RVB description of the low-energy singlets of the spin 1/2 kagomé antiferromagnet

Abstract

Abstract. Extensive calculations in the short-range RVB (Resonating valence bond) subspace on both the trimerized and the regular (non-trimerized) Heisenberg model on the kagomé lattice show that short-range dimer singlets capture the specific low-energy features of both models. In the trimerized case the singlet spectrum splits into bands in which the average number of dimers lying on one type of bonds is fixed. These results are in good agreement with the mean field solution of an effective model recently introduced. For the regular model one gets a continuous, gapless spectrum, in qualitative agreement with exact diagonalization results.

Accurate results from perturbation theory for strongly frustratedS=12Heisenberg spin clusters

“…In the case of C 20 , the ground and excited states at zero magnetic field are singlets. This result is in agreement with similar ones for strongly frustrated magnetic systems such as the Kagomé lattice and a one dimensional analogue of the pyrochlore lattice [18]. The non-magnetic nature of the excitation is attributed to the frustration and the connectivity of the system.…”

“…We see this behavior in a small range of the fields around the transition with roots around λ = 1, which is reflected in the rapid non-monotonic variation of < S z > around the critical field. Since the square root of function (18) has to eventually be taken, its zeros will turn into branch points in the complex λ plane.…”

Quantum Phases in Two-Dimensional Frustrated Spin-1/2 Antiferromagnets

“…33,34 The understanding of the low lying continuum of singlets is still incomplete but some progresses have been done in the last years. 37,38,39,40 Recent ED calculations 37 on a kagomé N = 24 sample depletted of two sites suggest that the elementary excitations likely consist of deconfined spinons: as shown in Fig 3, confined). 41 The low lying singlets could be related to a family of short range RVB dimer coverings of the lattice.…”

Quantum dimer model for the spin-12kagomeZ2spin liquid

“…In principle, such magnetically disordered phases can be described by short-range valence bonds [1][2][3][4]29], and in fact there are good reasons to believe that the qualitative physics is captured by the nearest-neighbor valence bond (NNVB) basis. This effort goes back to Zeng and Elser [30], who showed that the NNVB dynamics is governed by several tunneling processes, casted in a quantum dimer model (QDM) form [12,22,23,31,32]. Whether this description leads to a valence-bond crystal or to a disordered phase is still open however.…”

“…Assuming that the effective Hamiltonian can be written as a sum of local processes that consist in tunneling between two dimer coverings |φ b and |φ r (see first row of Fig. 2 for a sketch of the most important processes), the QDM parameters can in fact be simply determined from the overlap φ b |φ r ≡ ω and the matrix elements φ b |H|φ b = φ r |H|φ r ≡ E 0 and φ b |H|φ r ≡ v, which can be found from the transition graph following standard rules [11,22,30,32,37,38]. Indeed, the simplicity of the problem allows for a direct evaluation of O − 1 2 NNVB , giving…”