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Thermal Critical Properties of Two-Dimensional Generalized SU(N) Heisenberg Models

T. Suzuki, K. Harada, and H. Matsuo

In recent years, deconfined critical phenomena (DCP) [1] have attracted much attention in condensed matter physics. The transition that exhibits DCP is expected to take place between a magnetic ordered phase and valence bond solid (VBS) phase. The most famous model family that shows such phase transition is the two-dimensional Heisenberg models with multiple singlet-projection terms for SU(N) spins, namely SU(N) JQm models [2]. We investigated the quantum criticality between the Neel phase and the VBS phase in the JQ2 model on the square lattice and the JQ3 model on the honeycomb lattice by using quantum Monte Carlo (QMC) calculations [3]. From the finite-size scaling analysis, we found that data collapses for order parameters are obtained by the same scaling function independently of the lattice geometry. This result implies that the quantum phase transition in those models is of the second order transition. However, as the system size increases, the estimated value of the quantum critical exponent ν exhibits a monotonic change and it approaches the phenomenological value for the first order transition. To discuss the quantum criticality from the different viewpoint and clarify the whole phase diagrams, we have studied the thermal critical properties of those models.

Fig. 1. Critical temperature Tc and critical exponent ν of the SU(N) generalized Heisenberg model. (a) and (c) ((b) and (d)) are results of Tc (ν) for the square-lattice and honeycomb-lattice case, respectively. Vertical dotted lines correspond to the quantum critical point between the Neel phase and VBS phase. The horizontal axis λ is the coupling ratio between Heisenberg interaction J and the amplitude of the multiple singlet-projection term Qm, λ=J/(J+Qm).

When we focus on the thermal properties of the SU(N) JQm models, the thermal phase transition to the VBS phase is possible because the VBS phase is characterized by coverings of the singlet dimers on the square or honeycomb lattice. We calculated the temperature dependence of the VBS order parameter by the QMC method. In figure 1, we show the critical temperature Tc and the thermal exponent ν which were evaluated from the finite-size scaling analysis up to L=192 for the square lattice case and L=96 for the honeycomb lattice case. Since the dimer covering state in the VBS phase is related to the rotational symmetry breaking of the lattice, we can expect the presence of the classical spin models that belong to the same universality class. In the present cases, the universality class of the square-lattice case is expected to be the same as that of the classical XY model with π/2-rotational symmetry breaking field, namely the XY+Z4 model. In the honeycomb-lattice case, it may correspond to the three-state Potts model because the transition is characterized by π/3-rotational symmetry breaking. As shown in figure 1, ν increases monotonically in the square-lattice case when the system approaches the quantum critical point. It is obvious that the increase of ν survives in the vicinity of the quantum critical point. The similar behavior of ν is also observed when the classical XY+Z4 model approaches the XY model limit, where the Kosterlitz-Thouless transition is realized. In the honeycomb lattice case, ν is almost constant at ν ~ 5/6, the value of the three-state Potts universality class. If the system shows the first-order transition at a zero temperature, a shift of ν toward the first-order-transition value is expected in both cases. However, we found that the first-order transition is unlikely for Tc/(J+Qm) ≳1/100.


References
  • [1] T. Senthil et al., Phys. Rev. B 70, 144407 (2004); T. Senthil et al., Science 303, 1490 (2004).
  • [2] A. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).
  • [3] K. Harada et al., Phys. Rev. B 88, 220408 (2013).
  • [4] T. Suzuki et al., Phys. Rev. B 91, 094414 (2015); J. Phy.:Conf. Series. 592, 012114 (2015).
Authors
  • T. Suzukia, K. Haradab, H. Matsuoc, S. Todod, and N. Kawashima
  • aThe University of Hyogo
  • bKyoto University
  • cRIST
  • dThe University of Tokyo