Quantum fidelity for degenerate ground states in quantum phase transitions.
Phys Rev E Stat Nonlin Soft Matter Phys
; 88(3): 032110, 2013 Sep.
Article
em En
| MEDLINE
| ID: mdl-24125217
ABSTRACT
Spontaneous symmetry breaking in quantum phase transitions leads to a system having degenerate ground states in its broken-symmetry phase. In order to detect all possible degenerate ground states for a broken-symmetry phase, we introduce a quantum fidelity defined as an overlap measurement between a system ground state and an arbitrary reference state. If a system has N-fold degenerate ground states in a broken-symmetry phase, the quantum fidelity is shown to have N different values with respect to an arbitrarily chosen reference state. The quantum fidelity then exhibits an N-multiple bifurcation as an indicator of a quantum phase transition without knowing any detailed broken symmetry between a broken-symmetry phase and a symmetry phase as a system parameter crosses its critical value (i.e., a multiple bifurcation point). Each order parameter, characterizing a broken-symmetry phase from each degenerate ground state reveals an N-multiple bifurcation. Furthermore, it is shown that it is possible to specify how each order parameter calculated from degenerate ground states transforms under a subgroup of a symmetry group of the Hamiltonian. Examples are given through study of the quantum q-state Potts models with a transverse magnetic field by employing tensor network algorithms based on infinite-size lattices. For any q, a general relation between the local order parameters is found to clearly show the subgroup of the Z_{q} symmetry group. In addition, we systematically discuss criticality in the q-state Potts model.
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01-internacional
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MEDLINE
Idioma:
En
Ano de publicação:
2013
Tipo de documento:
Article