Thermal Phase Transition of Generalized Heisenberg Models for SU(N) Spins on Square and Honeycomb Lattices

Abstract

We investigate thermal phase transitions to a valence-bond solid phase in SU(N) Heisenberg models with four- or six-body interactions on a square or honeycomb lattice, respectively. In both cases, a thermal phase transition occurs that is accompanied by rotational symmetry breaking of the lattice. We perform quantum Monte Carlo calculations in order to clarify the critical properties of the models. The estimated critical exponents indicate that the universality classes of the square- and honeycomb-lattice cases are identical to those of the classical $XY$ model with a $Z_4$ symmetry-breaking field and the 3-state Potts model, respectively. In the square-lattice case, the thermal exponent, $\nu$, monotonically increases as the system approaches the quantum critical point, while the values of the critical exponents, $\eta$ and $\gamma /\nu$, remain constant. From a finite-size scaling analysis, we find that the system exhibits weak universality, because the $Z_4$ symmetry-breaking field is always marginal. In contrast, $\nu$ in the honeycomb-lattice case exhibits a constant value, even in the vicinity of the quantum critical point, because the $Z_3$ field remains relevant in the SU(3) and SU(4) cases.

7page, 10 figures

References in corpus (4)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Scaling in the Fan of an Unconventional Quantum Critical Point

Cited by in corpus (8)

• Kernel method for corrections to scaling
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Hidden superuniversality in systems with continuous variation of critical exponents
• Non-monotonic behavior of the Binder Parameter in the discrete spin systems
• Weak universality induced by $Q=\pm 2e$ charges at the deconfinement transition of a (2+1)-d $U(1)$ lattice gauge theory
• Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully non-universal
• Critical properties of the eight-vertex model in a field
• Transition from band insulator to Mott insulator and formation of local moment in half-filled ionic SU($N$) Hubbard model