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Physical Review Letters

Low-Energy Singlets in the Heisenberg Antiferromagnet on the Kagome Lattice

R. Budnik, Assa Auerbach

Published Oct 29, 2004• 90 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.93.187205

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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.
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.
This paper is concerned with physics of the low-energy singlet excitations found to exist below the spin gap in numerical studies of the Kagome lattice quantum Heisenberg antiferromagnet. Insight into the nature of these excitations is obtained by exploiting an approximate mapping to a fully frustrated transverse-field Ising model on the dual dice lattice. This Ising model is shown to possess at least two phases---an ordered phase that also breaks translational symmetry with a large unit cell, and a paramagnetic phase. The former is argued to be a likely candidate for the ground state of the original Kagome magnet which thereby exhibits a specific pattern of dimer ordering with a large unit cell. Comparisons with available numerical results are made.
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 low-energy singlet dynamics of the quantum Heisenberg antiferromagnet on the kagome lattice is described by a quantitative quantum dimer model. Using advanced numerical tools, the latter is shown to exhibit valence-bond crystal (VBC) order with a large 36-site unit cell and hidden degeneracy between even odd parities. Evidences are given that this ground state lies in the vicinity of a Z2{\mathbb{Z}}_{2}Z2​ dimer-liquid region separated by a quantum critical point (QCP). Implications regarding numerical analysis and experiments are discussed.
The low-energy singlet dynamics of the Quantum Heisenberg Antiferromagnet on the Kagome lattice is described by a quantitative Quantum Dimer Model. Using advanced numerical tools, the latter is shown to exhibit Valence Bond Crystal order with a large 36-site unit cell and hidden degeneracy between even and odd parities. Evidences are given that this groundstate lies in the vicinity of a Z2\mathbb{Z}_2Z2​ dimer liquid region separated by a Quantum Critical Point. Implications regarding numerical analysis and experiments are discussed.