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arXiv:cond-mat/9807247 · Physical Review Letters

Quantum Phase Transitions in the Triangular-Lattice Bilayer Heisenberg Model

Rajiv R. P. Singh, N. Elstner

Published Nov 23, 1998• 13 citations
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Abstract

We study the triangular-lattice bilayer Heisenberg model with antiferromagnetic interplane coupling ${J}_{\ensuremath{\perp}}$ and nearest-neighbor intraplane coupling $J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\lambda}{J}_{\ensuremath{\perp}}$ by expansions in $\ensuremath{\lambda}$. For negative $\ensuremath{\lambda}$ a phase transition is found to an ordered phase at a ${\ensuremath{\lambda}}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}0.2636\ifmmode\pm\else\textpm\fi{}0.0001$, which is in the 3D classical Heisenberg universality class. For $\ensuremath{\lambda}>0$, we find a transition at a rather large ${\ensuremath{\lambda}}_{c}\ensuremath{\approx}1.2$. The universality class of the transition is consistent with that of Kawamura's 3D antiferromagnetic stacked triangular lattice. The spectral weight for the triplet excitations, at the ordering wave vector, remains finite at the transition, suggesting that a phase with free spinons does not exist in this model.

DOI
10.1103/physrevlett.81.4732

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The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.
Critical properties of an Ising bilayer system, consisting of two triangular planes with antiferromagnetic (AF) JAJ_{\rm A}JA​ and ferromagnetic (FM) JBJ_{\rm B}JB​ exchange interactions, coupled by the interlayer exchange JABJ_{\rm AB}JAB​, are studied by Monte Carlo simulation. The FM plane is found to induce in the AF one some effects similar to those resulting from the joint presence of a next-nearest-neighbor FM coupling and an external magnetic field in the single triangular lattice Ising antiferromagnet. The similarities include the appearance of the quasi-long-range-order BKT phase with algebraically decaying correlations for smaller JABJ_{\rm AB}JAB​, as well as the phase transitions belonging to the three-state Potts universality class for larger JABJ_{\rm AB}JAB​. On the other hand, no first-order phase transitions are observed. A new phenomenon is a cross-over from the BKT to the Wannier state at higher temperatures, that can be stabilized over a relatively wide temperature range. In the strong JABJ_{\rm AB}JAB​ limit, the critical behavior of the entire bilayer is governed by the behavior of the plane with a dominant intraplane interaction. If JAJ_{\rm A}JA​ is dominant, then the strong JABJ_{\rm AB}JAB​ coupling makes the system kinetically freeze at lower temperatures.
Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice with allowance for intralayer next nearest neighbor interactions have been studied using the replica Monte Carlo algorithm. The character of phase transitions has been analyzed using the histogram method and the Binder cumulant method. It has been found that a transition from the collinear to paramagnetic phase in the model under study occurs as a second order phase transition. The statistical critical exponents of the specific heat α, susceptibility γ, order parameter β, and correlation radius ν, as well as the Fisher index η, have been calculated using the finite-size scaling theory. It has been shown that the three-dimensional Heisenberg model on the layered cubic lattice with allowance for the next nearest neighbor interaction belongs to the same universality class of the critical behavior as the antiferromagnetic Heisenberg model on a layered triangular lattice.
The critical behavior and phase transitions (PT) of the three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice with nearest-neighbor (J) and next-to-nearest neighbor (J1) interactions is studied by the replica Monte Carlo method. The first order phase transition has been revealed in the studied model based on the histogram method of processing data of the Monte Carlo for systems with large linear dimensions. Shown that the system exhibits the pseudouniversal critical behavior in the case of small lattices.
The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J 1) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J 1/J| = 0–0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.
Quantum phase diagram of a frustrated spin-12\frac{1}{2}21​ J1J_{1}J1​--J2J_{2}J2​--J1⊥J_{1}^{\perp}J1⊥​ Heisenberg model on an AAAAAA-stacked bilayer honeycomb lattice
The zero-temperature quantum phase diagram of the spin-12\frac{1}{2}21​ J1J_{1}J1​--J2J_{2}J2​--J1⊥J_{1}^{\perp}J1⊥​ model on an AAAAAA-stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths J1>0J_{1} > 0J1​>0 and J2≡κJ1>0J_{2} \equiv \kappa J_{1}>0J2​≡κJ1​>0. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength J1⊥≡δJ1J_{1}^{\perp} \equiv \delta J_{1}J1⊥​≡δJ1​. The complete phase boundaries of two quasiclassical collinear AFM phases, namely the Neel and Neel-II phases, are calculated in the κδ\kappa \deltaκδ half-plane with κ>0\kappa > 0κ>0. Whereas on each monolayer in the Neel state all NN pairs of spins are antiparallel, in the Neel-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter MMM and the excitation energy Δ\DeltaΔ from the sTz=0s^{z}_{T}=0sTz​=0 ground state to the lowest-lying ∣sTz∣=1|s^{z}_{T}|=1∣sTz​∣=1 excited state (where sTzs^{z}_{T}sTz​ is the total zzz component of spin for the system as a whole, and where the collinear ordering lies along the zzz direction) for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders (n≤10n \leq 10n≤10) in a systematic series of approximations involving nnn-spin clusters. The sole approximation made is then to extrapolate the sequences of nnnth-order results for MMM and Δ\DeltaΔ to the exact limit, n→∞n \to \inftyn→∞.