Generalized mutual information of quantum critical chains

2015/01/31 by F. C. Alcaraz, F C Alcaraz, M. A. Rajabpour · 1 citation
Mathematics · Physics and Astronomy · #Anisotropy #Central charge #Conformal field theory #Conformal map #Ground state #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Wave function #cond-mat.stat-mech #cond-mat.str-el #hep-th

paper · pdf · doi:10.1103/physrevb.91.155122

published as Phys. Rev. B 91, 155122 (2015) · 10 pages, 11 figures V2: published version, 11 pages 13 figures

arxiv created 2015/04/15 · openalex publication_date 2015/04/15 · arxiv updated 2015/04/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study the generalized mutual information \stackrel\ifmmode \else \~\fiI_n of the ground state of different critical quantum chains. The generalized mutual information definition that we use is based on the well established concept of the R'enyi divergence. We calculate this quantity numerically for several distinct quantum chains having either discrete Z(Q) symmetries (Q-state Potts model with Q=2,3,4 and Z(Q) parafermionic models with Q=5,6,7,8 and also Ashkin-Teller model with different anisotropies) or the U(1) continuous symmetries (Klein-Gordon field theory, XXZ and spin-1 Fateev-Zamolodchikov quantum chains with different anisotropies). For the spin chains these calculations were done by expressing the ground-state wave functions in two special bases. Our results indicate some general behavior for particular ranges of values of the parameter n that defines \stackrel\ifmmode \else \~\fiI_n. For a system, with total size L and subsystem sizes \ensuremathℓ and L\ensuremath-\ensuremathℓ, the \stackrel\ifmmode \else \~\fiI_n has a logarithmic leading behavior given by \frac\stackrel\ifmmode \else \~\fic_n4log[\fracL\ensuremathπsin(\frac\ensuremathπ\ensuremathℓL)] where the coefficient \stackrel\ifmmode \else \~\fic_n is linearly dependent on the central charge c of the underlying conformal field theory describing the system's critical properties.

Citations

• The classical-quantum boundary for correlations: discord and related measures
• Entanglement in many-body systems

Cited by

• On the simplest scale invariant tree-tensor-states preserving the quantum symmetries of the antiferromagnetic XXZ chain

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