Supersymmetric spin chains with nonmonotonic dispersion relation: criticality and entanglement entropy



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Carrasco, José A. and Finkel Morgenstern, Federico and González López, Artemio and Rodríguez, Miguel A. (2017) Supersymmetric spin chains with nonmonotonic dispersion relation: criticality and entanglement entropy. Physical review E, 95 (1). ISSN 2470-0045

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We study the critical behavior and the ground-state entanglement of a large class of su(1|1) supersymmetric spin chains with a general (not necessarily monotonic) dispersion relation. We show that this class includes several relevant models, with both short-and long-range interactions of a simple form. We determine the low temperature behavior of the free energy per spin, and deduce that the models considered have a critical phase in the same universality class as a (1 + 1)-dimensional conformal field theory (CFT) with central charge equal to the number of connected components of the Fermi sea. We also study the Renyi entanglement entropy of the ground state, deriving its asymptotic behavior as the block size tends to infinity. In particular, we show that this entropy exhibits the logarithmic growth characteristic of (1 + 1)-dimensional CFTs and one-dimensional (fermionic) critical lattice models, with a central charge consistent with the low-temperature behavior of the free energy. Our results confirm the widely believed conjecture that the critical behavior of fermionic lattice models is completely determined by the topology of their Fermi surface.

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©2017 American Physical Society.
The authors would like to thank P. Tempesta for several enlightening discussions. This work was partially supported by Spain’s MINECO under Research Grant No. FIS2015-63966- P. J.A.C. would also like to acknowledge the financial support of the Universidad Complutense de Madrid through a 2015 predoctoral scholarship.

Uncontrolled Keywords:Toeplitz determinants; Energy
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:41879
Deposited On:27 Mar 2017 17:04
Last Modified:10 Dec 2018 15:09

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