Fidelity susceptibility in two-dimensional spin-orbit models

Abstract

We study the quantum phase transitions in the two-dimensional spin-orbit models in terms of fidelity susceptibility and reduced fidelity susceptibility. An order-to-order phase transition is identified by fidelity susceptibility in the two-dimensional Heisenberg XXZ model with Dzyaloshinsky-Moriya interaction on a square lattice. The finite size scaling of fidelity susceptibility shows a power-law divergence at criticality, which indicates the quantum phase transition is of second order. Two distinct types of quantum phase transitions are witnessed by fidelity susceptibility in Kitaev-Heisenberg model on a hexagonal lattice. We exploit the symmetry of two-dimensional quantum compass model, and obtain a simple analytic expression of reduced fidelity susceptibility. Compared with the derivative of ground-state energy, the fidelity susceptibility is a bit more sensitive to phase transition. The violation of power-law behavior for the scaling of reduced fidelity susceptibility at criticality suggests that the quantum phase transition belongs to a first-order transition. We conclude that fidelity susceptibility and reduced fidelity susceptibility show great advantage to characterize diverse quantum phase transitions in spin-orbit models.

Tuning into the Kitaev spin liquid phase: A spin model on the honeycomb lattice with two types of Heisenberg exchange couplings

“…Experiments for the iridates, however, found a zig-zag AFM order [6][7][8][9]. These progresses drive a number of further researches [10][11][12][13][14][15][16][17][18].…”

Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: Global thermodynamics from renormalisation group theory

“…This quantum phase transition at ∆ = −1 is infinite-order in d = 1 and second-order in d = 2. 133 The ground-state energy peak at ∆ = −1 was also observed by Monte Carlo simulations on square lattice 134 , while the concurrence peak at ∆ = −1 was observed in d = 2 135 as well as in d = 1 123,131,135,136 . We should emphasize that the relevance of entanglement with the quantum phase transitions has been suggested by many authors before.…”

Phase Diagram of the Spin-1/2 Heisenberg Alternating Chain in a Magnetic Field*

“…Fortunately, with the development of quantum information, various information measures, e.g., quantum coherence, entanglement entropy, and fidelity, can help us to study quantum critical phenomena in spin chains. It is found that the quantum critical points can be well characterized by both the ground-state entanglement and fidelity on large system [27][28][29][30][31][32][33][34]. In this paper we study the entanglement, coherence and fidelity of the spin-1/2 Heisenberg alternating chain under a transverse magnetic field, and finally the phase diagram will be given.…”