Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture

2003/04/30 by Bai-Qi Jin, B. -Q. Jin, B.-Q. Jin +1 · 44 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.stat-mech #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1023/b:joss.0000037230.37166.42

published as Journal of Statistical Physics, vol 116, Nos. 1-4, pages 79-95, August 2004 · LATEX, 17 pages, 1 fig

arxiv created 2003/12/16 · crossref issued 2004/08/01 · crossref published 2004/08/01 · crossref published-print 2004/08/01 · openalex publication_date 2004/08/01 · crossref created 2004/08/10 · arxiv updated 2016/09/08 · crossref deposited 2025/07/07 · openalex created_date 2025/10/10 · crossref indexed 2026/06/18 · openalex updated_date 2026/08/05

Abstract

We consider one-dimensional quantum spin chain, which is called XX model, XX0 model or isotropic XY model in a transverse magnetic field. We study the model on the infinite lattice at zero temperature. We are interested in the entropy of a subsystem [a block of L neighboring spins]. It describes entanglement of the block with the rest of the ground state. G. Vidal, J.I. Latorre, E. Rico, and A. Kitaev showed that for large blocks the entropy scales logarithmically. We prove the logarithmic formula for the leading term and calculate the next term. We discovered that the dependence on the magnetic field interacting with spins is very simple: the magnetic field effectively reduce the size of the subsystem. We also calculate entropy of a subsystem of a small size. We also evaluated Renyi and Tsallis entropies of the subsystem. We represented the entropy in terms of a Toeplitz determinant and calculated the asymptotic analytically.

Citations

• Universality of Entropy Scaling in One Dimensional Gapless Models
• Two soluble models of an antiferromagnetic chain

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