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arXiv:2308.15871 · Physical review. B./Physical review. B

Anomalous scaling corrections and quantum phase diagram of the Heisenberg antiferromagnet on the spatially anisotropic honeycomb lattice

Alexander Sushchyev, Stefan Weßel

Published Dec 14, 2023• 4 citations
arXivHTMLPDF

Abstract

Using large-scale quantum Monte Carlo simulations, we determine the ground state phase diagram of the spin-1/2 antiferromagnetic Heisenberg model on the honeycomb lattice for the most generic case of three varying interaction strengths along the different lattice directions. We identify continuous quantum phase transition lines that separate the long-range ordered antiferromagnetic regime from three distinct quantum-disordered phases, each characterized by dominant dimer-singlet formations. The finite-size behavior along these phase transition lines exhibits anomalously large corrections to scaling, which we relate to similar recent findings in certain dimerized quantum spin systems and to singular one-dimensional limits in the model parameter space. We also comment more generally on the nonuniversality of critical cumulant ratios in anisotropic systems and attempts to restore universality by varying the aspect ratio.

DOI
10.1103/physrevb.108.235146

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Using large-scale quantum Monte Carlo simulations, we determine the ground state phase diagram of the spin-1/2 antiferromagnetic Heisenberg model on the honeycomb lattice for the most generic case of three varying interaction strengths along the different lattice directions. We identify continuous quantum phase transition lines that separate the long-range ordered antiferromagnetic regime from three distinct quantum-disordered phases, each characterized by dominant dimer-singlet formations. The finite-size behavior along these phase transition lines exhibits anomalously large corrections to scaling, which we relate to similar recent findings in certain dimerized quantum spin systems and to singular one-dimensional limits in the model parameter space. We also comment more generally on the nonuniversality of critical cumulant ratios in anisotropic systems and attempts to restore universality by varying the aspect ratio.
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The S=1/2S=1/2S=1/2 and S=1S=1S=1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S=1,S=1,S=1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.
In this paper, we investigate the ground-state phase diagram of the S=1/2S=1/2S=1/2 Heisenberg-$\mathrm{\ensuremath{\Gamma}}$ model on a honeycomb lattice by dimer series expansion and exact diagonalization. We focus on the effects of the anisotropy of the interactions; by tuning the coupling constants, the system changes between the isolated dimer and the spin-chain models. We find that, in the spin-chain limit, there are three kinds of states: A Tomonaga-Luttinger liquid and two magnetically long-range-ordered states. All three states become two-dimensional long-range-ordered states by the infinitesimal interchain interaction except for the case where the Heisenberg interaction is much weaker than the off-diagonal symmetric $(\mathrm{\ensuremath{\Gamma}})$ interaction. Starting from the isolated dimer limit, a triplet dimer phase survives up to the isotropically interacting system in a large part of the phase diagram where the Heisenberg and $\mathrm{\ensuremath{\Gamma}}$ interactions are ferromagnetic and antiferromagnetic, respectively. Otherwise, a phase transition to a magnetically ordered phase occurs before the interaction becomes isotropic. This indicates that the quantum spin liquid proposed in the $\mathrm{\ensuremath{\Gamma}}$ model [A. Catuneanu et al., npj Quantum Mater. 3, 23 (2018)] is unstable against the anisotropy of the interactions.
We study the spin-1/2 Heisenberg antiferromagnet on a bilayer honeycomb lattice including interlayer frustration. Using a set of complementary approaches, namely, Schwinger bosons, dimer series expansion, bond operators, and exact diagonalization, we map out the quantum phase diagram. Analyzing ground-state energies and elementary excitation spectra, we find four distinct phases, corresponding to three collinear magnetic long-range ordered states, and one quantum disordered interlayer dimer phase. We detail that the latter phase is adiabatically connected to an exact singlet product ground state of the bilayer, which exists along a line of maximum interlayer frustration. The order within the remaining three phases will be clarified.
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 (JcJ_cJc​) to intradimer (JDJ_DJD​) coupling is obtained as Jc/JD=0.3615(5)J_c/J_D = 0.3615(5)Jc​/JD​=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.
In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.