Quantum Spin Chain, Toeplitz Determinants and the Fisher—Hartwig Conjecture
Abstract
We consider the one-dimensional quantum spin chain, which is called the XX model (XX0 model or isotropic XY model) in a transverse magnetic field. We are mainly interested in the entropy of a block of Lneighboring spins at zero temperature and of an infinite system. We represent the entropy in terms of a Toeplitz determinant and calculate the asymptotic analytically. We derive the first two terms of the asymptotic decomposition. Interestingly, these two terms of decomposition clearly show a length scale related to the field h.
- Publication:
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Journal of Statistical Physics
- Pub Date:
- August 2004
- DOI:
- 10.1023/B:JOSS.0000037230.37166.42
- arXiv:
- arXiv:quant-ph/0304108
- Bibcode:
- 2004JSP...116...79J
- Keywords:
-
- quantum spin chain;
- XX0 model;
- entropy;
- Toeplitz determinant;
- quantum entanglement;
- Quantum Physics;
- Condensed Matter - Statistical Mechanics;
- Mathematical Physics
- E-Print:
- LATEX, 17 pages, 1 fig