Using the Bethe-Ansatz technique, we diagonalize exactly the one-dimensional t-J Hamiltonian for the supersymmetric case t=J. In this limit it is identical with models considered previously by Sutherland and by Schlottmann. The ground state is a liquid of singlet pairs of varying spatial separation for all band fillings. We find two types of gapless excitations with effective Fermi surfaces at 2 ${\mathit{k}}_{\mathit{F}}$ and ${\mathit{k}}_{\mathit{F}}$ which we identify with the holon and the spinon excitations near half filling.Using the Bethe-Ansatz technique, we diagonalize exactly the one-dimensional t-J Hamiltonian for the supersymmetric case t=J. In this limit it is identical with models considered previously by Sutherland and by Schlottmann. The ground state is a liquid of singlet pairs of varying spatial separation for all band fillings. We find two types of gapless excitations with effective Fermi surfaces at 2${\mathit{k}}_{\mathit{F}}$ and ${\mathit{k}}_{\mathit{F}}$ which we identify with the holon and the spinon excitations near half filling.

Physical Review LettersMay 21, 1990193 citations

Exact solution of thet-Jmodel in one dimension at 2t=±J: Ground state and excitation spectrum

P.-A. Bares, G. Blatter, Masao Ogata

The one dimensional t-J Hamiltonian is diagonalized exactly for the supersymmetric case 2t=\ifmmode\pm\else\textpm\fi{}J using the Bethe ansatz. In this limit it is identical with models previously considered by Lai, Sutherland, and Schlottmann. In the present paper we discuss the ground-state properties and excitation spectrum in zero magnetic field. The ground state is a liquid of singlet bonds with varying spatial separation. Its most remarkable feature is the presence of bonds connecting particles at arbitrarily large distances. The ground-state energy is an analytic function of the band filling. There is no difference in the chemical potential for adding one or two particles and no evidence for the binding of holes. The low-lying part of the spectrum consists of two types of gapless excitations (charge and spin) with effective Fermi surfaces at 2 ${\mathit{k}}_{\mathit{F}}$ and ${\mathit{k}}_{\mathit{F}}$ , respectively. An interpretation of the energy spectrum in terms of spinons and holons is appropriate at low energies.The one dimensional t-J Hamiltonian is diagonalized exactly for the supersymmetric case 2t=\ifmmode\pm\else\textpm\fi{}J using the Bethe ansatz. In this limit it is identical with models previously considered by Lai, Sutherland, and Schlottmann. In the present paper we discuss the ground-state properties and excitation spectrum in zero magnetic field. The ground state is a liquid of singlet bonds with varying spatial separation. Its most remarkable feature is the presence of bonds connecting particles at arbitrarily large distances. The ground-state energy is an analytic function of the band filling. There is no difference in the chemical potential for adding one or two particles and no evidence for the binding of holes. The low-lying part of the spectrum consists of two types of gapless excitations (charge and spin) with effective Fermi surfaces at 2${\mathit{k}}_{\mathit{F}}$ and ${\mathit{k}}_{\mathit{F}}$, respectively. An interpretation of the energy spectrum in terms of spinons and holons is appropriate at low energies.

Physical review. B, Condensed matterJul 1, 1991182 citations

Intertwined spin and charge dynamics in one-dimensional supersymmetric t-J model

Yunjing Gao, Jianda Wu

Following the Bethe ansatz we determine the dynamical spectra of the one-dimensional supersymmetric t-J model. A series of fractionalized excitations are identified through two sets of Bethe numbers. Typical patterns in each set are found to yield wavefunctions containing elementary spin and charge carriers, manifested as distinct boundaries of the collective excitations in the spectra of single electron Green functions. In spin channels, gapless excitations fractionalized into two spin and a pair of postive and negative charge carriers, extending to finite energy as multiple continua. These patterns connect to the half-filling limit where only fractionalized spinons survive. In particle density channel, apart from spin-charge fractionalization, excitations involving only charge fluctuations are observed. Furthermore, nontrivial Bethe strings encoding bound state structure appear in channels of reducing or conserving magnetization, where spin and charge constituents can also be identified. These string states contribute significantly even to the low-energy sector in the limit of vanishing magnetization.Following the Bethe ansatz we determine the dynamical spectra of the one-dimensional supersymmetric t-J model. A series of fractionalized excitations are identified through two sets of Bethe numbers. Typical patterns in each set are found to yield wavefunctions containing elementary spin and charge carriers, manifested as distinct boundaries of the collective excitations in the spectra of single electron Green functions. In spin channels, gapless excitations fractionalized into two spin and a pair of postive and negative charge carriers, extending to finite energy as multiple continua. These patterns connect to the half-filling limit where only fractionalized spinons survive. In particle density channel, apart from spin-charge fractionalization, excitations involving only charge fluctuations are observed. Furthermore, nontrivial Bethe strings encoding bound state structure appear in channels of reducing or conserving magnetization, where spin and charge constituents can also be identified. These string states contribute significantly even to the low-energy sector in the limit of vanishing magnetization.

arXiv:2603.24453Mar 25, 20260 citations

Ground state properties and excitation spectrum of the degenerate supersymmetric t-J model in one dimension

P. Schlottmann

The authors considers the one-dimensional SU(N)-invariant t-J model which consists of electrons with N spin components on a lattice with nearest-neighbour hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighbouring lattice sites. The model is integrable at the supersymmetric point t=J. The ground state Bethe ansatz equations are analysed and solved numerically for arbitrary band filling and several values of N. The ground state energy, the chemical potential and the spin susceptibility are obtained as a function of band filling. The elemental charge and spin excitations are derived for arbitrary N and band filling. The energy of the charge excitations vanishes at the Fermi surface. The Fermi velocity has a maximum as a function of band filling, vanishing for the empty and full bands. The spinwave velocity is inversely proportional to the susceptibility. For exactly one electron per site the charge fluctuations are suppressed and the Bethe ansatz equations map onto those of the SU(N)-invariant Heisenberg chain.The authors considers the one-dimensional SU(N)-invariant t-J model which consists of electrons with N spin components on a lattice with nearest-neighbour hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighbouring lattice sites. The model is integrable at the supersymmetric point t=J. The ground state Bethe ansatz equations are analysed and solved numerically for arbitrary band filling and several values of N. The ground state energy, the chemical potential and the spin susceptibility are obtained as a function of band filling. The elemental charge and spin excitations are derived for arbitrary N and band filling. The energy of the charge excitations vanishes at the Fermi surface. The Fermi velocity has a maximum as a function of band filling, vanishing for the empty and full bands. The spinwave velocity is inversely proportional to the susceptibility. For exactly one electron per site the charge fluctuations are suppressed and the Bethe ansatz equations map onto those of the SU(N)-invariant Heisenberg chain.

Journal of Physics Condensed MatterJan 18, 19939 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.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/0009075Journal of the Physical Society of JapanDec 15, 20002 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.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/9907215Journal of the Physical Society of JapanNov 15, 199911 citations

{\mathit{k}}_{\mathit{F}}

and

{\mathit{k}}_{\mathit{F}}

which we identify with the holon and the spinon excitations near half filling.

{\mathit{k}}_{\mathit{F}}

and

{\mathit{k}}_{\mathit{F}}

which we identify with the holon and the spinon excitations near half filling.

{\mathit{k}}_{\mathit{F}}

and

{\mathit{k}}_{\mathit{F}}

, respectively. An interpretation of the energy spectrum in terms of spinons and holons is appropriate at low energies.