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arXiv:2505.17772 · Physical review. B./Physical review. B

Symmetry breaking and thermal phase transition of the spin-1 quantum magnet with SU(3) symmetry on the simple cubic lattice

Nils Caci, Dominik Chudy, Pablo Daniel Mendez Mariscal, Daniel Ueltschi, Stefan Weßel

Published Sep 25, 2025• 0 citations
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Abstract

Using a combined analysis from Poisson-Dirichlet and symmetry-breaking calculations as well as quantum Monte Carlo simulations, we examine the ordered phase and the thermal phase transition of the three-dimensional spin-1 quantum magnet on the simple cubic lattice with bilinear and biquadratic interactions and SU(3) internal symmetry. We obtain exact results for the order parameter distribution function that compare well to the quantum Monte Carlo data. Furthermore, based on a detailed finite-size analysis, we provide evidence that the thermal melting transition at the SU(3) point is either weakly first order in this system or, if continuous, it falls beyond the unitarity bounds of conformal field theory.

DOI
10.1103/w7fl-yy4x

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We investigate thermal phase transitions to a valence-bond solid phase in SU(N)\mathrm{SU}(N)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 XYXYXY model with a Z4{Z}_{4}Z4​ symmetry-breaking field and the three-state Potts model, respectively. In the square-lattice case, the thermal exponent, $\ensuremath{\nu}$, monotonically increases as the system approaches the quantum critical point, while the values of the critical exponents, $\ensuremath{\eta}$ and $\ensuremath{\gamma}/\ensuremath{\nu}$, remain constant. From a finite-size scaling analysis, we find that the system exhibits weak universality, because the Z4{Z}_{4}Z4​ symmetry-breaking field is always marginal. In contrast, $\ensuremath{\nu}$ in the honeycomb-lattice case exhibits a constant value, even in the vicinity of the quantum critical point, because the Z3{Z}_{3}Z3​ field remains relevant in the SU(3) and SU(4) cases.
Using a combination of unbiased quantum Monte Carlo simulations and a decoupled dimer mean-field theory, we investigate the thermal and quantum phase transitions of the spin- 1 2 Heisenberg model on the dimerized diamond lattice. We find that at sufficiently strong dimerization the system exhibits a quantum disordered ground state, in contrast to the antiferromagnetic phase stabilized at weak dimerization. We determine the quantum critical point and examine the thermodynamic responses in both regimes. The ratio for the critical interdimer ( J c ) to intradimer ( J D ) coupling is obtained as J c / J D = 0.3615 ( 5 ) . Our results show that the decoupled dimer mean-field theory well captures the competition between the local singlet formation and the antiferromagnetic ordering tendency, and thus provides an appropriate qualitative description of this three-dimensional quantum magnet, in contrast to the conventional mean-field decoupling. We also examine the differences in the ordering temperatures between the antiferromagnetic and the ferromagnetic spin- 1 2 Heisenberg model on the diamond lattice based on quantum Monte Carlo simulations.
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We study a spin-1 Heisenberg model with exchange interaction JJJ, uniaxial single-ion exchange anisotropy DDD, and Zeeman coupling to a magnetic field BBB parallel to the symmetry axis. We compute the (D/J,B/J)(D/J,B/J)(D/J,B/J) quantum phase diagram for square and simple cubic lattices by combining analytical and quantum Monte Carlo approaches, and find a transition between XYXYXY antiferromagnetic and ferronematic phases that spontaneously break the U(1)U(1)U(1) symmetry of the model. In the language of bosonic gases, this is a transition between a Bose-Einstein condensate (BEC) of single bosons and a BEC of pairs. Our work opens up new avenues for measuring this transition in real magnets.
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