Finite temperature hole dynamics in the t − J model : exact results for high dimensions

Finite temperature hole dynamics in the t−J model: exact results for high dimensions PACS. 71.10.Fd – Lattice fermion models (Hubbard model, etc.). Abstract. – We discuss the dynamics of a single hole in the t−J model at finite temperature, in the limit of large spatial dimensions. The problem is shown to yield a simple and physically transparent solution, that exemplifies the continuous thermal evolution of the underlying string picture from the T = 0 string-pinned limit through to the paramagnetic phase. Following early pioneering work [1,2], and given added impetus by the discovery of high-T c superconductivity, the study of single-particle excitations in magnetic insulators remains highly topical. At possibly its simplest, the dynamics of a single hole in an antiferromagnet (AF) is captured by the t − J model [3], itself the strong coupling limit of the Hubbard model and a paradigm for the physics of strong, local electron correlations: hole motion, with nearest neighbour (NN) hopping amplitude t, occurs in a restricted subspace of no doubly occupied sites, and in a background of AF coupled spins with NN exchange couplings J = 4t 2 /U. The string picture (see e.g. [4,5]), wherein the hole is pinned by the string of upturned spins its motion creates, has proven central in understanding the t−J model at T = 0: since spins in the resultant string are flipped relative to the Néel configuration, resulting for J > 0 in energetically unfavourable exchange fields that generate a potential growing linearly with distance from its point of creation, the hole is thereby confined. And while string unwinding, and hence a finite hole mobility, is in general induced both by spin-flip interactions and Trugman loop motion [6], the underlying picture is robust even in d = 2 dimensions (see e.g.[5]). The limit of large spatial dimensions, d = ∞, has also proven highly fruitful in study of the t−J model [7-11]. Here the string picture has been shown to be exact, and the model solved at T = 0 [7,8]; the additional roles of disorder [8], and of second NN hopping [9], have also been investigated. Moreover, in addition to providing exact solutions, the d ∞ limit serves as a starting point for 1/d expansions, enabling a systematic approach to the finite-d case. Given the success and utility of the large-d approach, we use it here to investigate another key element of hole dynamics …