Published February 11, 2015
| Submitted
Discussion Paper
Open
Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems
- Creators
-
Brandão, Fernando G. S. L.
- Cramer, Marcus
Chicago
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Abstract
We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians of N spins arranged on a d-dimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up to O(N^(1/(d+1))) spins. The proof rests on a variant of the Berry-Esseen theorem for quantum lattice systems and ideas from quantum information theory.
Additional Information
FB acknowledges EPSRC for financial support. MC acknowledges the EU Integrated Project SIQS and the Alexander von Humboldt foundation for financial support. Part of this work was done while FB was visiting the Simons Institute for the Theory of Computing in the program Quantum Hamiltonian Complexity.Attached Files
Submitted - 1502.03263v1.pdf
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1502.03263v1.pdf
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Additional details
- Eprint ID
- 67759
- Resolver ID
- CaltechAUTHORS:20160608-092309554
- Engineering and Physical Sciences Research Council (EPSRC)
- European Union
- Alexander von Humboldt Foundation
- Created
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2016-06-08Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field