RT Journal Article
T1 Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies
A1 Carrasco, José A.
A1 Finkel Morgenstern, Federico
A1 González López, Artemio
A1 Rodríguez González, Miguel Ángel
A1 Tempesta, Piergiulio
AB We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced density matrix of a block of Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, where the coefficient a is equal to (m  −  k)/2 in the ground state phase with k vanishing   magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi entropy R_q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1) Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3). This is also true in the su(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m  +  1)-simplex in R^m whose vertices are the weights of the fundamental representation of  su(m+1).
PB IOP Publishing
SN 1742-5468
YR 2016
FD 2016-03
LK https://hdl.handle.net/20.500.14352/24560
UL https://hdl.handle.net/20.500.14352/24560
LA eng
NO © 2016 IOP Publishing Ltd and SISSA Medialab srl.This work was supported in part by Spain's MINECO under grant no. FIS2011-22566 and by the Universidad Complutense de Madrid and Banco Santander under grant no. GR3/14-910556. JAC would also like to thank the Madrid township and the 'Residencia de Estudiantes' for their financial support. The authors would also like to thank the anonymous referees of a previous version of this manuscript for their helpful remarks and suggestions.
NO Ministerio de Economía y Competitividad (MINECO)
NO Universidad Complutense de Madrid (UCM)
NO Banco Santander Central Hispano (BSCH)
NO Municipio de Madrid
NO Residencia de Estudiantes, Madrid
DS Docta Complutense
RD 10 abr 2025