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:cond-mat/0102333 · Physical Review Letters

Electron Addition Spectrum in the Supersymmetric t−J Model with Inverse-Square Interaction

Mitsuhiro Arikawa, Yasuhiro Saiga, Yoshio Kuramoto

Published Apr 2, 2001• 32 citations
arXivHTMLPDF

Abstract

The electron addition spectrum A+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r2 interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of A+(k,omega) has a simple analytic form with contributions from one spinon, one holon, and one antiholon-all of which obey fractional statistics. The upper edge of A+(k,omega) in the (k,omega) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.

DOI
10.1103/physrevlett.86.3096

Related papers

Exact Charge Dynamics in the Supersymmetrict-JModel with Inverse-Square Interaction

Mitsuhiro Arikawa, Takashi Yamamoto, Yasuhiro Saiga +1 more

Dynamical charge structure factor $N(Q,ω)$ with $Q$ smaller than the Fermi wave number is derived analytically for the one-dimensional supersymmetric t-J model with $1/r^2$ interaction. Strong spin-charge separation in dynamics is found. $N(Q,ω)$ with given electron density does not depend on the spin polarization for arbitrary size of the system. In the thermodynamic limit, only two holons and one antiholon contribute to $N(Q,ω)$. These results together with generalized ones for the SU($K$,1) supersymmetric t-J model are derived via solution of the Sutherland model in the strong coupling limit.

arXiv:cond-mat/9907139•Journal of the Physical Society of Japan•Dec 15, 1999•12 citations

Dynamical Properties of the One-Dimensional Supersymmetrict-JModel: A View from Elementary Excitations

Yasuhiro Saiga, Yoshio Kuramoto

Dynamical properties, such as dynamical spin and charge structure factors and single-particle spectral functions, are studied for the one-dimensional supersymmetric t-J model with inverse-square interaction. Exact diagonalization and the recursion method are used for finite systems up to 16 sites. A simple rule is proposed to understand the supermultiplet structure in the excitation spectrum. Numerical calculations show that the dynamical spin structure factor is independent of the electron density in the region where only two spinons contribute. In the electron removal spectrum from half-filling, close correspondence is found between the dominant contribution from three-spinon plus one-holon states in the t-J model and the two-spinon excitations in the Haldane-Shastry model. Comparison is made with dynamics of the nearest-neighbor supersymmetric t-J model.

arXiv:cond-mat/9907215•Journal of the Physical Society of Japan•Nov 15, 1999•11 citations

Spinon-Holon Attraction in the Supersymmetric t−J Model with 1/r2 Interaction

Bogdan Andrei Bernevig, Domenico Giuliano, R. B. Laughlin

We derive the coordinate representation of the one-spinon one-holon wave function for the supersymmetric t-J model with 1/r(2) interaction. This result allows us to show that a spinon and a holon attract each other at short distance. The attraction gets stronger as the size of the system is increased and, in the thermodynamic limit, it is responsible for the square-root singularity in the hole spectral function [Y. Kato, Phys. Rev. Lett. 81, 5402 (1998)].

arXiv:cond-mat/0105523•Physical Review Letters•Oct 9, 2001•15 citations

Dynamical Properties of the 1/r2-Type Supersymmetrict-JModel in a Magnetic Field: Manifestation of Spin-Charge Separation

Yasuhiro Saiga, Yoshio Kuramoto

Quasi-particle picture in a magnetic field is pursued for dynamical spin and charge correlation functions of the one-dimensional supersymmetric t-J model with inverse-square interaction. With use of exact diagonalization and the asymptotic Bethe-ansatz equations for finite systems, excitation contents of relevant excited states are identified which are valid in the thermodynamic limit. The excitation contents are composed of spinons, antispinons, holons and antiholons obeying fractional statistics. Both longitudinal and transverse components of the dynamical spin structure factor are independent of the electron density in the region where only quasi-particles with spin degrees of freedom (spinons and antispinons) contribute. The dynamical charge structure factor does not depend on the spin-polarization density in the region where only quasi-particles with charge (holons and antiholons) are excited. These features indicate the strong spin-charge separation in dynamics, reflecting the high symmetry of the model.

arXiv:cond-mat/0009075•Journal of the Physical Society of Japan•Dec 15, 2000•2 citations

Exact spin dynamics of the 1/r2supersymmetrict–Jmodel in a magnetic field

Mitsuhiro Arikawa, Yasuhiro Saiga

The dynamical spin structure factor S zz ( Q , ω) in the small momentum region is derived analytically for the one-dimensional supersymmetric t – J model with 1/ r 2 interaction. Strong spin–charge separation is found in the spin dynamics. The structure factor S zz ( Q , ω) with a given spin polarization does not depend on electron density in the small momentum region. In the thermodynamic limit, only two spinons and one antispinon (magnon) contribute to S zz ( Q , ω). These results are derived via solution of the SU (2,1) Sutherland model in the strong coupling limit.

arXiv:cond-mat/0607444•Journal of Physics A Mathematical and General•Aug 9, 2006•8 citations

Hole Dynamics of the One-Dimensional Supersymmetric t−J Model with a Long-Range Interaction: An Exact Result

Yusuke S. Kato

We obtain an exact result on the single-hole dynamics in one-dimensional Mott-Hubbard insulators through a study of the supersymmetric $t\ensuremath{-}J$ model with long-range interaction at half filling. We calculate the expression ${G}_{1s1h}(x,t)$ for the one-spinon one-holon contribution to the hole propagator, which contributes $75%$ of the total spectral weight. The matrix element is independent of the holon momentum. The spectral weight has an inverse square root singularity along the holon band. Comparison with the hole dynamics of the $U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$ Hubbard model is also made.

Physical Review Letters•Dec 14, 1998•18 citations
The electron addition spectrum A+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r2 interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of A+(k,omega) has a simple analytic form with contributions from one spinon, one holon, and one antiholon-all of which obey fractional statistics. The upper edge of A+(k,omega) in the (k,omega) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.
Dynamical charge structure factor N(Q,ω)N(Q,ω)N(Q,ω) with QQQ smaller than the Fermi wave number is derived analytically for the one-dimensional supersymmetric t-J model with 1/r21/r^21/r2 interaction. Strong spin-charge separation in dynamics is found. N(Q,ω)N(Q,ω)N(Q,ω) with given electron density does not depend on the spin polarization for arbitrary size of the system. In the thermodynamic limit, only two holons and one antiholon contribute to N(Q,ω)N(Q,ω)N(Q,ω). These results together with generalized ones for the SU(KKK,1) supersymmetric t-J model are derived via solution of the Sutherland model in the strong coupling limit.
Dynamical properties, such as dynamical spin and charge structure factors and single-particle spectral functions, are studied for the one-dimensional supersymmetric t-J model with inverse-square interaction. Exact diagonalization and the recursion method are used for finite systems up to 16 sites. A simple rule is proposed to understand the supermultiplet structure in the excitation spectrum. Numerical calculations show that the dynamical spin structure factor is independent of the electron density in the region where only two spinons contribute. In the electron removal spectrum from half-filling, close correspondence is found between the dominant contribution from three-spinon plus one-holon states in the t-J model and the two-spinon excitations in the Haldane-Shastry model. Comparison is made with dynamics of the nearest-neighbor supersymmetric t-J model.
Quasi-particle picture in a magnetic field is pursued for dynamical spin and charge correlation functions of the one-dimensional supersymmetric t-J model with inverse-square interaction. With use of exact diagonalization and the asymptotic Bethe-ansatz equations for finite systems, excitation contents of relevant excited states are identified which are valid in the thermodynamic limit. The excitation contents are composed of spinons, antispinons, holons and antiholons obeying fractional statistics. Both longitudinal and transverse components of the dynamical spin structure factor are independent of the electron density in the region where only quasi-particles with spin degrees of freedom (spinons and antispinons) contribute. The dynamical charge structure factor does not depend on the spin-polarization density in the region where only quasi-particles with charge (holons and antiholons) are excited. These features indicate the strong spin-charge separation in dynamics, reflecting the high symmetry of the model.
The dynamical spin structure factor S zz ( Q , ω) in the small momentum region is derived analytically for the one-dimensional supersymmetric t – J model with 1/ r 2 interaction. Strong spin–charge separation is found in the spin dynamics. The structure factor S zz ( Q , ω) with a given spin polarization does not depend on electron density in the small momentum region. In the thermodynamic limit, only two spinons and one antispinon (magnon) contribute to S zz ( Q , ω). These results are derived via solution of the SU (2,1) Sutherland model in the strong coupling limit.
We obtain an exact result on the single-hole dynamics in one-dimensional Mott-Hubbard insulators through a study of the supersymmetric $t\ensuremath{-}J$ model with long-range interaction at half filling. We calculate the expression G1s1h(x,t){G}_{1s1h}(x,t)G1s1h​(x,t) for the one-spinon one-holon contribution to the hole propagator, which contributes 7575%75 of the total spectral weight. The matrix element is independent of the holon momentum. The spectral weight has an inverse square root singularity along the holon band. Comparison with the hole dynamics of the $U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$ Hubbard model is also made.