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Physical review. B, Condensed matter

Quantum dimer calculations on the spin-1/2 kagome ´ Heisenberg antiferromagnet

Chen Zeng, Veit Elser

Published Apr 1, 1995• 123 citations
Publisher

Abstract

In analogy to the quantum dimer model on the square lattice introduced by Rokhsar and Kivelson, we identify the low-energy Hilbert space of the spin-1/2 kagom\'e Heisenberg antiferromagnet with the set of dimerized states (nearest-neighbor singlets) and derive an effective Hamiltonian which describes resonance and includes fluctuations into next-nearest-neighbor singlets. Complete diagonalization of this effective Hamiltonian for systems as large as 36 spins makes possible the study of the low-energy thermodynamics of this quantum antiferromagnet and strongly supports the double peak feature in the heat capacity.

DOI
10.1103/physrevb.51.8318

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In analogy to the quantum dimer model on the square lattice introduced by Rokhsar and Kivelson, we identify the low-energy Hilbert space of the spin-1/2 kagom'e Heisenberg antiferromagnet with the set of dimerized states (nearest-neighbor singlets) and derive an effective Hamiltonian which describes resonance and includes fluctuations into next-nearest-neighbor singlets. Complete diagonalization of this effective Hamiltonian for systems as large as 36 spins makes possible the study of the low-energy thermodynamics of this quantum antiferromagnet and strongly supports the double peak feature in the heat capacity.
The spin half Heisenberg antiferromagnet on the Kagome lattice, is mapped by Contractor Renormalization to a Spin-Pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale. Our results explain the large density of low energy singlets observed numerically, and the non magnetic T-squared specific heat observed experimentally.
The spin-1/2 Heisenberg antiferromagnet on the kagomé lattice, is mapped by contractor renormalization to a spin-pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale. Our results explain the large density of low-energy singlets observed numerically, and the nonmagnetic T2 specific heat observed experimentally.
We revisit the description of the low-energy singlet sector of the spin-12\frac{1}{2}21​ 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-neighbor valence-bond basis. The resulting parameters are consistent with a Z2{Z}_{2}Z2​ spin liquid rather than with a valence-bond crystal, in agreement with the last density matrix renormalization group results.
We obtain a quantum dimer model (QDM) containing a Rokhsar-Kivelson (RK) point expressed by spin-12\frac{1}{2}21​ Heisenberg antiferromagnets on a diamond-like decorated square lattice. This lattice has macroscopically degenerated nonmagnetic ground states, which are equivalent to the Hilbert space of a square-lattice QDM. Then, a square-lattice QDM containing the RK point as a second-order effective Hamiltonian is obtained by introducing further neighbor couplings as perturbation. Our model can provide a new method for the experimental realization of a resonating valence bond state in the QDM.
The singlet dynamics, which plays a major role in the physics of the spin-1/2 quantum Heisenberg antiferromagnet (QHAF) on the kagome lattice, can be approximately described by projecting onto the nearest-neighbor valence bond (NNVB) singlet subspace. We revisit here the effective quantum dimer model, which originates from the latter NNVB-projected Heisenberg model via a nonperturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact diagonalization on a 108-site cluster supplemented by a careful symmetry analysis, it is shown that a previously found 36-site valence bond crystal (VBC) in fact competes with a new type of 12-site ``resonating-columnar'' VBC. Interestingly, these two VBCs ``emerge'' in different topological sectors. The exceptionally large degeneracy of the ground-state multiplets (144 on our 108-site cluster) and the proximity of a Z2{\mathbb{Z}}_{2}Z2​ dimer liquid have implications for the interpretation of numerical results on the QHAF, which are outlined. The possibility of a chiral VBC (i.e., spontaneously breaking time-reversal symmetry) is also discussed.
An effective spin-orbit Hamiltonian is derived for a spin-1∕21∕21∕2 trimerized kagom\'e antiferromagnet in the second-order of perturbation theory in the ratio of two coupling constants. Low-energy singlet states of the obtained model are mapped to a quantum dimer model on a triangular lattice. The quantum dimer model is dominated by dimer resonances on a few shortest loops of the triangular lattice. The characteristic energy scale for the dimer model constitutes only a small fraction of the weaker exchange coupling constant.