$XY$-VBS phase boundary for the square-lattice $J_1$-$J_2$ $XXZ$ model with the ring exchange

Abstract

The square-lattice $J_1$-$J_2$ $XXZ$ model with the ring-exchange interaction $K$ was investigated numerically. As for the hard-core-boson model with the nearest-neighbor hopping $J_1/2$, namely, the $J_1$-$K$ $XY$ model, it has been reported that the ring exchange leads to a variety of exotic phases such as the valence-bond-solid (VBS) phase. In this paper, we extend the parameter space in order to investigate the phase boundary between the $XY$ (superfluid) and VBS phases. A notable feature is that the phase boundary terminates at the fully-frustrated point, $J_2/J_1\to 0.5^{-}$. As a scaling parameter for the multi-criticality, the distance from the multi-critical point $\delta (\ge 0)$ is introduced. In order to detect the phase transition, we employed the high-order fidelity susceptibility ${\chi }_F^{(3)}$, which is readily evaluated via the exact-diagonalization scheme. As a demonstration, for a fixed value of $\delta$, the $XY$-VBS criticality was analyzed by the probe ${\chi }_F^{(3)}$. Thereby, with properly scaling $\delta$, the ${\chi }_F^{(3)}$ data were cast into the crossover-scaling formula to determine the multi-criticality.

References in corpus (26)

• Ground state overlap and quantum phase transitions
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Dynamics of Loschmidt echoes and fidelity decay
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• The critical exponents of the superfluid transition in He4
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Quantum Critical Scaling of Fidelity Susceptibility
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Striped phase in a quantum XY-model with ring exchange
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• High Precision Measurement of the Thermal Exponent for the Three-Dimensional XY Universality Class
• Critical behavior at m-axial Lifshitz points: field-theory analysis and $\epsilon$-expansion results
• Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points
• Fidelity susceptibility in the two-dimensional transverse field Ising and XXZ models
• Fidelity susceptibility in the two-dimensional spin-orbit models
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Spinon deconfinement in doped frustrated quantum antiferromagnets
• Chiral phases of two-dimensional hard-core bosons with frustrated ring-exchange
• First-order superfluid to valence bond solid phase transitions in easy-plane SU($N$) magnets for small-$N$
• First order phase transitions in the square lattice "easy-plane" J-Q model
• Two supersolid phases in hard-core extended Bose-Hubbard model
• Evidence of spin liquid with hard-core bosons in a square lattice
• Neel-VBS phase boundary of the extended J_1-J_2 model with biquadratic interaction
• Plaquette valence bond state in spin-1/2 J1-J2 XY model on square lattice