Valence-bond crystalline order in thes= 1/2J₁–J₂model on the honeycomb lattice

Abstract

Using the coupled cluster method we study the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with nearest-neighbour exchange coupling J1 > 0 and frustrating next-nearest-neighbour coupling J2 ≡ xJ1 > 0. In the range 0 < x < 1 we find four phases exhibiting respectively Néel, 6-spin plaquette, staggered dimer and Néel-II orderings, with quantum critical points at xc1 ≈ 0.207(3), xc2 ≈ 0.385(10) and xc3 ≈ 0.65(5). The transitions at xc1 and xc3 appear to be continuous (and hence deconfined) ones, while that at xc2 appears to be a direct first-order one.

High-order study of the quantum critical behavior of a frustrated spin- 12 antiferromagnet on a stacked honeycomb bilayer

“…We also note, however, that a (4m − 2)/4m staggering effect, where m ∈ Z + is a positive integer, has been observed [86,87,93] in LSUBn sequences of CCM results for various physical parameters on frustrated honeycomblattice monolayers. Such staggering implies that the two sub-sequences with n = 4m − 2 and with n = 4m need to be extrapolated separately from one another.…”

Frustrated spin-12J1–J2isotropicXYBishop1, Li2, Campbell3 2014Phys. Rev. B320460View full textAdd to dashboardCite

“…(2) on the honeycomb lattice for the case s = 1 2 . We found previously 14,15 that for the corresponding Heisenberg model of Eq. (1) quantum fluctuations are strong enough in the spin-1 2 case to change the GS phase diagram very substantially from its classical counterpart discussed above.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] Particular attention has focused on the spin-1 2 J 1 -J 2 model in which nearest-neighbor (NN) pairs of spins interact via an isotropic Heisenberg interaction with exchange coupling parameter J 1 , and next-nearest-neighbor (NNN) pairs interact via a similar isotropic Heisenberg interaction with exchange coupling parameter J 2 . When the NN interaction is antiferromagnetic in nature (i.e., J 1 > 0), a corresponding antiferromagnetic NNN interaction (i.e., J 2 > 0) acts to frustrate the Néel order that is preferred by the NN bonds acting by themselves.…”

“…For example, in a recent calculation 15 by the present authors, using the coupled cluster method (CCM) carried out to very high orders of approximation, the T = 0 GS phase diagram of the spin-1 2 isotropic J 1 -J 2 Heisenberg model on a honeycomb lattice was studied for the case J 1 > 0 in the range 0 ≤ κ ≤ 1 for the frustration parameter. Four phases were found, which exhibited, respectively, Néel, 6-spin plaquette, staggered dimer, and Néel-II orderings, with corresponding quantum critical points (QCPs) at κ c1 = 0.207 ± 0.003, κ c2 = 0.385 ± 0.010, and κ c3 ≈ 0.65 ± 0.05.…”

Valence bond phases inS= 1/2 Kane–Mele–Heisenberg model

“…0.5 [11][12][13][14][15][16][17][18] . For J2 J1 > 0.5, a long ranged collinear ordered ground state is proposed 13,18 .…”