Valence-bond crystals in the kagomé spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study

Abstract

In this paper, we do a complete classification of valence-bond crystals (VBCs) on the kagomé lattice based on general arguments of symmetry only and thus identify many new VBCs for different unit cell sizes. For the spin-1/2 Heisenberg antiferromagnet, we study the relative energetics of competing gapless spin liquids (SLs) and VBC phases within the class of Gutzwillerprojected fermionic wave functions using variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. By using a state-of-the-art optimization method, we conclusively show that the U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12-and 36-site unit cell VBCs. This stability is also preserved on addition of a next-nearest-neighbor super-exchange coupling of both antiferromagnetic and ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is stabilized on addition of a very small next-nearest-neighbor FM super-exchange coupling, i.e. |J 2 | ≈ 0.045, and this VBC is the same in terms of space-group symmetry as that obtained in an effective quantum dimer model study. It breaks reflection symmetry, has a nontrivial flux pattern and is a strong dimerization of the uniform RVB SL.

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

“…These results confirm earlier DMRG studies performed at J 2 = 0 [29,30], in agreement with an extended Z 2 spin-liquid region around J 2 = 0. Notice that our data does not support an algebraic U(1) spin liquid, which would imply a vanishing spin gap, in contrast with what has been found recently by variational Monte Carlo methods [7]. Also, from the present data, we cannot exclude a transition from the Z 2 spin liquid to a valence bond crystal (VBC) for small ferromagnetic J 2 , as it was reported in Ref.…”

“…Also, from the present data, we cannot exclude a transition from the Z 2 spin liquid to a valence bond crystal (VBC) for small ferromagnetic J 2 , as it was reported in Ref. [7]. Notice that the breaking of the lattice symmetry is hard to detect [57] using the cylinder geometry.…”

“…Despite substantial analytical and numerical effort, no agreement has been reached yet in the community. The proposed ground states include several valence bond crystals (VBCs) [1][2][3][4][5][6][7], and both gapped and gapless spin liquids [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Ghost modes and continuum scattering in the dimerized distorted kagome lattice antiferromagnet Rb2Cu3SnF12

“…2 The classical Néel state is apparently replaced by a dynamic quantum state, the details of which remain to be established. Proposed ground states include a gapless U (1)-Dirac-spin-liquid state, [3][4][5][6] a gapped-spin-liquid, [7][8][9][10][11] and valence-bond-solid (VBS) states. [12][13][14][15][16] These states are very close in energy so small perturbations and intrinsic limitations of numerical methods make it difficult to reach a firm conclusion.…”

Spin-12HeisenbergJ1−J2antiferromagnet on the kagome lattice

“…A fully gapped Z 2 topological spin-liquid ground state has been claimed for using density-matrix renormalization group (DMRG) [7][8][9][10][11], pseudofermion functional renormalization group [12], and Schwinger boson mean-field calculations [13][14][15][16]. On the other hand, a gapless (algebraic) and fully symmetric U (1) Dirac spin liquid has been proposed as the ground state and widely studied using a variational Monte Carlo approach [17][18][19][20][21][22][23][24][25][26]. In addition, valence-bond crystals of different unit cell sizes and symmetries have been also suggested from other techniques [27][28][29][30][31][32][33][34][35][36][37].…”