Frustrated spin-12J1–J2isotropicXY

Abstract

Frustrated spin- We study the zero-temperature ground-state (GS) phase diagram of a spin-half J1-J2 XY model on the honeycomb lattice with nearest-neighbor exchange coupling J1 > 0 and frustrating nextnearest-neighbor exchange coupling J2 ≡ κJ1 > 0, where both bonds are of the isotropic XY type, using the coupled cluster method. Results are presented for the GS energy per spin, magnetic order parameter, and staggered dimer valence-bond crystalline (SDVBC) susceptibility, for values of the frustration parameter in the range 0 ≤ κ ≤ 1. In this range we find phases exhibiting, respectively, Néel , is found to form the GS phase out to a first quantum critical point at κc 1 = 0.216(5), beyond which the stable GS phase has N(z) order over the range κc 1 < κ < κc 2 = 0.355(5). For values κ > κc 2 we find a strong competition to form the GS phase between states with N-II(p) and SDVBC forms of order. Our best estimate, however, is that the stable GS phase over the range κc 2 < κ < κc 3 ≈ 0.52(3) is a mixed state with both SDVBC and N-II(p) forms of order; and for values κ > κc 3 is the N-II(p) state, which is stable at the classical level only at the highly degenerate point κ = 1 2. Over the range 0 ≤ κ ≤ 1 we find no evidence for any of the spiral phases that are present classically for all values κ > 1 6, nor for any quantum spin-liquid state.

Polarized-neutron investigation of magnetic ordering and spin dynamics in BaCo 2 (AsO 4 ) 2 frustrated honeycomb-lattice magnet

“…Among other predictions, it was conjectured that for $J_1>0$, frustration (be it due to $J_2$ or $J_3$) could lead to the disappearance of the ferromagnetic phase at the expense of a spin-liquid phase with short-range IP correlations and the opening of spin-gaps in the excitation spectrum, which seem in qualitative agreement with the experimental results in BCAO. The presence of a frustration-enhanced gapped spin-liquid phase for a quantum-spin (spin-1/2) system on the honeycomb lattice has also been predicted by Takano [42] and more recently by Bishop et al [43], [44], [45], [46]. Unfortunately, almost nothing exists for the $J_1-J_2-J_3$ planar model on the honeycomb lattice in applied magnetic field.…”

Phase diagram of a frustrated spin-12J1-J2X<

“…For the XXX model the Néel order that exists for κ < κ c 1 ≈ 0.2 is predicted by different methods to give way either to a GS phase with plaquette valence-bond crystalline (PVBC) order [6,7,[10][11][12][13][14] or to a quantum spin-liquid (QSL) state [5,9,15,16] in the range κ c 1 < κ < κ c 2 ≈ 0.4. By contrast, for the XX model the Néel xy planar [N(p)] ordering that exists for κ < κ c 1 is predicted by different methods to yield either to a GS phase with Néel z-aligned [N(z)] order [19,23] or to a QSL state [17,20] in a corresponding range κ c 1 < κ < κ c 2 . There is broad agreement for both models that for (1 >) κ > κ c 2 there is a strong competition to form the GS phase between states with collinear Néel-II xy planar [N-II(p)] and staggered dimer valence-bond crystalline (SDVBC) forms of order, which lie very close in energy.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], and references cited therein) or an isotropic XY (XX) form (see, e.g., Refs. [17][18][19][20][21][22][23]). Although the classical (s → ∞) versions of these two models have identical zero-temperature (T = 0) ground-state (GS) phase diagrams [1,2], their s = 1 2 counterparts differ in significant ways.…”

“…[11,12,[23][24][25][26][27][28][29][30][31] for more details. Any CCM calculation starts with the choice of a suitable model (or reference) state | .…”

Spin conductivity of the two-dimensional anisotropic frustrated Heisenberg model in the honeycomb lattice

“…Frustrated spin systems have been object of intense research in the recent years [1] where the competitive interactions in quantum magnetic systems especially on a honeycomb lattice have much interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The main effects of frustrating interactions, in the neighborhood of a Neel state, are the increase of the coupling and the decrease of the spin-wave velocity.…”