Abstract The square-lattice $$J_1$$ J 1 - $$J_2$$ 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 $$J_1/2$$ J 1 / 2 , namely, the $$J_1$$ J 1 -KXY 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 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, $$J_2/J_1 \rightarrow 0.5^-$$ J 2 / J 1 → 0 . 5 - . As a scaling parameter for the multi-criticality, the distance from the multi-critical point $$\delta (\ge 0)$$ δ ( ≥ 0 ) is introduced. To detect the phase transition, we employed the high-order fidelity susceptibility $$\chi ^{(3)}_F$$ χ F ( 3 ) , which is readily evaluated via the exact-diagonalization scheme. As a demonstration, for a fixed value of $$\delta $$ δ , the XY-VBS criticality was analyzed by the probe $$\chi ^{(3)}_F$$ χ F ( 3 ) . Thereby, with properly scaling $$\delta $$ δ , the $$\chi ^{(3)}_F$$ χ F ( 3 ) data were cast into the crossover-scaling formula to determine the multi-criticality. Graphic abstract

arXiv:2410.03046The European Physical Journal BOct 1, 20240 citations

Bulletin of the American Physical Society

Magnetic to valence-bond-solid transition in an S=1/2 XY model with ring-exchange

Anders W. Sandvik

Published Mar 21, 2005• 0 citations

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Yoshihiro Nishiyama

Abstract The square-lattice $J_1$ J 1 - $J_2$ 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 $J_1/2$ J 1 / 2 , namely, the $J_1$ J 1 -KXY 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 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, $J_2/J_1 \rightarrow 0.5^-$ J 2 / J 1 → 0 . 5 - . As a scaling parameter for the multi-criticality, the distance from the multi-critical point $\delta (\ge 0)$ δ ( ≥ 0 ) is introduced. To detect the phase transition, we employed the high-order fidelity susceptibility $\chi ^{(3)}_F$ χ F ( 3 ) , which is readily evaluated via the exact-diagonalization scheme. As a demonstration, for a fixed value of $\delta$ δ , the XY-VBS criticality was analyzed by the probe $\chi ^{(3)}_F$ χ F ( 3 ) . Thereby, with properly scaling $\delta$ δ , the $\chi ^{(3)}_F$ χ F ( 3 ) data were cast into the crossover-scaling formula to determine the multi-criticality. Graphic abstractAbstract The square-lattice $$J_1$$ J 1 - $$J_2$$ 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 $$J_1/2$$ J 1 / 2 , namely, the $$J_1$$ J 1 -KXY 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 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, $$J_2/J_1 \rightarrow 0.5^-$$ J 2 / J 1 → 0 . 5 - . As a scaling parameter for the multi-criticality, the distance from the multi-critical point $$\delta (\ge 0)$$ δ ( ≥ 0 ) is introduced. To detect the phase transition, we employed the high-order fidelity susceptibility $$\chi ^{(3)}_F$$ χ F ( 3 ) , which is readily evaluated via the exact-diagonalization scheme. As a demonstration, for a fixed value of $$\delta $$ δ , the XY-VBS criticality was analyzed by the probe $$\chi ^{(3)}_F$$ χ F ( 3 ) . Thereby, with properly scaling $$\delta $$ δ , the $$\chi ^{(3)}_F$$ χ F ( 3 ) data were cast into the crossover-scaling formula to determine the multi-criticality. Graphic abstract

arXiv:2410.03046The European Physical Journal BOct 1, 20240 citations

We present the zero-temperature phase diagram of a square lattice quantum spin-1/2

\mathrm{XY}

model with four-site ring exchange in a uniform external magnetic field. Using quantum Monte Carlo techniques, we identify various quantum phase transitions between the

\mathrm{XY}

order, striped or valence bond solid, staggered N\'eel antiferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.

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 1 -

J_2

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

J 1 / 2 , namely, the

J_1

J 1 -KXY 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 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 \rightarrow 0.5^-

J 2 / J 1 → 0 . 5 - . As a scaling parameter for the multi-criticality, the distance from the multi-critical point

\delta (\ge 0)

δ ( ≥ 0 ) is introduced. To detect the phase transition, we employed the high-order fidelity susceptibility

\chi ^{(3)}_F

χ F ( 3 ) , which is readily evaluated via the exact-diagonalization scheme. As a demonstration, for a fixed value of

\delta

δ , the XY-VBS criticality was analyzed by the probe

\chi ^{(3)}_F

χ F ( 3 ) . Thereby, with properly scaling

\delta

δ , the

\chi ^{(3)}_F

χ F ( 3 ) data were cast into the crossover-scaling formula to determine the multi-criticality. Graphic abstract