Quantum fidelity for degenerate groundstates in quantum phase transitions

Abstract

Spontaneous symmetry breaking mechanism in quantum phase transitions manifests the existence of degenerate groundstates in broken symmetry phases. To detect such degenerate groundstates, we introduce a quantum fidelity as an overlap measurement between system groundstates and an arbitrary reference state. This quantum fidelity is shown a multiple bifurcation as an indicator of quantum phase transitions, without knowing any detailed broken symmetry, between a broken symmetry phase and symmetry phases as well as between a broken symmetry phase and other broken symmetry phases, when a system parameter crosses its critical value (i.e., multiple bifurcation point). Each order parameter, characterizing a broken symmetry phase, from each of degenerate groundstates is shown similar multiple bifurcation behavior. Furthermore, to complete the description of an ordered phase, it is possible to specify how each order parameter from each of degenerate groundstates transforms under a symmetry group that is possessed by the Hamiltonian because each order parameter is invariant under only a subgroup of the symmetry group although the Hamiltonian remains invariant under the full symmetry group. Examples are given in the quantum $q$-state Potts models with a transverse magnetic field by employing the 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 the criticality in the $q$-state Potts model.

10 pages, 10 figures

References in corpus (10)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Scaling of entanglement support for Matrix Product States
• Ground state fidelity from tensor network representations
• Quantum fidelity in the thermodynamic limit
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Operator fidelity susceptibility: an indicator of quantum criticality
• Reduced fidelity in topological quantum phase transitions
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Reduced fidelity in Kitaev honeycomb model
• Bifurcation in ground-state fidelity for a one-dimensional spin model with competing two-spin and three-spin interactions

Cited by in corpus (11)

• Geometry of quantum phase transitions
• Quantum coherence and spin nematic to nematic quantum phase transitions in biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy
• Ground-state properties of the one-dimensional transverse Ising model in a longitudinal magnetic field
• Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction
• Degenerate groundstates and multiple bifurcations in a two-dimensional q-state quantum Potts model
• Non universality of entanglement convertibility
• Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model
• The antiferromagnetic cross-coupled spin ladder: quantum fidelity and tensor networks approach
• Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach
• Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
• Are degenerate groundstates induced by spontaneous symmetry breakings in quantum phase transitions?