Phase diagram of the antiferromagnetic XXZ model on the triangular lattice

Abstract

We determine the quantum phase diagram of the antiferromagnetic spin-1/2 XXZ model on the triangular lattice as a function of magnetic field and anisotropic coupling Jz. Using the density matrix renormalization group (DMRG) algorithm in two dimensions we establish the locations of the phase boundaries between a plateau phase with 1/3 Néel order and two distinct coplanar phases. The two coplanar phases are characterized by a simultaneous breaking of both translational and U(1) symmetries, which is reminiscent of supersolidity. A translationally invariant umbrella phase is entered via a first order phase transition at relatively small values of Jz compared to the corresponding case of ferromagnetic hopping and the classical model. The phase transition lines meet at two tricritical points on the tip of the lobe of the plateau state, so that the two coplanar states are completely disconnected. Interestingly, the phase transition between the plateau state and the upper coplanar state changes from second order to first order for large values of Jz > ∼ 2.5J.PACS numbers: 75.10. Jm, 67.80.kb, 05.30.Jp Competing interactions between quantum spins can prevent conventional magnetic order at low temperatures. In the search of interesting and exotic quantum phases frustrated systems are therefore at the center of theoretical and experimental research in different areas of physics . One of the most straight-forward frustrated system is the spin-1/2 antiferromagnet (AF) on the triangular lattice, which was also the first model to be discussed as a potential candidate for spin-liquid behavior without conventional order by Anderson [2]. It is now known that the isotropic Heisenberg model on the triangular lattice is not a spin liquid and does show order at zero temperature [3]. Nonetheless, the phase diagram as a function of magnetic field is still actively discussed with recent theoretical calculations [4,5] as well as experimental results [6-9] on Ba 3 CoSb 2 O 9 , which appears to be very well described by a triangular AF. Interesting phases have also been found for anisotropic triangular lattices [11][12][13] and for the triangular extended Hubbard model [14]. Hard-core bosons with nearest neighbor interaction on a triangular lattice correspond to the xxz model with ferromagnetic exchange in the xy-plane, which has been studied extensively [15][16][17][18][19][20]. In this case a so-called supersolid phase near half-filling has been established for large interactions [15], which is characterized by two order parameters, namely a superfluid density and a √ 3 × √ 3 charge density order. Impurity effects show that the two order parameters are competing [17] and the transition to the superfluid state is first order [19,20].However, surprisingly little attention has been paid to the role of an antiferromagnetic anisotropic exchange interaction away from half-filling [24][25][26][27], even though the XXZ model on the triangular lattice H = J ij (Ŝ x iŜ x j +Ŝ y iŜ y j ) + J z ij Ŝ z iŜ z j − B iŜ z i , (1) is arguable one of the...

Exact diagonalization and cluster mean-field study of triangular-lattice XXZ antiferromagnets near saturation

“…The results also give a resolution to the contradiction between the CMF+S analysis [29] and the argument by Sellmann et al [36] regarding the existence of the π-coplanar phase. We carry out the ED calculations of the model (1) at S = 1/2 on finite-size clusters of N spins with periodic boundary condition.…”

“…Second, however, the lowest eigenstate that disappears in the thermodynamic limit is not the finite-size π-coplanar state, contrary to Sellmann et al's speculation [36], but actually a chirally symmetric superposition of finite-size umbrella states. Third, the large-J/J z region is occupied by a chirally antisymmetric superposition of umbrella states.…”

“…[36]. From the identification analysis, we demonstrated that the spurious phase which is present in finite-size calculations and disappears in the thermodynamic limit is actually a chirally symmetric combination of finite-size umbrella states.…”

“…This is because Ψ Γ3 is not the π-coplanar state but the chirally symmetric combination of finite-size umbrella states (unlike the interpretation of Ref. [36]). (ii) The double degeneracy of the lowest-energy eigenstates Ψ Γ1 and Ψ Γ2 in the region of J/J z 2.218 (N → ∞) should correspond to a coplanar phase according to Eq.…”

Static and Dynamical Properties of the Spin-1/2Equilateral Triangular-Lattice AntiferromagnetBa3CoSbMa1, Kamiya2, Hong3 et al. 2016Phys. Rev. Lett.129201454View full textAdd to dashboardCite

“…Introduction.-The S = 1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF) is the paradigmatic example of a two-dimensional (2D) frustrated quantum magnet [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The combination of frustration, strong quantum fluctuations and low dimensionality is anticipated to produce strong deviations from semiclassical theories.…”