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arXiv:2410.03046 · The European Physical Journal B

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

Yoshihiro Nishiyama

Published Oct 1, 2024• 0 citations
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Abstract

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

DOI
10.1140/epjb/s10051-024-00793-2

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The J1{J}_{1}J1​-J2{J}_{2}J2​ model with the biquadratic (plaquette-four-spin) interaction was simulated with the numerical diagonalization method. Some limiting cases of this model have been investigated thoroughly. Taking advantage of the extended parameter space, we survey the phase boundary separating the N\'eel and valence-bond-solid phases. According to the deconfined-criticality scenario, the singularity of this phase boundary is continuous, accompanied with unconventional critical indices. Diagonalizing the finite-size cluster with $N\ensuremath{\leqslant}36$ spins, we observe a signature of continuous phase transition. Our tentative estimate for the correlation-length critical exponent is $\ensuremath{\nu}=1.1(3)$. In order to elucidate a nonlocal character of criticality, we evaluated the Roomany-Wyld $\ensuremath{\beta}$ function around the critical point.
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