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arXiv:cond-mat/9702046 · Physical review. B, Condensed matter

Phase diagrams of the S= quantum antiferromagnetic XY model on the triangular lattice in magnetic fields

Naoki Suzuki, Fumitaka Matsubara

Published May 1, 1997• 7 citations
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Abstract

We study the S= quantum antiferromagnetic XY model on finite triangular lattices with N sites in both longitudinal and transverse magnetic fields. We calculate physical quantities in the ground state using a diagonalization for spins N\ensuremath{\leqslant}27, and those at finite temperatures using a quantum transfer Monte Carlo method for N\ensuremath{\leqslant}24. In the longitudinal magnetic field, the long-range chiral order parameter seems to have a finite, nonzero value at low temperatures suggesting the occurrence of a classical umbrella-type phase. In the transverse magnetic field, the 1/3 plateau of the magnetization curve appears even at low temperatures, in contrast with the classical model. The magnetic-field dependences of the order parameters suggest that the chiral-ordered, the ferrimagnetic, and the spin-flop phases appear successively as the magnetic field is increased. The transition temperatures are estimated from the peak position of the specific heat, and the phase diagrams are predicted in both longitudinal and transverse magnetic fields.

DOI
10.1103/physrevb.55.12331

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We study the S= quantum antiferromagnetic XY model on finite triangular lattices with N sites in both longitudinal and transverse magnetic fields. We calculate physical quantities in the ground state using a diagonalization for spins N\ensuremath{\leqslant}27, and those at finite temperatures using a quantum transfer Monte Carlo method for N\ensuremath{\leqslant}24. In the longitudinal magnetic field, the long-range chiral order parameter seems to have a finite, nonzero value at low temperatures suggesting the occurrence of a classical umbrella-type phase. In the transverse magnetic field, the 1/3 plateau of the magnetization curve appears even at low temperatures, in contrast with the classical model. The magnetic-field dependences of the order parameters suggest that the chiral-ordered, the ferrimagnetic, and the spin-flop phases appear successively as the magnetic field is increased. The transition temperatures are estimated from the peak position of the specific heat, and the phase diagrams are predicted in both longitudinal and transverse magnetic fields.
We study the S=1/2 anisotropic Heisenberg antiferromagnet on finite triangular lattices with N\ensuremath{\le}24 sites: H=2JJ〈i,{\mathcal{J}}_{\mathrm{〈}\mathit{i},}J〈i,​j〉{\mathit{j}}_{\mathrm{〉}}j〉​(Six{\mathit{S}}_{\mathit{i}}^{\mathit{x}}Six​Sjx{\mathit{S}}_{\mathit{j}}^{\mathit{x}}Sjx​ +Siy{\mathit{S}}_{\mathit{i}}^{\mathit{y}}Siy​Sjy{\mathit{S}}_{\mathit{j}}^{\mathit{y}}Sjy​ +\ensuremath{\Delta}Siz{\mathit{S}}_{\mathit{i}}^{\mathit{z}}Siz​Sjz{\mathit{S}}_{\mathit{j}}^{\mathit{z}}Sjz​) with 0\ensuremath{\le}\ensuremath{\Delta}\ensuremath{\le}1. The specific heat C and the chiral-order parameter 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 are calculated using a quantum transfer Monte Carlo method. Remarkable differences in the size dependences of C and 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 are found between the cases of \ensuremath{\Delta}\ensuremath{\le}0.4 and of \ensuremath{\Delta}\ensuremath{\ge}0.6. For \ensuremath{\Delta}\ensuremath{\le}0.4, the peak height of C increases with increasing N and an extrapolation of 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 to the thermodynamic limit gives a finite, nonzero value at low temperatures. In contrast with these, for \ensuremath{\Delta}\ensuremath{\ge}0.6, the peak height does not increase and the extrapolation of 〈${\mathrm{\ensuremath{\chi}}}^{2}$〉 gives a smaller value even at very low temperatures indicating the absence of a long-range chiral order. From the results, we suggest that the chiral-ordered phase transition occurs at a finite, nonzero temperature when \ensuremath{\Delta}\ensuremath{\le}${\mathrm{\ensuremath{\Delta}}}_{\mathit{c}}$ with ${\mathrm{\ensuremath{\Delta}}}_{\mathit{c}}$\ensuremath{\gtrsim}0.4. The phase diagram of the model is predicted.
An antiferromagnetic Ising system on a triangular lattice is studied by means of a transfer matrix and the phenomenological scaling method. System consists of a semi-infinite strip and helical boundary conditions are imposed at the end of each row. At external magnetic fields h =0 and 6 J , where J is a nearest neighbor coupling constant, a unite residual entropy is obtained at the zero temperature. With a small field, specific heat is found to have two peaks; a high-temperature peak corresponding to the enhanced short-range order, and a low-temperature peak to the appearance of a long-range order. A phase diagram in h - T space is obtained by means of the phenomenological scaling, and agrees fairly well with the one obtained by Monte Carlo simulation. The main deficiency is the finite transition temperature at h =0, which may be due to a crossover to the XY-like phase transition.
The behavior of the paradigmatic J 1 − J 2 triangular lattice Heisenberg antiferromagnet in a magnetic field remains unsettled despite decades of study. We map out the phase diagram using three complementary approaches, including self-consistent nonlinear spin-wave theory, density-matrix renormalization group, and variational Monte Carlo. This combined analysis resolves the competition among different field-induced magnetic orders and magnetization plateaus across the classically frustrated parameter range. In particular, there is a finite range in the parameter regime around J 2 / J 1 = 1 8 in which (i) upon the application of the external field, the gapless quantum spin liquid acquires a finite density of monopoles, and (ii) by further increasing the field, two plateaus are clearly obtained at m = 1 3 and m = 1 2 . We discuss the experimental importance of the consecutive magnetization plateau transitions as a signature of an underlying quantum spin-liquid phase.
The calculation of two- and four-spin correlations of the [Formula: see text] antiferromagnet has been extended to an N = 21 site triangular lattice. By fitting a quadratic in 1/N to the nearest neighbour transverse spin correlations, we have estimated the ground-state energy per bond on the infinite lattice to be E0/3NJ = −0.2716 ± 0.005. The nearest neighbour longitudinal correlation is estimated to be [Formula: see text]. A short-range order parameter, the chirality, is defined and estimated for the infinite lattice. From the N dependence of the three sublattice or helical magnetization, the spin correlation is conjectured to decay algebraically as [Formula: see text].
We present the zero-temperature phase diagram of a Heisenberg antiferromagnet on a frustrated triangular lattice with nearest-neighbor (J1)({J}_{1})(J1​) and next-nearest-neighbor (J2)({J}_{2})(J2​) interactions, in a magnetic field. We show that the classical model has an accidental degeneracy for all J2/J1{J}_{2}/{J}_{1}J2​/J1​ and all fields, but the degeneracy is lifted by quantum fluctuations. We show that at large spin SSS, for J2/J1<1/8{J}_{2}/{J}_{1}<1/8J2​/J1​<1/8, quantum fluctuations select the same sequence of three sublattice co-planar states in a field as for J2=0{J}_{2}=0J2​=0, and for 1/8<J2/J1<11/8<{J}_{2}/{J}_{1}<11/8<J2​/J1​<1, they select the canted stripe state for all nonzero fields. The transition between the two states is first order in all fields, with the hysteresis width set by quantum fluctuations. We study the model with arbitrary SSS, including S=1/2S=1/2S=1/2, near the saturation field by exploring the fact that near saturation the density of bosons is small for all SSS. We show that for S>1S>1S>1, the transition remains first order, with a finite hysteresis width, but for S=1/2S=1/2S=1/2 and, possibly, S=1S=1S=1, there appears a new intermediate phase without a quasiclassical long-range order.
We calculate the magnetic phase diagram of the spin-1/21/21/2 nearest neighbor XXZ pyrochlore model using the pseudo-Majorana functional renormalization group in the temperature flow formalism. Our phase diagram as a function of temperature and coupling ratio, allowing both longitudinal and transverse couplings to be ferromagnetic and antiferromagnetic, reveals a large non-magnetic regime at low temperatures, which includes the quantum spin ice phase near the antiferromagnetic Ising model, as well as the antiferromagnetic Heisenberg and XY models. We are able to detect magnetic phase transitions via critical finite size scaling down to temperatures two orders of magnitude smaller than the spin interactions, demonstrating the remarkably good performance of our method upon approaching the ground state. Specifically, the low temperature transition from the zero-flux quantum spin ice phase into the transverse ferromagnetic phase shows very good agreement with previous quantum Monte Carlo results. Comparing our findings with classical results, we identify a quantum order-by-disorder effect near the antiferromagnetic XY model. In magnetically disordered regimes, we find characteristic patterns of broadened pinch points in the spin structure factor and investigate their evolution when approaching magnetically ordered phases. We also compute linear responses to lattice symmetry breaking perturbations and identify a possible lattice nematic ground state of the antiferromagnetic XY model.