Interaction and thermodynamics of spinons in theXXchain

Abstract

Abstract. The mapping between the fermion and spinon compositions of eigenstates in the one-dimensional spin-1/2 XX model on a lattice with N sites is used to describe the spinon interaction from two different perspectives: (i) For finite N the energy of all eigenstates is expressed as a function of spinon momenta and spinon spins, which, in turn, are solutions of a set of Bethe ansatz equations. The latter are the basis of an exact thermodynamic analysis in the spinon representation of the XX model. (ii) For N → ∞ the energy per site of spinon configurations involving any number of spinon orbitals is expressed as a function of reduced variables representing momentum, filling, and magnetization of each orbital. The spins of spinons in a single orbital are found to be coupled in a manner well described by an Ising-like equivalent-neighbor interaction, switching from ferromagnetic to antiferromagnetic as the filling exceeds a critical level. Comparisons are made with results for the Haldane-Shastry model.

Quasiparticles in the XXZ model

“…(i) Consider the vertical lines dividing the space of the I 1 α into two domains, the inside and the outside, the latter wrapping around at ±N/2. (ii) Every I figure 6 establishes the much needed link between spinon motif of the fermion representation at ∆ = 0 introduced in [13,14] and the spinon motif of the string representation at ∆ = 1 introduced in figure 5. Unlike the solitons at ∆ → ∞, the spinons at ∆ = 0 are not free.…”

“…However, neither corrections nor exceptions affect macroscopic systems. In the Ising limit, where the spread of imaginary parts in (14) diverges, all corrections and exceptions disappear even for finite N . A given string solution of (11) with magnetization M z = N/2 − r is described by r rapidities that breaks down into configurations of strings such that the constraint,…”

“…, n m distinguishes different strings of the same size. The string ansatz (14) produces only asymptotic solutions of the BAE (11) for N → ∞. The finite-N corrections are, in general, exponentially small, and not all finite-N solutions fit the string template (14) [7].…”

“…In the Haldane-Shastry model, which has higher symmetry, that coupling is absent and these particular S T -multiplets remain degenerate [27,28]. In the XX model, which has lower symmetry, even the S T -multiplets split up energetically as will be discussed in section 3.3 [14].…”

“…These multiplets split up energetically at ∆ = 1. At ∆ = 0 the energy levels join up in new degenerate configurations, reflecting different symmetries [12][13][14][15][16][17]. A more natural classification scheme for the XX spectrum is then based on string fragments.…”