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.

arXiv comment7page, 10 figures

References in corpus (16)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• The ALPS project release 2.0: Open source software for strongly correlated systems
• 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
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Three-Dimensional 3-State Potts Model Revisited With New Techniques
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• Deconfined criticality critically defined
• Crossover scaling in two dimensions
• Thermal valence-bond-solid transition of quantum spins in two dimensions

Cited by in corpus (12)

• Kernel method for corrections to scaling
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Parallel loop cluster quantum Monte Carlo simulation of quantum magnets based on global union-find graph algorithm
• Quantum phase transition, universality and scaling behaviors in the spin-1/2 Heisenberg model with ferromagnetic and antiferromagnetic competing interactions on honeycomb lattice
• Hidden superuniversality in systems with continuous variation of critical exponents
• Quasi Long Range Order and Vortex Lattice in the Three State Potts Model
• 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
• Critical exponents of nonlinear sigma model on Grassmann manifold $U(N)/U(m)U(N-m)$ by $1/N$ expansion
• Transition from band insulator to Mott insulator and formation of local moment in half-filled ionic SU($N$) Hubbard model
• 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