Work

Eigenstate thermalization hypothesis for off-diagonal matrix elements in integrable spin chains

Year: 2026

Type: article

Abstract: We investigate off-diagonal matrix elements of local operators in integrable spin chains, focusing on the isotropic spin- 1 / 2 Heisenberg chain ( X X X chain). We employ state-of-the-art algebraic Bethe ansatz results, which allow us to efficiently compute matrix elements of operators with support up to two sites between generic energy eigenstates. We consider both matrix elements between eigenstates that are in the same thermodynamic macrostate, as well as eigenstates that belong to different macrostates. In the former case, focusing on thermal states we numerically show that matrix elements are compatible with the exponential decay as exp ( − L | M i j O | ) . The probability distribution functions of M i j O depend on the observable and on the macrostate, and are well described by Gumbel distributions. On the other hand, matrix elements between eigenstates in different macrostates decay faster as exp ( − | M ′ i j O | L 2 ) , with M ′ i j O , again, compatible with a Gumbel distribution.

Source: Physical review. B./Physical review. B

DOI: 10.1103/m317-w58w

Authors: Federico Rottoli, Vincenzo Alba

Institutions: University of Pisa, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: European Commission, Ministero dell’Istruzione, dell’Università e della Ricerca

Awards: G1946586944, G8951614284