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
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