu Chen
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.14134
UR - https://arxiv.org/abs/2609.14134
AB - 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.
ER -