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

Arias, Raúl; Zhang, Jiaju

doi:10.1088/1742-5468/ababfd

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

Raúl Arias
(
- SISSA, Trieste and
- INFN, Trieste and
- Buenos Aires, CONICET and
- La Plata U.
)
,
Jiaju Zhang
(
- INFN, Trieste and
- SISSA, Trieste
)

Apr 27, 2020

36 pages

Published in:

J.Stat.Mech. 2008 (2020) 083112

Published: Aug 27, 2020

e-Print:

2004.13096 [cond-mat.stat-mech]

DOI:

10.1088/1742-5468/ababfd (publication)

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Abstract: (IOP)

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.

Note:

v1, 32 pages, 15 figures; v2, 35 pages, 15 figures, published version

conformal field theory
entanglement entropies
integrable spinchains and vertex models
field theory: conformal
entropy: von Neumann
spin: chain
density matrix: reduced
fermion: Dirac
dimension: 2
continuum limit

References(99)

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