Physical review. B, Condensed matter

Anyons in theXYmodel induced by charged holes

D. Schmeltzer, A. R. Bishop

Published May 1, 1990• 7 citations

Abstract

We show that the inclusion of holes in a XY two-dimensional spin antiferromagnet gives rise to electrically charged particles which carry a flux. As a result two particles with the same electric charge can bind due to their opposite vorticity.

DOI: 10.1103/physrevb.41.9603

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We use a variational procedure to show, starting with the flux-phase state of a Heisenberg model, that holes added to the system behave as anyons. The hole distorts the gauge flux in its surroundings. The amount of flux carried by the hole depends on the ratio between the magnetic- (J) and the kinetic- (t) energy parameters. For J/t\ensuremath{\rightarrow}0 the quasiparticles are fermions, while for J/t\ensuremath{\rightarrow}\ensuremath{\infty} they are semions.

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Anyons: a possible mechanism for binding charged particles

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Phase diagram of the two-dimensional antiferromagnetic XY model in an external magnetic field

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Flux binding and superconductivity in thet-Jmodel

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Physical review. B, Condensed matter

Anyons in theXYmodel induced by charged holes

D. Schmeltzer, A. R. Bishop

Published May 1, 1990• 7 citations

Publisher

Abstract

DOI: 10.1103/physrevb.41.9603

Related papers

Anyons in spin liquids

K. Hallberg, C. A. Balseiro

Physical review. B, Condensed matterMay 1, 19911 citation

Anyons: a possible mechanism for binding charged particles

D. Schmeltzer, A. R. Bishop

The hard core boson gas in (2+1)-dimensions in the presence of a Chern-Simons term is considered, we find that the long wave description is given in terms of Coulomb (longitudinal) and transversal electrodynamics. The longitudinal part is described in terms of electric charges which carry vorticity. When binding of electrical charges occurs the transversal part is described by a photon field and corresponds to a superfluid. Using the same language we find that a spinless fermion is described by a massive photon. We use these concepts to understand the relation between the negative-U Hubbard model in the presence of a magnetic field, and vortices which carry electric charge induced by doping in the repulsive Hubbard model.The hard core boson gas in (2+1)-dimensions in the presence of a Chern-Simons term is considered, we find that the long wave description is given in terms of Coulomb (longitudinal) and transversal electrodynamics. The longitudinal part is described in terms of electric charges which carry vorticity. When binding of electrical charges occurs the transversal part is described by a photon field and corresponds to a superfluid. Using the same language we find that a spinless fermion is described by a massive photon. We use these concepts to understand the relation between the negative-U Hubbard model in the presence of a magnetic field, and vortices which carry electric charge induced by doping in the repulsive Hubbard model.

International Journal of Modern Physics BJun 1, 19912 citations

Effective models of doped quantum ladders of non-Abelian anyons

Medha Soni, Matthias Troyer, Didier Poilblanc

Quantum spin models have been studied extensively in one and higher dimensions. Furthermore, these systems have been doped with holes to study $t\text{\ensuremath{-}}J$ models of $\mathrm{SU}(2)$ spin-1/2. Their anyonic counterparts can be built from non-Abelian anyons, such as Fibonacci anyons described by $\mathrm{SU}{(2)}_{3}$ theories, which are quantum deformations of the $\mathrm{SU}(2)$ algebra. Inspired by the physics of $\mathrm{SU}(2)$ spins, several works have explored ladders of Fibonacci anyons and also one-dimensional (1D) $t\text{\ensuremath{-}}J$ models. Here, we aim to explore the combined effects of extended dimensionality and doping by studying ladders composed of coupled chains of interacting itinerant Fibonacci anyons. We show analytically that in the limit of strong rung couplings these models can be mapped onto effective 1D models. These effective models can either be gapped models of hole pairs, or gapless models described by $t\text{\ensuremath{-}}J$ (or modified $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$) chains of Fibonacci anyons, whose spectrum exhibits a fractionalization into charge and anyon degrees of freedom. The charge degrees of freedom are described by the hardcore boson spectra while the anyon sector is given by a chain of localized interacting anyons. By using exact diagonalizations for two-leg and three-leg ladders, we show that indeed the doped ladders show exactly the same behavior as that of $t\text{\ensuremath{-}}J$ chains. In the strong ferromagnetic rung limit, we can obtain a new model that hosts two different kinds of Fibonacci particles, which we denote as the heavy $\ensuremath{\tau}$'s and light $\ensuremath{\tau}$'s. These two particle types carry the same (non-Abelian) topological charge but different (Abelian) electric charges. Once again, we map the two-dimensional ladder onto an effective chain carrying these heavy and light $\ensuremath{\tau}$'s. We perform a finite size scaling analysis to show the appearance of gapless modes for certain anyon densities, whereas a topological gapped phase is suggested for another density regime.Quantum spin models have been studied extensively in one and higher dimensions. Furthermore, these systems have been doped with holes to study $t\text{\ensuremath{-}}J$ models of $\mathrm{SU}(2)$ spin-1/2. Their anyonic counterparts can be built from non-Abelian anyons, such as Fibonacci anyons described by $\mathrm{SU}{(2)}_{3}$ theories, which are quantum deformations of the $\mathrm{SU}(2)$ algebra. Inspired by the physics of $\mathrm{SU}(2)$ spins, several works have explored ladders of Fibonacci anyons and also one-dimensional (1D) $t\text{\ensuremath{-}}J$ models. Here, we aim to explore the combined effects of extended dimensionality and doping by studying ladders composed of coupled chains of interacting itinerant Fibonacci anyons. We show analytically that in the limit of strong rung couplings these models can be mapped onto effective 1D models. These effective models can either be gapped models of hole pairs, or gapless models described by $t\text{\ensuremath{-}}J$ (or modified $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$) chains of Fibonacci anyons, whose spectrum exhibits a fractionalization into charge and anyon degrees of freedom. The charge degrees of freedom are described by the hardcore boson spectra while the anyon sector is given by a chain of localized interacting anyons. By using exact diagonalizations for two-leg and three-leg ladders, we show that indeed the doped ladders show exactly the same behavior as that of $t\text{\ensuremath{-}}J$ chains. In the strong ferromagnetic rung limit, we can obtain a new model that hosts two different kinds of Fibonacci particles, which we denote as the heavy $\ensuremath{\tau}$'s and light $\ensuremath{\tau}$'s. These two particle types carry the same (non-Abelian) topological charge but different (Abelian) electric charges. Once again, we map the two-dimensional ladder onto an effective chain carrying these heavy and light $\ensuremath{\tau}$'s. We perform a finite size scaling analysis to show the appearance of gapless modes for certain anyon densities, whereas a topological gapped phase is suggested for another density regime.

arXiv:1508.04160Physical review. B./Physical review. BJan 21, 20168 citations

Phase diagram of the two-dimensional antiferromagnetic XY model in an external magnetic field

Виктор Степанович Доценко, G. Uimin

ZhETF Pisma RedaktsiiuSep 1, 19840 citations

On the possibility of binding of two holes in an antiferromagnetic state

Yusuke Takahashi

The European Physical Journal BDec 1, 198733 citations

Flux binding and superconductivity in thet-Jmodel

Zheng-Yu Weng, D. N. Sheng, C. S. Ting

A generalized slave-particle scheme is introduced to study the t-J model with nonlocal effects included. A charge-spin decoupled state is found in this scheme, in which the nonlocal gauge fields play a role of attaching fictitious quantized fluxes to the particles as an effective way to describe antiferromagnetic correlation. As a result, the gauge fluctuation is suppressed in the long-wavelength limit, which shows the stability of flux binding, and the electromagnetic response function of such a state exhibits the Meissner effect. An important consequence of the present approach is that the electron, as a combination of the charge and spin degrees of freedom, does not show time-reversal and parity-symmetry-broken behavior, in contrast to the usual anyon theory. This is consistent with experimental results. The robustness of this conclusion relies on the exactness of the constraint between the charge and spin degrees of freedom as well as the flux binding condition. We also calculate the momentum distribution of electrons, which shows a characteristic scale equal to the Fermi momentum ${\mathit{k}}_{\mathit{f}}$ .A generalized slave-particle scheme is introduced to study the t-J model with nonlocal effects included. A charge-spin decoupled state is found in this scheme, in which the nonlocal gauge fields play a role of attaching fictitious quantized fluxes to the particles as an effective way to describe antiferromagnetic correlation. As a result, the gauge fluctuation is suppressed in the long-wavelength limit, which shows the stability of flux binding, and the electromagnetic response function of such a state exhibits the Meissner effect. An important consequence of the present approach is that the electron, as a combination of the charge and spin degrees of freedom, does not show time-reversal and parity-symmetry-broken behavior, in contrast to the usual anyon theory. This is consistent with experimental results. The robustness of this conclusion relies on the exactness of the constraint between the charge and spin degrees of freedom as well as the flux binding condition. We also calculate the momentum distribution of electrons, which shows a characteristic scale equal to the Fermi momentum ${\mathit{k}}_{\mathit{f}}$.

Physical review. B, Condensed matterJan 1, 199410 citations

Quantum spin models have been studied extensively in one and higher dimensions. Furthermore, these systems have been doped with holes to study $t\text{\ensuremath{-}}J$ models of

\mathrm{SU}(2)

spin-1/2. Their anyonic counterparts can be built from non-Abelian anyons, such as Fibonacci anyons described by

\mathrm{SU}{(2)}_{3}

theories, which are quantum deformations of the

\mathrm{SU}(2)

algebra. Inspired by the physics of

\mathrm{SU}(2)

spins, several works have explored ladders of Fibonacci anyons and also one-dimensional (1D) $t\text{\ensuremath{-}}J$ models. Here, we aim to explore the combined effects of extended dimensionality and doping by studying ladders composed of coupled chains of interacting itinerant Fibonacci anyons. We show analytically that in the limit of strong rung couplings these models can be mapped onto effective 1D models. These effective models can either be gapped models of hole pairs, or gapless models described by $t\text{\ensuremath{-}}J$ (or modified $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$) chains of Fibonacci anyons, whose spectrum exhibits a fractionalization into charge and anyon degrees of freedom. The charge degrees of freedom are described by the hardcore boson spectra while the anyon sector is given by a chain of localized interacting anyons. By using exact diagonalizations for two-leg and three-leg ladders, we show that indeed the doped ladders show exactly the same behavior as that of $t\text{\ensuremath{-}}J$ chains. In the strong ferromagnetic rung limit, we can obtain a new model that hosts two different kinds of Fibonacci particles, which we denote as the heavy $\ensuremath{\tau}$'s and light $\ensuremath{\tau}$'s. These two particle types carry the same (non-Abelian) topological charge but different (Abelian) electric charges. Once again, we map the two-dimensional ladder onto an effective chain carrying these heavy and light $\ensuremath{\tau}$'s. We perform a finite size scaling analysis to show the appearance of gapless modes for certain anyon densities, whereas a topological gapped phase is suggested for another density regime.

{\mathit{k}}_{\mathit{f}}