Locality of temperature

By Martin Kliesch, Christian Gogolin, Michael J. Kastoryano, Arnau Riera, Jens Eisert. 2013

180 citations recorded by the source corpus.

This work is concerned with thermal quantum states of Hamiltonians on spin and fermionic lattice systems with short range interactions. We provide results leading to a local definition of temperature, thereby extending the notion of "intensivity of temperature" to interacting quantum models. More precisely, we derive a perturbation formula for thermal states. The influence of the perturbation is exactly given in terms of a generalized covariance. For this covariance, we prove exponential clustering of correlations above a universal critical temperature that upper bounds physical critical temperatures such as the Curie temperature. As a corollary, we obtain that above the critical temperature, thermal states are stable against distant Hamiltonian perturbations. Moreover, our results imply that above the critical temperature, local expectation values can be approximated efficiently in the error and the system size.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/83036f76f8a0918b178d71e691a33307b0281ab0

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In Atomic and Molecular Physics, and Optics

1. B. Doyon
2. D. Bernard
3. Pasquale Calabrese

In Condensed Matter Physics

1. D. Bernard
2. B. Doyon

In Statistical and Nonlinear Physics

1. B. Doyon
2. D. Bernard
3. Herbert Spohn
4. Pasquale Calabrese
5. T. Yoshimura

Citations in the corpus

• Conformal field theory out of equilibrium: a review (2016, background): “(5)Such a clustering was shown mathematically, in particular for finite-temperature quantum chains with finite local degrees of freedom, in [65].”