Elementary excitations of one-dimensional t-J model with inverse-square exchange.

We identify exact excitation content of the intermediate states for the oneparticle Green’s functions, spin-spin and (charge) density-density correlation functions of the periodic one-dimensional t-J model with inverse square exchange. The excitations consist of neutral S = 1/2 spinons and spinless (charge −e) holons with semionic fractional statistics, and bosonic (charge +2e) “anti-holons” which are excitations of the holon condensate. Due to the supersymmetric Yangian quantum symmetry of this model, only the excited states with finite number of elementary excitations contribute to the spectral functions. We find a set of selection rules, and this allows us to map out the regions of non-vanishing spectral weight in the energy-momentum space for the various correlation functions. PACS 05.30-d, 71.10.+x, 71.27.+a Typeset using REVTEX 1 Recently, there have been many developments in understanding the family of CalogeroSutherland models (CSM) which are identified with their peculiar inverse-square exchange (ISE) [1–3,6,8–10,17]. An important feature of these models is that they belong to the same low-energy universality class as the family of Bethe-ansatz solvable models and may provide a new fully soluble paradigm next to the non-interacting models [2]. The one-dimensional supersymmetric ISE t-J model [3] represents a fixed point model where the elementary excitations form an ideal gas obeying fractional statistics. In contrast to this model, the NNE t-J model [4,5], which has essentially the same low energy spectra spanned by the same elementary excitations, obscures the simple low energy structure intrinsic to this class of models. We rediscover the spinons, the holons and the antiholons— the elementary excitations of the NNE t-J model [5]—in the context of the supersymmetric Yangian of the ISE model. Furthermore, we find that only the states with finite number of these elementary excitations contribute to the spectral functions of the one-particle Green’s functions (G), the charge density-density (C) and the spin-spin correlation functions (C). First, we examine the symmetry in the ISE supersymmetric t-J model. The model with periodic boundary conditions possesses, in addition to the global SU(m|n) supersymmetry, a hidden dynamical “quantum group” symmetry algebra called the supersymmetric Yangian [2,6,7]. This symmetry is responsible for the “supermultiplets” in the energy spectrum and the ideal gas-like features of the elementary excitations and, furthermore, provides us with a simple numerical way to identify the exact content of the elementary excitations relevant for the various correlation functions. The supersymmetric generalization of the SU(n) Haldane-Shastry model Hamiltonian [8–10] is given by