Weak Plaquette Valence Bond Order in theS=1/2HoneycombJ1−J2Heisenberg Model

Abstract

Using the density matrix renormalization group, we investigate the S = 1/2 Heisenberg model on the honeycomb lattice with first (J(1)) and second (J(2)) neighbor interactions. We are able to study long open cylinders with widths up to 12 lattice spacings. For J(2)/J(1) near 0.3, we find an apparently paramagnetic phase, bordered by an antiferromagnetic phase for J(2) ≲ 0.26 and by a valence bond crystal for J(2) ≳ 0.36. The longest correlation length that we find in this intermediate phase is for plaquette valence bond order. This correlation length grows strongly with cylinder circumference, indicating either quantum criticality or weak plaquette valence bond order.

Possible nematic spin liquid in spin-1 antiferromagnetic system on the square lattice: Implications for the nematic paramagnetic state of FeSe

“…For the geometry induced nematic order such as the order in the neighboring Néel phase without a C 4 symmetry breaking, one can see that the order decays very fast to vanish with growing cylinder width, in contrast to the scaling behavior in the intermediate phase. As a numerical method, we would like to point out that for detecting lattice symmetry breaking, edge bond pinning has been shown effective in quantum Monte Carlo 60 and DMRG simulations 58,59,61 . In the recent DMRG calculations for the spin-1/2 J 1 − J 2 triangular Heisenberg model [62][63][64] , a strong nematic order is also found, which is considered as an evidence of a spontaneous rotational symmetry breaking of the identified spin liquid phase.…”

Nature of the phases in the frustratedXYmodel on the honeycomb lattice

“…A remarkable example where the existence of such a state has been inferred is the spin-1/2 kagome-lattice Heisenberg antiferromagnet, which has been extensively studied both theoretically and experimentally [1][2][3], even though the precise nature of the spin-liquid state (gapped vs gapless) is still under debate [3][4][5][6]. Another model that has recently received considerable attention for its potential to realize spin-liquid states is the spin-1/2 Heisenberg model on the honeycomb lattice, with nearest-neighbor (NN) J 1 and next-to-nearest neighbor (NNN) J 2 exchange interactions [7][8][9][10][11][12][13][14][15][16]. This is in part motivated by its close relation to the Hubbard model, for which the possibility of having a spin-liquid ground state has been under close scrutiny [17][18][19].…”

“…For the 6 × 6 × 2 cluster we also explored the breaking of spatial symmetry on states constructed on a larger 18-site unit cell, inspired by the plaquette-like phases found in Ref. [14,15] for the Heisenberg model. The first state we considered was constructed by defining two different real NN hopping amplitudes assigned to different bonds as depicted in Fig.…”

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 .…”