Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2103.02317 · Condensed Matter

Fractional Statistics of Charge Carriers in the One- and Two-Dimensional t-J Model: A Hint for the Cuprates?

Pieralberto Marchetti

Published Feb 21, 2020• 2 citations
arXivHTMLPDF

Abstract

We show that we can interpret the exact solution of the one-dimensional t-J model in the limit of small J in terms of charge carriers with both exchange (braid) and exclusion (Haldane) statistics with parameter 1/2. We discuss an implementation of the same statistics in the two-dimensional t-J model, emphasizing similarities and differences with respect to one dimension. In both cases, the exclusion statistics is a consequence of the no-double occupation constraint. We argue that the application of this formalism to hole-doped high Tc cuprates and the derived composite nature of the hole give a hint to grasp many unusual properties of these materials.

DOI
10.3390/condmat5010012

Related papers

Charge carriers with fractional exclusion statistics in cuprates

P. A. Marchetti, F. Ye, Z. B. Su +1 more

We show that in the $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ spin-charge gauge approach we developed earlier one can attribute consistently an exclusion statistics with parameter 1/2 to the spinless charge carriers of the $t\text{\ensuremath{-}}J$ model in two dimensions, as it occurs in one dimension. Like the one-dimensional case, the no-double occupation constraint is at the origin of this fractional exclusion statistics. With this statistics we recover a large Fermi volume of holes at high dopings, close to that of the tight binding approximation. Furthermore, the composite nature of the hole, made of charge and spin carriers only weakly bounded, can provide a natural explanation of many unusual experimental features of the hole-doped cuprates.

arXiv:1907.05081•Physical review. B./Physical review. B•Jul 3, 2019•4 citations

Fractional Exclusion Statistics for thet-JModel with Long Range Exchange and Hopping

Yusuke S. Kato, Yoshio Kuramoto

We construct thermodynamics of the one-dimensional supersymmetric t-J model with the 1/sin 2 interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component t-J model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.

Journal of the Physical Society of Japan•Jun 15, 1996•25 citations

Fractional Exclusion Statistics for the t-J Model

Yusuke S. Kato, Yoshio Kuramoto

We construct thermodynamics of the one-dimensional supersymmetric {\it t-J} model with the $ 1/\sin^2$ interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component {\it t-J} model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.

arXiv:cond-mat/9601132•Jan 27, 1996•0 citations

Asymmetry in the Hole-Doped and Electron-Doped t-J Model

P. W. Leung, Kwai-Kong Ng

We model electron-doped high Tc materials using the t-t′-t′′-J model. This model is solved on a cluster with 32 sites using the method of exact diagonalization. Our purpose is to study the symmetry and asymmetry between hole- and electron-doped high Tc materials by comparing the results with those of the t-J model. In the electron-doped model with one charge carrier, we find a strong quasiparticle peak at (π,0). Compared to the t-J model, the bandwidth is larger, reflecting the fact that the charge carrier moves more freely in the electron-doped model. In the two-carrier model the ground state has robust dx2-y2 symmetry. This is in contrary to the two-hole t-J model whose ground state is a competition between low-energy states with dx2-y2 and p symmetries. The spatial distribution function of the carriers shows that they move almost freely on different sublattices.

International Journal of Modern Physics B•Aug 10, 2003•1 citation

On the possibility of fractional statistics in the two-dimensional t-J model at low doping

T. Beck

The purpose of this work is the derivation of an effective field theory for the low-energy magnetic modes of the t-J model on a two-dimensional square lattice and for small values of doping, which is of relevance to the physics of high-temperature superconductors. In particular, we address the possibility of low-energy excitations that obey fractional spin and statistics. For temperatures where kBT is considerably smaller than the magnetic exchange coupling J and for low values of doping, the system is close to an antiferromagnetically ordered Néel state and the spin correlation length takes values significantly larger than the lattice constant a, such that a field theoretic analysis is justified. The effective model is obtained by means of a gradient expansion around the antiferromagnetically ordered reference state. Dimensional analysis shows that in (2+1) dimensions only terms up to order O(a2) in the effective action are relevant to the behaviour at large scales, whereas O(a3)-terms are marginal and higher order terms are irrelevant. Even though marginal, the O(a3)-contributions may drastically influence the properties of excitations, as they might feature a term of topological nature which endows field histories with a statistical phase factor. In fact, all field histories can be characterized as mappings from compactified spacetime, the three-sphere S3, to the order parameter space S2 and thus fall into different homotopy classes. The topological invariant characterizing these homotopy classes is given by the Hopf invariant. Consequently, if the Hopf invariant emerges in the effective field theory, the spin and statistics of low-energy excitations fractionalize. The analysis is based on a path integral representation of the t-J model which was obtained recently by means of Dirac quantization. After introducing a staggered quantization axis, the single occupancy constraint which is inherent to the t-J model can be taken into account exactly. We perform a long-wavelength, low-frequency gradient expansion of the effective action and integrate over the fermionic degrees of freedom as well as the fast-fluctuating bosonic modes. Since our derivation is based on a microscopic model, we obtain an effective action where the doping dependence of the coupling constants is made explicit.

•Jan 1, 2012•0 citations

Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics

Zou Ha

One-dimensional model of nonrelativistic particles with inverse-square interaction potential known as the Calogero-Sutherland model is shown to possess fractional statistics. Using the theory of Jack polynomials the exact dynamical density-density correlation function and the hole propagator part of one-particle Green's function at any rational interaction coupling constant are obtained and used to show clear evidences of the fractional exclusion statistics in the sense of Haldane's "generalized Pauli exclusion principle." This model is also endowed with the corresponding natural exchange statistics.

arXiv:cond-mat/9405063•Physical Review Letters•Sep 19, 1994•188 citations
We show that we can interpret the exact solution of the one-dimensional t-J model in the limit of small J in terms of charge carriers with both exchange (braid) and exclusion (Haldane) statistics with parameter 1/2. We discuss an implementation of the same statistics in the two-dimensional t-J model, emphasizing similarities and differences with respect to one dimension. In both cases, the exclusion statistics is a consequence of the no-double occupation constraint. We argue that the application of this formalism to hole-doped high Tc cuprates and the derived composite nature of the hole give a hint to grasp many unusual properties of these materials.
We show that in the $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ spin-charge gauge approach we developed earlier one can attribute consistently an exclusion statistics with parameter 1/2 to the spinless charge carriers of the $t\text{\ensuremath{-}}J$ model in two dimensions, as it occurs in one dimension. Like the one-dimensional case, the no-double occupation constraint is at the origin of this fractional exclusion statistics. With this statistics we recover a large Fermi volume of holes at high dopings, close to that of the tight binding approximation. Furthermore, the composite nature of the hole, made of charge and spin carriers only weakly bounded, can provide a natural explanation of many unusual experimental features of the hole-doped cuprates.
We construct thermodynamics of the one-dimensional supersymmetric t-J model with the 1/sin 2 interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component t-J model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.
We construct thermodynamics of the one-dimensional supersymmetric {\it t-J} model with the $ 1/\sin^2$ interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component {\it t-J} model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.
We model electron-doped high Tc materials using the t-t′-t′′-J model. This model is solved on a cluster with 32 sites using the method of exact diagonalization. Our purpose is to study the symmetry and asymmetry between hole- and electron-doped high Tc materials by comparing the results with those of the t-J model. In the electron-doped model with one charge carrier, we find a strong quasiparticle peak at (π,0). Compared to the t-J model, the bandwidth is larger, reflecting the fact that the charge carrier moves more freely in the electron-doped model. In the two-carrier model the ground state has robust dx2-y2 symmetry. This is in contrary to the two-hole t-J model whose ground state is a competition between low-energy states with dx2-y2 and p symmetries. The spatial distribution function of the carriers shows that they move almost freely on different sublattices.
The purpose of this work is the derivation of an effective field theory for the low-energy magnetic modes of the t-J model on a two-dimensional square lattice and for small values of doping, which is of relevance to the physics of high-temperature superconductors. In particular, we address the possibility of low-energy excitations that obey fractional spin and statistics. For temperatures where kBT is considerably smaller than the magnetic exchange coupling J and for low values of doping, the system is close to an antiferromagnetically ordered Néel state and the spin correlation length takes values significantly larger than the lattice constant a, such that a field theoretic analysis is justified. The effective model is obtained by means of a gradient expansion around the antiferromagnetically ordered reference state. Dimensional analysis shows that in (2+1) dimensions only terms up to order O(a2) in the effective action are relevant to the behaviour at large scales, whereas O(a3)-terms are marginal and higher order terms are irrelevant. Even though marginal, the O(a3)-contributions may drastically influence the properties of excitations, as they might feature a term of topological nature which endows field histories with a statistical phase factor. In fact, all field histories can be characterized as mappings from compactified spacetime, the three-sphere S3, to the order parameter space S2 and thus fall into different homotopy classes. The topological invariant characterizing these homotopy classes is given by the Hopf invariant. Consequently, if the Hopf invariant emerges in the effective field theory, the spin and statistics of low-energy excitations fractionalize. The analysis is based on a path integral representation of the t-J model which was obtained recently by means of Dirac quantization. After introducing a staggered quantization axis, the single occupancy constraint which is inherent to the t-J model can be taken into account exactly. We perform a long-wavelength, low-frequency gradient expansion of the effective action and integrate over the fermionic degrees of freedom as well as the fast-fluctuating bosonic modes. Since our derivation is based on a microscopic model, we obtain an effective action where the doping dependence of the coupling constants is made explicit.
One-dimensional model of nonrelativistic particles with inverse-square interaction potential known as the Calogero-Sutherland model is shown to possess fractional statistics. Using the theory of Jack polynomials the exact dynamical density-density correlation function and the hole propagator part of one-particle Green's function at any rational interaction coupling constant are obtained and used to show clear evidences of the fractional exclusion statistics in the sense of Haldane's "generalized Pauli exclusion principle." This model is also endowed with the corresponding natural exchange statistics.