63 research outputs found
Two-dimensional quantum antiferromagnets
This review presents some theoretical advances in the field of quantum
magnetism in two-dimensional systems, and quantum spin liquids in particular.
It is to be published as a chapter in the second edition of the book
"Frustrated spin systems", edited by H. T. Diep (World-Scientific). The section
(Sec. 7) devoted to the kagome antiferromagnet has been completely
rewritten/updated, as well as the concluding section (Sec. 8). The other
sections (Secs. 1-6) are unchanged from the first edition of the book
(published in 2005)Comment: 87 pages. 396 references. To be published as a chapter in the second
edition of the book "Frustrated spin systems", edited by H. T. Diep
(World-Scientific
From Neel long-range order to spin-liquids in the multiple-spin exchange model
The phase diagram of the multiple-spin exchange model on the triangular
lattice is studied using exact diagonalizations. The two-spin (J_2) and
four-spin (J_4) exchanges have been taken into account for 12, 16, 19, 21, 24,
and 27 site samples in the parameter region J_4=0 - 0.25 (for a fixed J_2=1).
It is found that the three-sublattice N\'eel ordered state built up by the pure
two-spin exchange can be destroyed by the four-spin exchange, forming a
spin-liquid state. The different data suggest that the phase diagram in this
range of parameters exhibits two phases. The pure J_2 phase is a
three-sublattice Neel ordered phase, a small J_4 drives it into a spin-liquid
state with a spin gap filled of a large number of singlets. This spin-liquid
phase is not of the same generic kind as the phase studied by Misguich et al.
[Phys. Rev. B 60, 1064 (1999)]. It is observed on the finite-size samples that
the spin liquid phase, as the Neel ordered phase, exhibits a magnetization
plateau at m = 1/3, and for J_4 >0.15 a second plateau atm=1/2. These two
plateaus are associated respectively to the semi-classical orderings uud and
uuud.Comment: 6 pages (RevTex), 5 figures (eps). Published versio
Quantum dimer model with Z_2 liquid ground-state: interpolation between cylinder and disk topologies and toy model for a topological quantum-bit
We consider a quantum dimer model (QDM) on the kagome lattice which was
introduced recently [Phys. Rev. Lett. 89, 137202 (2002)]. It realizes a Z_2
liquid phase and its spectrum was obtained exactly. It displays a topological
degeneracy when the lattice has a non-trivial geometry (cylinder, torus, etc).
We discuss and solve two extensions of the model where perturbations along
lines are introduced: first the introduction of a potential energy term
repelling (or attracting) the dimers along a line is added, second a
perturbation allowing to create, move or destroy monomers. For each of these
perturbations we show that there exists a critical value above which, in the
thermodynamic limit, the degeneracy of the ground-state is lifted from 2 (on a
cylinder) to 1. In both cases the exact value of the gap between the first two
levels is obtained by a mapping to an Ising chain in transverse field. This
model provides an example of solvable Hamiltonian for a topological quantum bit
where the two perturbations act as a diagonal and a transverse operator in the
two-dimensional subspace. We discuss how crossing the transitions may be used
in the manipulation of the quantum bit to optimize simultaneously the frequency
of operation and the losses due to decoherence.Comment: 11 pages, 7 (.eps) figures. Improved discussion of the destruction of
the topological degeneracy and other minor corrections. Version to appear in
Phys. Rev.
The kagome antiferromagnet: a chiral topological spin liquid ?
Inspired by the recent discovery of a new instability towards a chiral phase
of the classical Heisenberg model on the kagome lattice, we propose a specific
chiral spin liquid that reconciles different, well-established results
concerning both the classical and quantum models. This proposal is analyzed in
an extended mean-field Schwinger boson framework encompassing time reversal
symmetry breaking phases which allows both a classical and a quantum phase
description. At low temperatures, we find quantum fluctuations favor this
chiral phase, which is stable against small perturbations of second and third
neighbor interactions. For spin-1/2 this phase may be, beyond mean-field, a
chiral gapped spin liquid. Such a phase is consistent with Density Matrix
Renormalization Group results of Yan et al. (Science 322, 1173 (2011)).
Mysterious features of the low lying excitations of exact diagonalization
spectra also find an explanation in this framework. Moreover, thermal
fluctuations compete with quantum ones and induce a transition from this flux
phase to a planar zero flux phase at a non zero value of the renormalized
temperature (T/S^2), reconciling these results with those obtained for the
classical system.Comment: 4 pages, 4 figures, 1 tabl
Thermal destruction of chiral order in a two-dimensional model of coupled trihedra
We introduce a minimal model describing the physics of classical
two-dimensional (2D) frustrated Heisenberg systems, where spins order in a
non-planar way at T=0. This model, consisting of coupled trihedra (or
Ising- model), encompasses Ising (chiral) degrees of freedom,
spin-wave excitations and vortices. Extensive Monte Carlo simulations
show that the T=0 chiral order disappears at finite temperature in a continuous
phase transition in the 2D Ising universality class, despite misleading
intermediate-size effects observed at the transition. The analysis of
configurations reveals that short-range spin fluctuations and vortices
proliferate near the chiral domain walls explaining the strong renormalization
of the transition temperature. Chiral domain walls can themselves carry an
unlocalized topological charge, and vortices are then preferentially
paired with charged walls. Further, we conjecture that the anomalous
size-effects suggest the proximity of the present model to a tricritical point.
A body of results is presented, that all support this claim: (i) First-order
transitions obtained by Monte Carlo simulations on several related models (ii)
Approximate mapping between the Ising- model and a dilute Ising
model (exhibiting a tricritical point) and, finally, (iii) Mean-field results
obtained for Ising-multispin Hamiltonians, derived from the high-temperature
expansion for the vector spins of the Ising- model.Comment: 15 pages, 12 figures, 1 tabl
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