Degenerate ground states and multiple bifurcations in a two-dimensionalq-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 Z q 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 Z q 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).

Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models

“…For each of the values of q, a maximal value is detected for the GE curve, where a jump also occurs. The estimates for the transition points λ c are well matched with those obtained via the local order parameters and also via the observed multi-bifurcation points in the magnetization [38]. It is clear that the measure of GE can distinguish between discontinuous and continuous phase transitions in the 2D quantum q-state Potts model.…”

“…For a regular lattice, classical mean-field solutions [37] and extensive computations (see, e.g., Refs. [37,38] and references therein) have suggested that the 3D classical q-state Potts model, and thus the 2D q-state quantum version, undergo a continuous phase transition for q ≤ 2 and a discontinuous phase transition for q > 2. We now turn to this 2D q-state quantum model and examine the GE per site and local order parameters in the vicinity of the phase transition points for the values q = 3, 4 and 5.…”

Critical exponents of block-block mutual information in one-dimensional infinite lattice systems

“…Then numerical iMPS wavefunctions for ground states are obtained for the truncation dimensions between χ = 20 and χ = 150. Actually, in the broken-symmetry phases, randomly chosen several initial states can reach different orthogonal groundstates that are degenerate ground states for a spontaneous symmetry breaking and can be distinguished by using quantum fidelity [30,31]. Our iMPS approach gives the full description of the groundstate in a pure state by the iMPS groundstate wave function |ψ g .…”

The antiferromagnetic cross-coupled spin ladder: Quantum fidelity and tensor networks approach

“…It has been demonstrated to directly (i) capture phase transition points due to changes of ground-state wave functions in the vicinity of quantum critical points [27][28][29][30] and (ii) detect degenerate ground-states due to spontaneous symmetry breaking. [31][32][33] The quantum fidelity approach can thus be utilized to provide evidence for the existence or not of the CD phase, because by its definition, 17,22,23,25 the CD phase is to be induced by a spontaneous breaking of lattice translational symmetry. Motivated by the conflicting results for the existence of the CD phase in the antiferromagnetic regime and the advantages of the quantum fidelity and tensor networks approach, we have examined the cross-coupled ladder model, paying particular attention to the previously studied line J × = 0.2.…”