Degenerate groundstates and multiple bifurcations in a two-dimensional q-state quantum Potts model

Abstract

We numerically investigate the two-dimensional q-state quantum Potts model on the infinite square lattice by using the infinite projected entangled-pair state (iPEPS) algorithm. We show that the quantum fidelity, defined as an overlap measurement between an arbitrary reference state and the iPEPS groundstate of the system, can detect q-fold degenerate groundstates for the Zq broken-symmetry phase. Accordingly, a multiple-bifurcation of the quantum groundstate fidelity is shown to occur as the transverse magnetic field varies from the symmetry phase to the broken-symmetry phase, which means that a multiple-bifurcation point corresponds to a critical point. A (dis-)continuous behavior of quantum fidelity at phase transition points characterizes a (dis-)continuous phase transition. Similar to the characteristic behavior of the quantum fidelity, the magnetizations, as order parameters, obtained from the degenerate groundstates exhibit multiple bifurcation at critical points. Each order parameter is also explicitly demonstrated to transform under the subgroup of the Zq symmetry group. We find that the q-state quantum Potts model on the square lattice undergoes a discontinuous (first-order) phase transition for q = 3 and q = 4, and a continuous phase transition for q = 2 (the 2D quantum transverse Ising model).

arXiv comment7pages, 4figures

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Cited by in corpus (8)

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• Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
• Emergent O(n) Symmetry in a series of three-dimensional Potts Models
• The antiferromagnetic cross-coupled spin ladder: quantum fidelity and tensor networks approach
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Critical exponents of block-block mutual information in one-dimensional infinite lattice systems
• Hierarchy of the low-lying excitations for the $(2+1)$-dimensional $q=3$ Potts model in the ordered phase