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

Abstract

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 inversesquare 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 HaldaneShastry model. Comparison is made with dynamics of the nearest-neighbor supersymmetric t-J model. KEYWORDS: dynamical spin structure factor, dynamical charge structure factor, single-particle spectral function, t-J model, supersymmetry, inverse-square interaction, nearest-neighbor interaction, exact diagonalization, recursion method §1. IntroductionOne-dimensional (1D) electron systems show strong quantum fluctuations, and have been investigated intensively both theoretically and experimentally. Most of real quasi-1D systems have localized electrons and are regarded as spin systems. Recently some systems with doped holes have also been studied experimentally. For example, Yb 4 As 3 has a small number of carriers, and shows a heavy-fermion behavior in resistivity, magnetic susceptibility and specific heat.1) The spin dynamics in Yb 4 As 3 probed at low temperature suggests that the nature of low-energy spin excitations is similar to that of the 1D antiferromagnetic Heisenberg model.2, 3) On the other hand, a compound Sr 14 Cu 24 O 41 consists of two-leg Cu 2 O 3 ladders and edge-sharing CuO 2 chains. The number of holes in the chain is estimated to be 60% of the number of Cu ions. 4) One may ask how the existence of holes affects dynamical properties of quasi-1D systems. In the presence of both spin and charge degrees of freedom, one can expect much richer physics as compared with spin-only systems.Recent angle-resolved photoemission measurements have revealed the existence of spin-charge separation in quasi-1D systems. In Mott insulators such as SrCuO 2 5, 6)and Sr 2 CuO 3 , 7) angle-resolved photoemission data show two distinct dispersions in the energy-momentum space. One is assigned to the holon band, and the other is regarded as the spinon band. This is an indication of the spin-charge separation. More recently, an angleresolved photoemission study on PrBa 2 Cu 3 O 7 has been performed.8) Signals from the doped CuO 3 chain re- * E-mail: saiga@ginnan.issp.u-tokyo.ac.jp veal the spinon and holon bands in the range of momenta from 0 to π/4 in units of the reciprocal lattice parameter. This indicates that the CuO 3 chain is nearly quarter-filled. In order to investigate theoretically dynamics of these systems with holes, one can take the 1D t-J model 9, 10)...

Supersymmetric t-J models with long-range interactions: partition function and spectrum

“…This yields an exhaustive description of the spectrum in the subspaces with well-defined magnon content in terms of suitably restricted bond configurations of the equivalent vertex model, which are closely connected with supersymmetric versions of Haldane's motifs and their related skew Young tableaux. For the particular case m = 2, this description provides a rigorous proof of a long-standing conjecture by Saiga and Kuramoto [21] based on numerical evidence.…”

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

“…( 4) are changed to 0 < q i < k F,↓ for i = 1 and 2. From comparison with numerical results [10,12], we find that a similar fact occurs also in the N (Q, ω). Namely, although analytic derivation of N (Q, ω) is restricted to the region 0 < Q < k F,↓ , the expression of the (right-moving) two-holon plus one-antiholon contribution can be extended to the integration range shown in Eq.…”

“…In the absence of magnetic field (h = 0), the dynamical spin structure factor was exactly obtained at n = 1 [7,8,9]. It was numerically demonstrated that the weight of the dynamical spin structure factor in the t-J model does not depend on n in the region where only two spinons contribute [10]. This is an indication of the strong spin-charge separation in dynamics.…”

Exact electron addition spectrum in 1D supersymmetric t–J model with interaction

“…We have checked the validity of Eqs. ( 16) and (18) by comparison with numerical results up to N = 16 [21]. In the special case ν = (0 N h ), momenta of the holon and the antiholon are both zero, and we obtain a form different from Eq.…”