Exact thermal properties of free-fermionic spin chains

Białończyk, Michał; Gómez-Ruiz, Fernando; del Campo, Adolfo

doi:10.21468/SciPostPhys.11.1.013

SciPost Physics

Exact thermal properties of free-fermionic spin chains

Michał Białończyk, Fernando Javier Gómez-Ruiz, Adolfo del Campo

SciPost Phys. 11, 013 (2021) · published 15 July 2021

doi: 10.21468/SciPostPhys.11.1.013
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Abstract

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.11.1.013
TI  - Exact thermal properties of free-fermionic spin chains
PY  - 2021/07/15
UR  - https://www.scipost.org/SciPostPhys.11.1.013
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 11
IS  - 1
SP  - 013
A1  - Białończyk, Michał
AU  - Gómez-Ruiz, Fernando
AU  - del Campo, Adolfo
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.11.1.013,
	title={{Exact thermal properties of free-fermionic spin chains}},
	author={Michał Białończyk and Fernando Javier Gómez-Ruiz and Adolfo del Campo},
	journal={SciPost Phys.},
	volume={11},
	pages={013},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.11.1.013},
	url={https://scipost.org/10.21468/SciPostPhys.11.1.013},
}

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Funders for the research work leading to this publication

Ministerio de Ciencia e Innovación
Narodowe Centrum Nauki / National Science Center [NCN]
Uniwersytet Jagielloński w Krakowie (through Organization: Uniwersytet Jagielloński / Jagiellonian University)