REAL

Excited state correlations of the finite Heisenberg chain

Pozsgai, Balázs (2017) Excited state correlations of the finite Heisenberg chain. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 50 (7). ISSN 1751-8113

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Abstract

We consider short range correlations in excited states of the finite XXZ and XXX Heisenberg spin chains. We conjecture that the known results for the factorized ground state correlations can be applied to the excited states too, if the so-called physical part of the construction is changed appropriately. For the ground state we derive simple algebraic expressions for the physical part; the formulas only use the ground state Bethe roots as an input. We conjecture that the same formulas can be applied to the excited states as well, if the exact Bethe roots of the excited states are used instead. In the XXZ chain the results are expected to be valid for all states (except certain singular cases where regularization is needed), whereas in the XXX case they only apply to singlet states or group invariant operators. Our conjectures are tested against numerical data from exact diagonalization and coordinate Bethe Ansatz calculations, and perfect agreement is found in all cases. In the XXX case we also derive a new result for the nearest-neighbour correlator 〈 σ1zσ2z〉 which is valid for non-singlet states as well. Our results build a bridge between the known theory of factorized correlations, and the recently conjectured TBAlike description for the building blocks of the construction.

Item Type: Article
Uncontrolled Keywords: correlation functions; INTEGRABILITY; Bethe Ansatz; Heisenberg spin chain;
Subjects: Q Science / természettudomány > Q1 Science (General) / természettudomány általában
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 11 May 2023 13:48
Last Modified: 11 May 2023 13:48
URI: http://real.mtak.hu/id/eprint/165251

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