Thermodynamics of the Spin-1/2 Heisenberg–Ising Chain at High Temperatures: a Rigorous Approach
| Autor: | Frank Göhmann, Karol K. Kozlowski, Junji Suzuki, Salvish Goomanee |
|---|---|
| Přispěvatelé: | Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL) |
| Rok vydání: | 2020 |
| Předmět: |
010102 general mathematics
Statistical and Nonlinear Physics Observable 01 natural sciences Integral equation [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] 0103 physical sciences 010307 mathematical physics Uniqueness Quantum inverse scattering method Limit (mathematics) 0101 mathematics Asymptotic expansion Mathematical Physics Eigenvalues and eigenvectors Spin-½ Mathematical physics Mathematics |
| Zdroj: | Commun.Math.Phys. Commun.Math.Phys., 2020, 377 (1), pp.623-673. ⟨10.1007/s00220-020-03749-6⟩ |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-020-03749-6 |
| Popis: | International audience; This work develops a rigorous setting allowing one to prove several features related to the behaviour of the Heisenberg–Ising (or XXZ) spin-1/2 chain at finite temperature T. Within the quantum inverse scattering method the physically pertinent observables at finite T, such as the per-site free energy or the correlation length, have been argued to admit integral representations whose integrands are expressed in terms of solutions to auxiliary non-linear integral equations. The derivation of such representations was based on numerous conjectures: the possibility to exchange the infinite volume and the infinite Trotter number limits, the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the existence and uniqueness of solutions to the auxiliary non-linear integral equations, as well as the possibility to take the infinite Trotter number limit on their level. We rigorously prove all these conjectures for temperatures large enough. As a by product of our analysis, we obtain the large-T asymptotic expansion for a subset of sub-dominant Eigenvalues of the quantum transfer matrix and thus of the associated correlation lengths. This result was never obtained previously, not even on heuristic grounds. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
| Nepřihlášeným uživatelům se plný text nezobrazuje | K zobrazení výsledku je třeba se přihlásit. |