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arXiv:cond-mat/9809150 · Europhysics Letters (EPL)

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

David E. Logan, M. P. H Stumpf

Published Jul 15, 1998• 4 citations
arXivHTMLPDF

Abstract

We discuss the dynamics of a single hole in 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.

DOI
10.1209/epl/i1998-00341-6

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We discuss the dynamics of a single hole in 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.
We investigate the t-J model including local disorder for a hole in an antiferromagnetic spin background on a hypercubic lattice in d dimensions. We show that the well-known approximation of a linear potential, caused by the Ising term of the spin-spin interaction, is correct up to order 1/d2{\mathit{d}}^{2}d2 and hence becomes exact in d=\ensuremath{\infty}. We also investigate the influence of disorder and compute exactly the Green function and the density of states for a hole in an antiferromagnetic spin background for arbitrary disorder and J in the limit d\ensuremath{\rightarrow}\ensuremath{\infty}. Moreover, for finite J and disorder we determine the dynamical conductivity in high dimensions exactly. Remarkable structure both in the density of states and in the dynamical conductivity is found. Finally, we systematically derive the retraceable path approximation by Brinkman and Rice via a self-consistent 1/d expansion, which is correct up to order 1/d4{\mathit{d}}^{4}d4.
The motion of a single hole in an arbitrary magnetic background is investigated for the two-dimensional $t\ensuremath{-}J$ model. The wave function of the hole is described within a generalized string picture which leads to a modified concept of spin polarons. We calculate the one-hole spectral function using a large-string basis for the limits of a N\'eel ordered and a completely disordered background. In addition we use a simple approximation to interpolate between these cases. For the antiferromagnetic background we reproduce the well-known quasiparticle band. In the disordered case the shape of the spectral function is found to be strongly momentum dependent, the quasiparticle weight vanishes for all hole momenta. Finally, we discuss the relevance of results for the lowest energy eigenvalue and its dispersion obtained from calculations using a polaron of minimal size as found in the literature.
Abstract The dynamics of a hole motion in a quantum antiferromagnet has been studied in the past three decades because of its relationship to models related to superconductivity in cuprates. The same problem has received significant attention because of its connection to very recent experiments of the dynamics of ultra-cold atoms in optical lattices where models of strongly correlated electrons can be simulated. In this paper we apply the diagrammatic Monte Carlo method to calculate the single-hole Green’s function in the t–J model, where the J term is linearized, in a wide range of imaginary-time with the aim to examine the polaron formation and in particular the details of the contribution of the so-called string excitations found in such recent experiments. We calculate the single-hole spectral function by analytic continuation from imaginary to real time and study the various aspects that constitute the string picture, such as, the energy–momentum dependence of the main quasiparticle peak and its residue, the internal excitations of the string which appear as multiple peaks in the spectral function as well as their momentum dependence. We find that the earlier analysis of the spectral function based on a mobile-hole connected with a string of overturn spins and the contribution of the internal string excitations as obtained from the non-crossing approximation is accurate.
This chapter turns to the O( N ) quantum rotor studied earlier in Chapter 6. We extend the earlier results to T > 0 aided by an exact solution obtained in the N → ∞ limit. The quantum Ising model studied in Chapter 10 had a discrete Z 2 symmetry. An important new ingredient in the rotor models is the presence of a continuous symmetry: the physics is invariant under a uniform, global O( N ) transformation on the orientation of the rotors, which is broken in the magnetically ordered state. Thus we have to use ideas on the spin stiffness which were introduced in Chapter 8. Apart from this, much of the technology and the physical ideas introduced earlier for the d = 1 Ising chain generalize straightforwardly, although we are no longer able to obtain exact results for crossover functions at finite N . The characterization of the physics in terms of three regions separated by smooth crossovers, the high- T and the two low- T regions on either side of the quantum critical point, continues to be extremely useful and is again the basis of our discussion. Because we consider models in spatial dimensions d > 1, it is possible to have a thermodynamic phase transition at a nonzero temperature, as in Fig. 1.2b. We are particularly interested in the interplay between the critical singularities of the finite-temperature transition and those of the quantum critical point.