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

Yoshihiro Nishiyama

doi:10.1140/epjb/s10051-024-00793-2

paper

$X Y$ -VBS phase boundary for the square-lattice $J_{1}$ - $J_{2}$ $X X Z$ model with the ring exchange

arXiv:2410.03046 · doi:10.1140/epjb/s10051-024-00793-2

Abstract

The square-lattice $J_{1}$ - $J_{2}$ $X X Z$ 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 $J_{1}$ - $K$ $X Y$ 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 $X Y$ (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 $δ (\geq 0)$ is introduced. In order to detect the phase transition, we employed the high-order fidelity susceptibility $χ_{F}^{(3)}$ , which is readily evaluated via the exact-diagonalization scheme. As a demonstration, for a fixed value of $δ$ , the $X Y$ -VBS criticality was analyzed by the probe $χ_{F}^{(3)}$ . Thereby, with properly scaling $δ$ , the $χ_{F}^{(3)}$ data were cast into the crossover-scaling formula to determine the multi-criticality.

XY-VBS phase boundary for the square-lattice J1​-J2​ XXZ model with the ring exchange

Abstract

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$X Y$ -VBS phase boundary for the square-lattice $J_{1}$ - $J_{2}$ $X X Z$ model with the ring exchange