We study the Rényi entropy and subsystem distances on one interval for the finite size and thermal states in the critical XY chains, focusing on the critical Ising chain and XX chain with zero transverse field. We construct numerically the reduced density matrices and calculate the von Neumann entropy, Rényi entropy, subsystem trace distance, Schatten two-distance, and relative entropy. As the continuum limit of the critical Ising chain and XX chain with zero field are, respectively, the two-dimensional free massless Majorana and Dirac fermion theories, which are conformal field theories, we compare the spin chain numerical results with the analytical results in conformal field theories and find perfect matches in the continuum limit.

Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains / Arias, R.; Zhang, J.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2020:8(2020), pp. 1-36. [10.1088/1742-5468/ababfd]

Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains

Arias R.;Zhang J.
2020

Abstract

We study the Rényi entropy and subsystem distances on one interval for the finite size and thermal states in the critical XY chains, focusing on the critical Ising chain and XX chain with zero transverse field. We construct numerically the reduced density matrices and calculate the von Neumann entropy, Rényi entropy, subsystem trace distance, Schatten two-distance, and relative entropy. As the continuum limit of the critical Ising chain and XX chain with zero field are, respectively, the two-dimensional free massless Majorana and Dirac fermion theories, which are conformal field theories, we compare the spin chain numerical results with the analytical results in conformal field theories and find perfect matches in the continuum limit.
JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT
2020
8
1
36
083112
https://iopscience.iop.org/article/10.1088/1742-5468/ababfd
https://arxiv.org/abs/2004.13096v2
Arias, R.; Zhang, J.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/115098
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