Electron Addition Spectrum in the Supersymmetrict−JModel with Inverse-Square Interaction

Abstract

The electron addition spectrum A + (k, ω) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r 2 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, ω) 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, ω) in the (k, ω) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.71.10. Pm, 75.10.Jm, The concept of spinons and holons, both of which obey the fractional statistics [1], has turned out to be useful in approaching to 1D electron systems. In terms of these quasi-particles one can inquire into not only the low-energy and low-wavelength limit, but the global feature of the dynamics. Hence special interest has been cherished in the global dynamics from both theoretical and experimental points of view. For example, angle resolved photoemission [2] has revealed some evidence of the spin-charge separation by resolution of holon and spinon contributions. On the theoretical side, numerical studies have been performed for the 1D t-J model for a small number of lattice sites [3] and some structures have been ascribed to spinons and holons. For deeper understanding of the overall dynamics, demand is growing for analytic theory which can go to the thermodynamic limit. Partly analytic theory is available for the single-particle spectral functions of the t-J model in the J → 0 limit [4]. A notable feature is that a satellite band is observed whose intensity is comparable to that of the main band. It is natural to ask how the finite J influences the dynamics.In the supersymmetric t-J model with 1/r 2 interaction [5], spinons and holons appear in the simplest manner. In fact exact thermodynamics for the model [6] can be interpreted in terms of free spinons and holons. Ha and Haldane [7] analyzed numerical results for dynamics in finite-sized systems, and found that only a few number of elementary excitations contribute to spectral functions. They proposed a momentum-frequency region where each spectral function takes nonzero values in the thermodynamic limit, but they did not obtain the spectral functions themselves. Recently, exact results have been derived for a particular component [8], and for a particular momentum range of the spectral weight [9].In this paper we report on the analytical result of the electron addition spectrum for the t-J model at zero temperature. The electron addition spectral function is relevant to the angle resolved inverse photoemission spectroscopy. Our result constitutes the first analytical knowledge for dynamical quantities of lattice electrons with no restriction on the system size, the density and the momentum-frequency range. Although we cannot provide the formal proof for the exactness, the analy...

Low energy properties of the supersymmetric Haldane–Shastry spin chain

“…(5.2) have been studied in Refs. [14] and [15] respectively. However, a chemical potential was implicitly introduced in those papers in order to consider ground states with a non-zero filling of the fermions.…”

“…Such supersymmetric spin chains play a role in describing some correlated systems in condensed matter physics, where holes moving in the dynamical background of spins behave as bosons, and spin-1/2 electrons behave as fermions [13,14,15]. The SU(m|n) supersymmetric HS spin chain exhibits the Y (gl (m|n) ) superYangian symmetry [3]; this is also the quantum group symmetry of the SU(m|n) supersymmetric Polychronakos spin chain.…”

One-electron singular branch lines of the Hubbard chain

“…There is some evidence that the correlation effects described by the 1D Hubbard model might contain such finite-energy mechanisms [1,2]. However, for finite values of the on-site repulsion U very little is known about its finite-energy spectral properties, in contrast to simpler models [3]. Bosonization [4] and conformal-field theory [5] do not apply at finite energy.…”

Finite-temperature structure factor in the Haldane–Shastry spin chain

“…The analysis performed at zero temperature could be extented at finite temperature. It would also be interesting to treat the finite-temperature dynamics of other inverse-square interaction models and compare it to their zero-temperature exact result [20,22]. It comes as a simple generalization of the method used in the present paper.…”

“…Our strategy will be to make use of the technology contained in [17] to compute the form factors involved in the spin-spin correlation function needed for the DSSF. This approach has already been used for T = 0 dynamical properties of the Haldane-Shastry spin chain [18,19] and related models (spin Calogero-Sutherland model [20], supersymmetric t − J model [21,22]). The present work is the first to address finite temperature dynamics.…”