Eigenstate thermalization beyond the envelope: exact two-point overlap statistics in random free fermions

• URL: http://arxiv.org/abs/2609.17037v1
• Date: Tue, 15 Sep 2026 11:44:11 GMT
• Title: Eigenstate thermalization beyond the envelope: exact two-point overlap statistics in random free fermions
• Abstract summary: Eigenstate thermalization constrains the smooth dependence of observables on energy, but it does not by itself fix the microscopic statistics of the overlaps between many-body eigenstates and a chosen basis.<n>We establish this distinction, and solve that fluctuation field exactly, in random free fermions.
• Score: 1.751364577113718
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Eigenstate thermalization constrains the smooth dependence of observables on energy, but it does not by itself fix the microscopic statistics of the overlaps between many-body eigenstates and a chosen basis: the smooth envelope is a one-point statement, and the fluctuation field it leaves undetermined carries a structured two-point covariance. We establish this distinction, and solve that fluctuation field exactly, in random free fermions---an ensemble of Slater-determinant eigenstates built from a Gaussian orthogonal single-particle Hamiltonian, whose eigenstate thermalization was established by Magán. In this ensemble every channel overlap is a minor of a Haar-distributed orthogonal matrix, so its statistics follow from classical random-matrix theory. The one-point law is exactly flat for every channel, with an exact moment hierarchy that is not Porter--Thomas: small intensities are enhanced algebraically rather than by the exponential Porter--Thomas form, and the mean sector carries a negative, order-one correlation correction of purely normalization origin. The two-point covariance closes exactly at the Gaussian fixed point: it is organized by the number of one-body modes shared by two eigenstates and by the number of modes shared by two channels, and its energy-resolved form factorizes into this geometry times the classical convolution of the single-particle semicircle, from which the two-resolvent covariance follows by an integral transform. Exact finite-size computations confirm all closed forms, and the structural identities of the dictionary hold at machine precision. The results provide an exactly solvable microscopic realization of the two-point fluctuation sector underlying multi-resolvent descriptions of eigenstate thermalization: a smooth envelope does not determine fine-grained fluctuations.

Related papers

• Full Inseparability and Genuine Multipartite Entanglement Coincide for Finite-Mode Gaussian States [39.7867986252164]
  We prove that a biseparable decomposition may switch the separable cut from term to term in general mixed states.<n>For any finite family of partitions, a Gaussian density operator in the trace-norm-closed convex class generated by states separable across those partitions is already separable across one fixed partition in the family.
  arXiv  Detail & Related papers  (2026-09-10T02:02:56Z)
• A Fixed Universal Determinant is Variationally Complete for Continuum Fermions [0.0]
  Exact expansions in a finite basis needly many, and state-of-the-art fermionic neural quantum states stack growing numbers of them.<n>We prove that, in the norms that govern variational calculations, at most two are needed, independently of the number of particles and of the target accuracy.
  arXiv  Detail & Related papers  (2026-08-14T16:54:47Z)
• Entanglement and non-local magic in a non-unitarily deformed non-Hermitian bipartite system [1.0293849768864847]
  A Hermitian operator with a degenerate eigenspace is transformed by an invertible non-unitary similarity map.<n> Entanglement grows monotonically with the non-Hermiticity parameter.<n>In larger bipartite spaces, the Page entropy and Haar-averaged purity provide reference values for eigenstate typicality.
  arXiv  Detail & Related papers  (2026-08-08T21:59:53Z)
• The Double Well Done Doubly-Well [0.17188280334580197]
  symmetric double-well potential is one of the simplest quantum-mechanical systems in which perturbative and non-perturbative physics are deeply entangled.<n>Resurgence ties the two features together, organizing the exact spectrum into a single tightly-constrained trans-series.<n>This paper gives a self-contained account of this trans-series from two complementary approaches.
  arXiv  Detail & Related papers  (2026-06-03T18:00:01Z)
• Defect Holonomy Near Rank-Deficient Mixed States [2.679171884680826]
  We investigate the geometry of mixed quantum states near rank-changing points.<n>We show that rank-deficient states form singular boundary strata where the bundle structure degenerates.<n>By restricting to a punctured state manifold that excludes the singular set, we obtain a well-defined gauge structure.
  arXiv  Detail & Related papers  (2026-06-01T14:51:19Z)
• GeoFlowVLM: Geometry-Aware Joint Uncertainty for Frozen Vision-Language Embedding [3.0708725114491293]
  We propose textbfGeoFlowVLM as a post-hoc adapter that learns the joint distribution of paired $ell$-normalised dual-encoder VLM embeddings.<n>A consistency result shows that, in the population limit, the trained network exposes the joint flow and both cross-modal conditional flows.<n>We derive two quantities from this single model: a conditional retrieval entropy that quantifies aleatoric ambiguity with a decision-theoretic interpretation via a Fano-type bound, and a marginaltypicality score justified by an exact chain-rule decomposition of the joint NLL
  arXiv  Detail & Related papers  (2026-05-13T11:12:18Z)
• Typical entanglement in anyon chains: Page curves beyond Lie group symmetries [41.99844472131922]
  We study bipartite entanglement statistics in one-dimensional anyon chains constrained by fusion rules of unitary pre-modular categories.<n>Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(sqrtL)$ or $O(1)$ symmetry-type corrections.<n> Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions.
  arXiv  Detail & Related papers  (2026-03-26T18:00:03Z)
• Continuum field theory of matchgate tensor network ensembles [36.94429692322632]
  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.
  arXiv  Detail & Related papers  (2026-03-06T12:15:35Z)
• Parity-dependent double degeneracy and spectral statistics in the projected dice lattice [0.0]
  We investigate an interacting fermionic system derived by projecting the Hubbard interaction onto the two lowest-energy, degenerate flat bands of the dice lattice subjected to a $$-flux.<n>For an even number of particles, the spectra conform to the Gaussian Orthogonal Ensemble, as expected for a time-reversal-symmetric Hamiltonian.<n>In stark contrast, the odd-parity sector exhibits exact double degeneracy of all eigenstates even after resolving all known symmetries.<n>The simultaneous emergence of two different random-matrix ensembles within a single physical system constitutes an unprecedented finding, opening new avenues for
  arXiv  Detail & Related papers  (2026-02-12T11:38:31Z)
• Eigenstate thermalization in thermal first-order phase transitions [39.146761527401424]
  The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize.<n>We show that it requires generalization in the presence of thermal first-order phase transitions.
  arXiv  Detail & Related papers  (2026-01-13T09:07:46Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• A minimal tensor network beyond free fermions [39.847063110051245]
  This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems.<n>A Jordan-Wigner transformation applied to a two-dimensional tensor network maps the partition sum of a classical statistical mechanics model to a Grassmann variable integral.<n>The resulting model is simple, featuring only two parameters: one governing spin-spin interaction and the other measuring the deviation from the free fermion limit.
  arXiv  Detail & Related papers  (2024-12-05T14:49:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.