Quantum dimer model for the spin-12kagomeZ2spin liquid

Abstract

We revisit the description of the low-energy singlet sector of the spin-1/2 Heisenberg antiferromagnet on kagome in terms of an effective quantum dimer model. With the help of exact diagonalizations of appropriate finite-size clusters, we show that the embedding of a given process in its kagome environment leads to dramatic modifications of the amplitudes of the elementary loop processes, an effect not accessible to the standard approach based on the truncation of the Hamiltonian to the nearest-neighbour valence-bond basis. The resulting parameters are consistent with a Z2 spin liquid rather than with a valence-bond crystal, in agreement with the last density matrix renormalization group results.

Detecting crystal symmetry fractionalization from the ground state: Application toZ2spin liquids on the kagome lattice

“…While some aspects of it have been studied for quite a while, crystal symmetry fractionalization has now received renewed attention, due to an increased interest in the role of crystal symmetry in topological phases of matter. This topic is also becoming timely in view of strong numerical evidence for spin liquids on kagome lattice found in the last few years [5][6][7][8][9]. In order to fully pin down the topological nature of the numerically found spin liquid liquid, the complete pattern of crystal symmetry fractionalization needs to be determined.…”

Spin-ordered ground state and thermodynamic behaviors of the spin-32kagome Heisenberg antiferromagnet

“…A2 (b)]. For a later convenience, we do not absorb the diagonal matrix λ 9 into W. Subsequently, we suppose W and λ 9 comprise a one-dimensional chain and perform a 1D canonicalization procedure [42] to get a renewedλ 9 andW, and what we have done to W is actually acting on tensors X and A and we get renewed tensorsX andÃ. In this way, we complete the regularization on the cluster tensor N 1 along the direction of λ 9 and obtain the renewed cluster tensor N 1 [ Fig.…”

“…As shown in Fig. A2 (b), by taking N 1 as an example, we build a double-layer structure of the cluster tensor and connect all We contract the double-layer tensor cluster to get tensor W, which will later be canonicalized for updating the effective environmentλ 9 , as well as the tensors X and A. (c) After the "canonicalization", we contract the hexagon tensor cluster with its conjugate layer, leaving onlyλ 9 and one physical bond open, and obtain the reduced density matrix M 1 .…”

“…Through continuous efforts of many scientists, its ground state is generally believed to be a spin liquid without any symmetry breaking [4,5]. However, whether or not there is a gap in this interesting system still remains controversial [5][6][7][8][9][10][11][12]. Meanwhile, the high spin (S > 1/2) kagome physics has also gained great interest currently.…”

Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice

“…Recently, other schemes to derive GQDM from Heisenberg model have been proposed claiming to refine the procedure in the context of the kagome and square-kagome antiferromagnets. 24,25 One has still however to perform a direct numerical comparison with the parent spin hamiltonian to understand whether its physical properties are well reproduced by the effective models. Here we will use the original GQDM scheme 12 and make a precise connection between the spin hamiltonianĤ K,θ Eq.…”