Local temperature in quantum thermal states

Artur García-Saez, Alessandro Ferraro, and Antonio Acín
Phys. Rev. A 79, 052340 – Published 28 May 2009

Abstract

We consider blocks of quantum spins in a chain at thermal equilibrium, focusing on their properties from a thermodynamical perspective. In a classical system the temperature behaves as an intensive magnitude, above a certain block size, regardless of the actual value of the temperature itself. However, a deviation from this behavior is expected in quantum systems. In particular, we see that under some conditions the description of the blocks as thermal states with the same global temperature as the whole chain fails. We analyze this issue by employing the quantum fidelity as a figure of merit, singling out in detail the departure from the classical behavior. As it may be expected, we see that quantum features are more prominent at low temperatures and are affected by the presence of zero-temperature quantum phase transitions. Interestingly, we show that the blocks can be considered indeed as thermal states with a high fidelity, provided an effective local temperature is properly identified. Such a result may originate from typical properties of reduced subsystems of energy-constrained Hilbert spaces. Finally, the relation between local and global temperatures is analyzed as a function of the size of the blocks and the system parameters.

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  • Received 12 March 2009

DOI:https://doi.org/10.1103/PhysRevA.79.052340

©2009 American Physical Society

Authors & Affiliations

Artur García-Saez1, Alessandro Ferraro1, and Antonio Acín1,2

  • 1ICFO–Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
  • 2ICREA–Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain

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Issue

Vol. 79, Iss. 5 — May 2009

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