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Critical behavior of su(1/1) supersymmetric spin chains with long-range interactions

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Carrasco, José A. and Finkel Morgenstern, Federico and González López, Artemio and Rodríguez González, Miguel Ángel and Tempesta, Piergiulio (2016) Critical behavior of su(1/1) supersymmetric spin chains with long-range interactions. Physical review E, 93 (6). ISSN 2470-0045

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Official URL: http://dx.doi.org/10.1103/PhysRevE.93.062103


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Abstract

We introduce a general class of su(1 / 1) supersymmetric spin chains with long-range interactions which includes as particular cases the su (1 / 1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1 / 1 ) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low- energy excitations and the low-temperature behavior of the free energy, hich coincides with that of a (1 + 1)-dimensional conformal field theory (CFT) with central charge c = 1 when the chemical potential lies in the critical interval (0, ε (π)), ε (p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1 + 1) –dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c = 1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1 / 1) elliptic chain.


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©2016 American Physical Society.
This work was partially supported by Spain’s MINECO under Grant No. FIS2015-63966-P, and by the Universidad Complutense de Madrid and Banco Santander under Grant No. GR3/14-910556. P.T. has been partly supported by the ICMAT Severo Ochoa Project SEV-2015-0554 (MINECO). J.A.C. would also like to thank the Universidad Complutense de Madrid, the Madrid township and the “Residencia de Estudiantes” for their financial support.

Uncontrolled Keywords:Conformal field-theory; Toeplitz determinants; Heisenberg chain; Model; Exchange; Propagation; Systems; Energy; Charge
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:41466
Deposited On:23 Feb 2017 12:41
Last Modified:10 Dec 2018 15:09

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