Isospectrality and Operator Complexity

• URL: http://arxiv.org/abs/2606.05294v1
• Date: Wed, 03 Jun 2026 18:00:05 GMT
• Title: Isospectrality and Operator Complexity
• Abstract summary: We study a pair of exactly solvable, isospectral fermion chains, one strongly interacting and one quadratic.<n>Despite their identical spectra, the two models realize distinct phases and sharply different notions of operator complexity.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study a pair of exactly solvable, isospectral fermion chains, one strongly interacting and one quadratic, that nevertheless display remarkably different phase structures and operator dynamics. A nonlocal nonlinear unitary transformation maps one onto the other while preserving the entire many-body spectrum and converting local fermion operators into extended many-body strings. Thus, operators that evolve within a closed linear subspace in the quadratic model become interacting operators that generate increasingly higher-body terms and exhibit asymptotic Lanczos growth $b_n\propto\sqrt n$. Despite their identical spectra, the two models realize distinct phases and sharply different notions of operator complexity. Our results demonstrate that free many-body spectra and interacting operator dynamics are fundamentally compatible.

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