Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model


Por: Gutierrez-Ruiz, Daniel, Gonzalez, Diego, Chavez-Carlos, Jorge, Hirsch, Jorge G., Vergara, J. David

Publicada: 10 may 2021
Resumen:
We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence of a ground-state quantum phase transition where a bifurcation occurs, showing a change in stability associated with an excited-state quantum phase transition. Symmetrically, for a sign change in one Hamiltonian parameter, the same phenomenon is observed in the highest-energy state. Employing the Holstein-Primakoff approximation, we derive analytic expressions for the quantum metric tensor and compute the scalar and Berry curvatures. We contrast the analytic results with their finite-size counterparts obtained through exact numerical diagonalization and find excellent agreement between them for large sizes of the system in a wide region of the parameter space except in points near the phase transition where the Holstein-Primakoff approximation ceases to be valid.

Filiaciones:
Gutierrez-Ruiz, Daniel:
 Univ Nacl Autonoma Mexico, Inst Ciencias Nucl, Apartado Postal 70-543, Mexico City 04510, DF, Mexico

Gonzalez, Diego:
 Univ Nacl Autonoma Mexico, Inst Ciencias Nucl, Apartado Postal 70-543, Mexico City 04510, DF, Mexico

 CINVESTAV, Dept Fis, Ave Inst Politecn Nacl 2508, Mexico City 07360, DF, Mexico

Chavez-Carlos, Jorge:
 Univ Nacl Autonoma Mexico, Inst Ciencias Fis, Cuernavaca 62210, Morelos, Mexico

Hirsch, Jorge G.:
 Univ Nacl Autonoma Mexico, Inst Ciencias Nucl, Apartado Postal 70-543, Mexico City 04510, DF, Mexico

Vergara, J. David:
 Univ Nacl Autonoma Mexico, Inst Ciencias Nucl, Apartado Postal 70-543, Mexico City 04510, DF, Mexico
ISSN: 24699950
Editorial
AMER PHYSICAL SOC, ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA, Estados Unidos America
Tipo de documento: Article
Volumen: 103 Número: 17
Páginas:
WOS Id: 000655862700001
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