An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Uniwersytet Jagielloński / Jagiellonian University
- 2 Donostia International Physics Center [DIPC]
- 3 Universidad de Los Andes
- 4 Université du Luxembourg / University of Luxembourg
- 5 University of Massachusetts Boston / University of Massachusetts Boston
- 6 Basque Foundation for Science / Ikerbasque
- Ministerio de Ciencia e Innovación
- Narodowe Centrum Nauki / National Science Center [NCN]
- Uniwersytet Jagielloński w Krakowie (through Organization: Uniwersytet Jagielloński / Jagiellonian University)