Abstract
We show that we can interpret the exact solution of the one-dimensional t-J model in the limit of small J in terms of charge carriers with both exchange (braid) and exclusion (Haldane) statistics with parameter 1/2. We discuss an implementation of the same statistics in the two-dimensional t-J model, emphasizing similarities and differences with respect to one dimension. In both cases, the exclusion statistics is a consequence of the no-double occupation constraint. We argue that the application of this formalism to hole-doped high Tc cuprates and the derived composite nature of the hole give a hint to grasp many unusual properties of these materials.
Highlights
This paper is a brief review of the attempt to assign 1/2 Haldane statistics to the charge carriers of the one- and two-dimensional t-J model, comparing the two cases and arguing that the second case is relevant for the low-energy physics of hole-doped high Tc cuprates
Using the fact that the probability for two brownian paths in R2 to intersect each other at a fixed time is zero, the hard-core condition is not necessary in 2D in the continuum [4]. Another kind of statistics can be defined for quasi-particles in finite-density quantum systems of identical particles: the Haldane’s fractional exclusion statistics, generalizing Pauli exclusion principle for fermions [5]
In this paper, following References [7,8,9], we show that we can attribute consistently both exchange and exclusion statistics 1/2 to the charge carriers of the one- and two- dimensional t-J model
Summary
This paper is a brief review of the attempt to assign 1/2 Haldane statistics to the charge carriers of the one- and two-dimensional t-J model, comparing the two cases and arguing that the second case is relevant for the low-energy physics of hole-doped high Tc cuprates. Using the fact that the probability for two brownian paths in R2 to intersect each other at a fixed time is zero, the hard-core condition is not necessary in 2D in the continuum [4] Another kind of statistics can be defined for quasi-particles in finite-density quantum systems of identical particles: the Haldane’s fractional exclusion statistics, generalizing Pauli exclusion principle for fermions [5]. The most interesting features of this approach applied to the cuprates are the following: First, the holes are composites made of only weakly bound spinless holons, charge carriers with Fermi surface, and spinons, spin carriers without Fermi surface, so that some physical responses dominated by the spinons have a totally non-Fermi liquid character This occurs in spite of the fact that the holes have, in the overdoped region, a Fermi surface satisfying Luttinger theorem, precisely due to the 1/2 Haldane statistics of the holons. Lowering the temperature such gas of vortices undergoes a Kosterlitz-Thouless-like transition, with the formation of a finite density of vortex-antivortex pairs and since the vortices are centered on the charge carriers, this provides a novel topological mechanism of charge-pairing leading to superconductivity [13]
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