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Quantum Simulation

Geometric mutual information at classical critical points

arXiv
Authors: Jean-Marie Stéphan, Stephen Inglis, Paul Fendley, Roger G. Melko

Year

2013

Paper ID

31430

Status

Preprint

Abstract Read

~2 min

Abstract Words

114

Citations

N/A

Abstract

A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior. It is exactly (c/3)ln ell for an interval of length ell in an infinite system, where c is the central charge of the conformal field theory. Here we define the geometric mutual information, an analogous quantity for classical critical points. We compute this for 2d conformal field theories in an arbitrary geometry, and show in particular that for a rectangle cut into two rectangles, it is proportional to c. This makes it possible to extract c in classical simulations, which we demonstrate for the critical Ising and 3-state Potts models.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2013 reference point for readers tracking recent quantum research.
  • A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1312.3954 [2] arXiv https://arxiv.org/abs/1312.3954 [3] Publisher https://arxiv.org/abs/1312.3954

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