arXiv:cond-mat/0010041 · Physical review. B, Condensed matter

Spinon deconfinement above a finite energy gap in two-dimensional quantum Heisenberg antiferromagnets

G. Baskaran

Published Dec 23, 2003• 18 citations

Abstract

The familiar spin-$\frac{1}{2}$ quantum Heisenberg antiferromanget in a two-dimensional (2D) square lattice is shown, within the nonlinear sigma model approximations, to be another state of matter that has excitations with fractional quantum numbers above a finite energy gap. The 1-skyrmion with an energy $\ensuremath{\approx}2\ensuremath{\pi}J$ is shown to be made of two ``deconfined spinons'' or ``O(3) vortices.'' The many skyrmion operator and the wave functions that we have found are strikingly similar to quantum Hall quasiparticle operators and wave functions. We also predict the presence of finite energy ``spin-$S$ spinon'' for a general spin S Heisenberg antiferromagnets in 2D. Some consequences are briefly discussed.

DOI: 10.1103/physrevb.68.212409

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arXiv:cond-mat/0010041 · Physical review. B, Condensed matter

Spinon deconfinement above a finite energy gap in two-dimensional quantum Heisenberg antiferromagnets

G. Baskaran

Published Dec 23, 2003• 18 citations

arXiv HTML PDF

Abstract

The familiar spin-

\frac{1}{2}

quantum Heisenberg antiferromanget in a two-dimensional (2D) square lattice is shown, within the nonlinear sigma model approximations, to be another state of matter that has excitations with fractional quantum numbers above a finite energy gap. The 1-skyrmion with an energy

\ensuremath{\approx}2\ensuremath{\pi}J

is shown to be made of two deconfined spinons'' or O(3) vortices.'' The many skyrmion operator and the wave functions that we have found are strikingly similar to quantum Hall quasiparticle operators and wave functions. We also predict the presence of finite energy ``spin-

S

spinon'' for a general spin S Heisenberg antiferromagnets in 2D. Some consequences are briefly discussed.

DOI: 10.1103/physrevb.68.212409

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We propose that the disordered state of a two-dimensional spin-1/2 Heisenberg antiferromagnet is physically equivalent to the incompressible liquid state of the fractional quantum Hall system. The fractional quantum Hall state for bosons is shown to be an exact spin singlet and to possess a low variational energy for the near-neighbor Heisenberg model on a triangular lattice. Variational wave functions for neutral spin-1/2 excitations are constructed and shown to form an exact spin doublet. Variational energies of these states are calculated, and their spin density profiles are determined. We find that a localized spin-1/2 quaisparticle has a size comparable to a lattice bond length and an excitation energy \ensuremath{\Delta}=1.3J. The energy-momentum dispersion of quasiparticles and spin-1 collective modes, obtained variationally, supports the hypothesis that the spin liquid state has a finite energy gap. The 1/2 fractional statistics exhibited by the quasiparticle excitations is explicitly demonstrated.We propose that the disordered state of a two-dimensional spin-1/2 Heisenberg antiferromagnet is physically equivalent to the incompressible liquid state of the fractional quantum Hall system. The fractional quantum Hall state for bosons is shown to be an exact spin singlet and to possess a low variational energy for the near-neighbor Heisenberg model on a triangular lattice. Variational wave functions for neutral spin-1/2 excitations are constructed and shown to form an exact spin doublet. Variational energies of these states are calculated, and their spin density profiles are determined. We find that a localized spin-1/2 quaisparticle has a size comparable to a lattice bond length and an excitation energy \ensuremath{\Delta}=1.3J. The energy-momentum dispersion of quasiparticles and spin-1 collective modes, obtained variationally, supports the hypothesis that the spin liquid state has a finite energy gap. The 1/2 fractional statistics exhibited by the quasiparticle excitations is explicitly demonstrated.

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Spin excitation spectra of two dimensional $S=1/2$ Heisenberg model with checkerboard structures.Spin excitation spectra of two dimensional $S=1/2$ Heisenberg model with checkerboard structures.

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On Spin 1/2 Excitations and Quantum Criticality in Two Dimensional O(3) Antiferromagnets

Zaira Nazario, David Santiago

arXiv:cond-mat/0411204Bulletin of the American Physical SocietyNov 8, 20040 citations

The familiar spin-

\frac{1}{2}

\ensuremath{\approx}2\ensuremath{\pi}J

S

spinon'' for a general spin S Heisenberg antiferromagnets in 2D. Some consequences are briefly discussed.

{\mathit{CP}}^{1}

representation of the

s=\frac{1}{2}

spin operator and integrate out the half of the

{\mathit{CP}}^{1}

variables at odd sites to obtain a

{\mathit{CP}}^{1}

nonlinear $\ensuremath{\sigma}$ model. The effective coupling constant is a function of $\ensuremath{\alpha}$, and at $\ensuremath{\alpha}=0$, the

{\mathit{CP}}^{1}

model is in the ordered phase that corresponds to the N\'eel state of the AF Heisenberg model. A phase transition to the dimer state occurs at a certain critical value of ${\ensuremath{\alpha}}_{C}$ as $\ensuremath{\alpha}$ increases. In the N\'eel state, the dynamical composite U(1) gauge field in the

{\mathit{CP}}^{1}

model is in a Higgs phase, and low-energy excitations are gapless spin waves. In the dimer phase, a confinement phase of the gauge theory with

s=1

excitations is realized. For the critical point, we argue that a deconfinement phase, which is similar to the Coulomb phase in three spatial dimensions, is realized and

s=\frac{1}{2}

spinons appear as low-energy excitations.

Spin excitation spectra of two dimensional

S=1/2

Heisenberg model with checkerboard structures.

We study the excitation spectra of two-dimensional spin-

1/2

Heisenberg model with checkerboard structures using stochastic analytic continuation of imaginary-time correlation function obtained from quantum Monte Carlo simulation. The checkerboard models have two different antiferromagnetic nearest-neighbor interactions

J_{1}

and

J_{2}

, and the tuning parameter

g

is defined as

J_{2}/J_{1}

. The dynamic structure factors are systematically calculated in all phases of the models as well as at the critical points. To give a full understanding of the dynamic spectra, wave theory is employed to explain some features of numerical results, especially for the low-energy part. When

g

is close to

1

, the features of the excitation spectra of each checkerboard model are roughly the same as those of the original square lattice antiferromagnetic Heisenberg model, and the high-energy continuum among them are discussed. In contrast to the other checkerboard structures investigated in this paper, the

3\times 3

checkerboard model has distinctive excitation features, like a gap between a low-energy gapless branch and a gapped high-energy part exists when

g

is small. The gapless branch in this case can be regarded as wave in N

\mathrm{\acute{e}}

el order formed by block spin in each

3\times 3

plaquette with effective exchange interaction originated from renormalization. One finding is that the continuum also appears in this low-energy branch, which may originated from nearly deconfined process in block spin.