Local temperature in quantum thermal states

Abstract

We consider blocks of quantum spins in a chain at thermal equilibrium, focusing on their properties from a thermodynamical perspective. Whereas in classical systems the temperature behaves as an intensive magnitude, 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. The influence in this sense of zero-temperature quantum phase transitions can be clearly observed within this approach. Then 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 originates from typical properties of reduced sub-systems of energy-constrained Hilbert spaces. Finally, the relation between local and global temperature is analyzed as a function of the size of the blocks and the system parameters.

10 pages, 10 figures. New fidelity measure with similar results

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• Intensive temperature and quantum correlations for refined quantum measurements
• Pushing the limits of the reaction-coordinate mapping
• Locality of temperature in spin chains
• Simulating the out-of-equilibrium dynamics of local observables by trading entanglement for mixture
• Critical quantum thermometry and its feasibility in spin systems
• Equivalence condition for the canonical and microcanonical ensembles in coupled spin systems
• Temperature Dependent Energy Diffusion in Chaotic Spin Chains
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• Some speculations about local thermalization of nonequilibrium extended quantum systems
• Properties of thermal quantum states: locality of temperature, decay of correlations, and more
• Locality of temperature and correlations in the presence of non-zero-temperature phase transitions
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model