Universality of Entropy Scaling in One Dimensional Gapless Models

2003/11/30 by V. E. Korepin, Vladimir Korepin · 27 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Quantum many-body systems #cond-mat.stat-mech #cond-mat.str-el #physics.atom-ph #quant-ph

paper · pdf · doi:10.1103/physrevlett.92.096402

published as Physical Review Letters, vol 92, issue 9, electronic identifier 096402, 05 March 2004 · A section on spin chains with arbitrary value of spin is included. The entropy of a subsystem is calculated explicitly as a function of spin. References updated

openalex publication_date 2004/03/05 · arxiv created 2005/07/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider critical models in one dimension. We study the ground state in the thermodynamic limit (infinite lattice). We are interested in an entropy of a subsystem. We calculate the entropy of a part of the ground state from a space interval (0,x). At zero temperature it describes the entanglement of the part of the ground state from this interval with the rest of the ground state. We obtain an explicit formula for the entropy of the subsystem at any temperature. At zero temperature our formula reproduces a logarithmic formula, discovered by Vidal, Latorre, Rico, and Kitaev for spin chains. We prove our formula by means of conformal field theory and the second law of thermodynamics. Our formula is universal. We illustrate it for a Bose gas with a delta interaction and for the Hubbard model.

Citations

• Infinite conformal symmetry in two-dimensional quantum field theory

Cited by

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• Vladimir Korepin [wikipedia]