arXiv:cond-mat/9308002 · Physical Review Letters

Realization of a spin liquid in a two dimensional quantum antiferromagnet

Alberto Parola, Sandro Sorella, Q. F. Zhong

Published Dec 27, 1993• 50 citations

Abstract

The ground state properties of the two dimensional spatially anisotropic Heisenberg model are investigated by use of field theory mappings, spin-wave expansion, and Lanczos technique. Evidence for a disorder transition induced by anisotropy at about ${\mathit{J}}_{\mathit{y}}$/${\mathit{J}}_{\mathit{x}}$0.1 is shown. We argue that the disordered phase is gapless and its long wavelength properties can be interpreted in terms of decoupled one dimensional chains.

DOI: 10.1103/physrevlett.71.4393

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arXiv:cond-mat/9308002 · Physical Review Letters

Realization of a spin liquid in a two dimensional quantum antiferromagnet

Alberto Parola, Sandro Sorella, Q. F. Zhong

Published Dec 27, 1993• 50 citations

arXiv HTML PDF

Abstract

{\mathit{J}}_{\mathit{y}}

{\mathit{J}}_{\mathit{x}}

0.1 is shown. We argue that the disordered phase is gapless and its long wavelength properties can be interpreted in terms of decoupled one dimensional chains.

DOI: 10.1103/physrevlett.71.4393

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{\mathit{J}}_{\mathit{y}}

{\mathit{J}}_{\mathit{x}}

0.1 is shown. We argue that the disordered phase is gapless and its long wavelength properties can be interpreted in terms of decoupled one dimensional chains.

Using (infinite) density-matrix renormalization-group techniques, ground-state properties of antiferromagnetic

S=1

Heisenberg spin chains with exchange and single-site anisotropies in an external field are studied. The phase diagram is known to display a plenitude of interesting phases. We elucidate quantum phase transitions between the supersolid and spin-liquid phases as well as the spin-liquid and ferromagnetic phases. Analyzing spin-correlation functions in the spin-liquid phase, commensurate and (two distinct) incommensurate regions are identified.

The ground-state properties of the quasi-one-dimensional spin-

1/2

antiferromagnetic Heisenberg model is investigated by using a variational method. Spins on chains along the

x

direction are antiferromagnetically coupled with exchange

J>0

, while spins between chains in the

y

direction are coupled either ferromagnetically (${J}^{\ensuremath{'}}<0$) or antiferromagnetically (${J}^{\ensuremath{'}}>0$). The staggered and the colinear antiferromagnetic magnetizations are computed and their dependence on the anisotropy parameter $\ensuremath{\lambda}=|{J}^{\ensuremath{'}}|/J$ is analyzed. It is found that an infinitesimal interchain coupling parameter is sufficient to stabilize a long-range order with either a staggered magnetization

{m}_{s}

(${J}^{\ensuremath{'}}>0$) or a colinear antiferromagnetic magnetization

{m}_{caf}

(${J}^{\ensuremath{'}}<0$), both behaving as $\ensuremath{\simeq}{\ensuremath{\lambda}}^{1/2}$ for $\ensuremath{\lambda}\ensuremath{\rightarrow}0$.

We explore the nature of the quantum phase transition between a magnetically ordered state with collinear spin pattern and a gapless

{Z}_{2}

spin liquid in the Heisenberg-Kitaev model. We construct a slave particle mean-field theory for the Heisenberg-Kitaev model in terms of complex fermionic spinons. It is shown that this theory, formulated in the appropriate basis, is capable of describing the Kitaev spin liquid as well as the transition between the gapless

{Z}_{2}

spin liquid and the so-called stripy antiferromagnet. Within our mean-field theory, we find a discontinuous transition from the

{Z}_{2}

spin liquid to the stripy antiferromagnet. We argue that subtle spinon confinement effects, associated with the instability of gapped

U(1)

spin liquid in two spatial dimensions, play an important role at this transition. The possibility of an exotic continuous transition is briefly addressed.