Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model

Abstract

The von Neumann entanglement entropy is used to estimate the critical point h c /J ≃ 0.143(3) of the mixed ferro-antiferromagnetic three-state quantum Potts model, where X i and R i are standard three-state Potts spin operators and J > 0 is the antiferromagnetic coupling parameter. This critical point value gives improved estimates for two Kosterlitz-Thouless transition points in the antiferromagnetic (β < 0) region of the ∆-β phase diagram of the three-state quantum chiral clock model, where ∆ and β are, respectively, the chirality and coupling parameters in the clock model. These are the transition points β c ≃ −0.143(3) at ∆ = 1 2 between incommensurate and commensurate phases and β c ≃ −7.0(1) at ∆ = 0 between disordered and incommensurate phases. The von Neumann entropy is also used to calculate the central charge c of the underlying conformal field theory in the massless phase h ≤ h c . The estimate c ≃ 1 in this phase is consistent with the known exact value at the particular point h/J = −1 corresponding to the purely antiferromagnetic three-state quantum Potts model. The algebraic decay of the Potts spin-spin correlation in the massless phase is used to estimate the continuously varying critical exponent η.

Quantum field theory for the chiral clock transition in one spatial dimension

“…The phase transitions of the quantum (classical) Z N chiral clock model in one (two) spatial dimensions have been the subject of a number of theoretical and numerical studies [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] For λ = 0, the QPT involves U (1) symmetry breaking whereas for nonzero λ, the symmetry broken is Z 3 .…”

Numerical study of the chiral Z3 quantum phase transition in one spatial dimension

“…For φ and θ both nonzero, time-reversal and spatial-parity (inversion) symmetries are separately broken, but their product is preserved. This asymmetry in the Hamiltonian has important ramifications: the spatial chirality (θ = 0) induces incommensurate (IC) floating phases with respect to the periodicity of the underlying lattice [27]. For applications to spatially ordered phases, we need φ = 0, whereupon time-reversal and spatial-parity are both symmetries of the Hamiltonian but the chirality is still present as a purely spatial one.…”

Quantum coherence and spin nematic to nematic quantum phase transitions in biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy

“…For our one-dimensional infinite lattices of the spin chains, a wave function |ψ of the Hamiltonian can be represented in the iMPS. By employing the iTEBD method, a numerical groundstate |ψ G can be obtained in the iMPS representation [67,[70][71][72]. When the initially chosen state approaches to a groundstate, the time step is chosen to decrease from dt = 0.1 to dt = 10 −6 according to a power law.…”

“…However, it should be noted that the groundstate energy e behaves in accordance with the quantum mutual information I and the relative entropy of coherence C re in detecting quantum phase transitions. Actually, our iMPS approach provide a way to detecting critical systems by using its characteristic scaling property of bipartite entanglement entropy [67,[70][71][72][74][75][76][77][78]. In the iMPS approach, it is known that the bipartite entanglement entropy diverges at a given parame-ter point in a critical system as the truncation dimension χ increases.…”

“…In order to get more insight into the conflicting point, let us then consider the bipartite entanglement entropy for the spin-2 system. Thus we calculate the bipartite entanglement entropy (the von Neumann entropy) by considering the bipartitioned two semi-infinite chains in the iMPS representation [67,[70][71][72]. We plot the bipartite entanglement entropy S vN (χ) as a function of the truncation dimension χ at R/J = 0 in Fig.…”