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arXiv:2209.01055 · Physical review. B./Physical review. B

Poisson-Dirichlet distributions and weakly first-order spin-nematic phase transitions

Nils Caci, Peter Mühlbacher, Daniel Ueltschi, Stefan Weßel

Published Jan 25, 2023• 3 citations
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Abstract

We provide a quantitative characterization of generic weakly first-order thermal phase transitions out of planar spin-nematic states in three-dimensional spin-one quantum magnets, based on calculations using Poisson-Dirichlet distributions (PDs) within a universal loop model formulation, combined with large-scale quantum Monte Carlo calculations. In contrast to earlier claims, the thermal melting of the nematic state is not continuous, instead a weakly first-order transition is identified from both thermal properties and the distribution of the nematic order parameter. Furthermore, based on PD calculations, we obtain exact results for the order parameter distribution and Binder cumulants at the discontinuous melting transition. Our findings establish the thermal melting of planar spin-nematic states as a generic platform for quantitative approaches to weakly first-order phase transitions in quantum systems with a continuous SU(2) internal symmetry.

DOI
10.1103/physrevb.107.l020409

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We provide a quantitative characterization of generic weakly first-order thermal phase transitions out of planar spin-nematic states in three-dimensional spin-one quantum magnets, based on calculations using Poisson-Dirichlet distributions (PDs) within a universal loop model formulation, combined with large-scale quantum Monte Carlo calculations. In contrast to earlier claims, the thermal melting of the nematic state is not continuous, instead a weakly first-order transition is identified from both thermal properties and the distribution of the nematic order parameter. Furthermore, based on PD calculations, we obtain exact results for the order parameter distribution and Binder cumulants at the discontinuous melting transition. Our findings establish the thermal melting of planar spin-nematic states as a generic platform for quantitative approaches to weakly first-order phase transitions in quantum systems with a continuous SU(2) internal symmetry.
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.
We use quantum Monte Carlo simulations to determine the finite temperature phase diagram and to investigate the thermal and quantum melting of stripe phases in a two-dimensional hard-core boson model. At half filling and low temperatures the stripes melt at a first order transition. In the doped system, the melting transitions of the smectic phase at high temperatures and the superfluid smectic (supersolid) phase at low temperatures are either very weakly first order, or of second order with no clear indications for an intermediate nematic phase.
We present a theory of the anisotropy-tuned quantum phase transition between spin-nematic and spin-Peierls phases in S=1S=1S=1 systems with significant biquadratic exchange interactions. Based on quantum Monte Carlo studies on finite-size systems, it has been proposed that this phase transition is second order with new deconfined fractional excitations that are absent in either of the two phases. The possibility of a weak first-order transition, however, cannot be ruled out. To elucidate the nature of the transition, we construct a large-NNN SO(3N)\text{SO}(3N)SO(3N) model for this phase transition and find in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit that the transition is generically of first-order. Furthermore, we find a critical point in the one-dimensional (1D) limit, where two transition lines, separating spin-nematic, ferromagnetic, and spin-Peierls phases, meet. Our study indicates that the spin-nematic phase is absent in 1D, while its correlation length diverges at the critical point. Predictions for 23Na^{23}\text{N}\text{a}23Na atoms trapped in an optical lattice, where the nematic to spin-Peierls quantum phase transition naturally arises are discussed.
The phase diagrams of highly frustrated quantum spin systems can exhibit first-order quantum phase transitions and thermal critical points even in the absence of any long-ranged magnetic order. However, all unbiased numerical techniques for investigating frustrated quantum magnets face significant challenges, and for generic quantum Monte Carlo methods the challenge is the sign problem. Here we report on a general quantum Monte Carlo approach with a loop-update scheme that operates in any basis, and we show that, with an appropriate choice of basis, it allows us to study a frustrated model of coupled spin-1/2 trimers: simulations of the trilayer Heisenberg antiferromagnet in the spin-trimer basis are sign-problem-free when the intertrimer couplings are fully frustrated. This model features a first-order quantum phase transition, from which a line of first-order transitions emerges at finite temperatures and terminates in a thermal critical point. The trimer unit cell hosts an internal degree of freedom that can be controlled to induce an extensive entropy jump at the quantum transition, which alters the shape of the first-order line. We explore the consequences for the thermal properties in the vicinity of the critical point, which include profound changes in the lines of maxima defined by the specific heat. Our findings reveal trimer quantum magnets as fundamental systems capturing in full the complex thermal physics of the strongly frustrated regime.
We consider a model Hamiltonian with two SU(4)\mathrm{SU}(4)SU(4) fermions per site on a square lattice, showing a competition between bilinear and biquadratic interactions. This model has generated interest due to possible realizations in ultra-cold-atom experiments and existence of spin-liquid ground states. Using a basis transformation, we show that part of the phase diagram is amenable to quantum Monte Carlo simulations without a sign problem. We find evidence for spin nematic and valence-bond crystalline phases, which are separated by a weak first-order phase transition. A U(1\mathrm{U}(1U(1) symmetry is found to emerge in the valence-bond crystal histograms, suggesting proximity to a deconfined quantum critical point. Our results are obtained with the help of a loop algorithm which allows large-scale simulations of bilinear-biquadratic SO(N\mathrm{SO}(NSO(N) models on arbitrary lattices in a certain parameter regime.
The quantum loop and dimer models are archetypal correlated systems with local constraints. With natural foundations in statistical mechanics, they are of direct relevance to various important physical concepts and systems, such as topological order, lattice gauge theories, geometric frustrations, or more recently Rydberg array quantum simulators. However, how the thermal fluctuations interact with constraints has not been explored in the important class of nonbipartite geometries. Here we study, via unbiased quantum Monte Carlo simulations and field theoretical analysis, the finite-temperature phase diagram of the quantum loop model on the triangular lattice. We discover that the recently identified, "hidden" vison plaquette (VP) quantum crystal [X. Ran et al., Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice, Commun. Phys. 7, 207 (2024)CMPYEL0868-316610.1038/s42005-024-01680-z] experiences a finite-temperature continuous transition, which smoothly connects to the (2+1)d Cubic* quantum critical point separating the VP and Z_{2} quantum spin liquid phases. This finite-temperature phase transition acquires a unique property of "remnants of fractionalization" at finite temperature, in that, both the cubic order parameter-the plaquette loop resonance-and its constituent-the vison field-exhibit independent criticality signatures. This phase transition is connected to a three-state Potts transition between the lattice nematic phase and the high-temperature disordered phase. We discuss the relevance of our results for current experiments on quantum simulation platforms.