Skip to Main content Skip to Navigation
Theses

Rigorous Approach to Quantum Integrable Models at Finite Temperature

Abstract : This thesis develops a rigorous framework allowing one to prove the exact representations for various observables in the XXZ Heisenberg spin-1/2 chain at finite temperature. Previously it has been argued in the literature that the per-site free energy or the correlation lengths admit integral representations whose integrands are expressed in terms of solutions of non-linear integral equations. The derivations of such representations relied on various conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the exchangeability of the infinite volume limit and the Trotter number limits, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations and finally the identification of the quantum transfer matrix’s Eigenvalues with solutions to the non-linear integral equation. We rigorously prove all these conjectures in the high temperature regime. Our analysis also allows us to prove that for temperatures high enough, one may describe a certain subset of sub-dominant Eigenvalues of the quantum transfer matrix described in terms of solutions to a spin-1 chain of finite length.
Document type :
Theses
Complete list of metadatas

Cited literature [188 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-02441831
Contributor : Abes Star :  Contact
Submitted on : Thursday, January 16, 2020 - 10:56:09 AM
Last modification on : Friday, January 17, 2020 - 1:37:14 AM
Long-term archiving on: : Friday, April 17, 2020 - 1:42:06 PM

File

GOOMANEE_Salvish_2019LYSEN039_...
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-02441831, version 1

Citation

Salvish Goomanee. Rigorous Approach to Quantum Integrable Models at Finite Temperature. Mathematical Physics [math-ph]. Université de Lyon, 2019. English. ⟨NNT : 2019LYSEN039⟩. ⟨tel-02441831⟩

Share

Metrics

Record views

125

Files downloads

105