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What is the true statistics of holons ?

Didier Poilblanc

par Didier Poilblanc - 7 mai 2008

The exact nature of holons, the charged spinless excitations of the (doped) celebrated RVB state, has been debated over the last two decades. In particular, their statistics (do they behave as fermions or bosons) was still controversial. Earlier work based on a variational RVB wavefunction by Read and Chakraborty (1989) suggested that hole excitations are (weakly interacting) fermions. Such a conclusion, although only justified for small enough kinetic energy, was reproduced in the context of the doped Quantum Dimer Model (QDM) introduced later on by Kivelson. Furthermore, it was argued that the holon statistics should in fact be dictated by energetics considerations and that, under some circonstancies, a holon could bind to a “vortex”, leading to a bosonic composite. "Modern" Z2 gauge theories have recently brought powerful new tools to describe such phenomena.

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Phase diagram

Phase diagram of the "non-Frobenius" doped Quantum Dimer Model studied in this work, compared to the one of the monomer-doped ("Frobenius" case) QDM studied previously in PRL 99, 127202 (2007).

Such ideas have been formulated on the basis of a microscopic model by one of us (D. P.). A "non-Frobenius" doped QDM is introduced in such a way that the original Fermi statistics of the electrons is preserved. Despites its complexity (in contrast to previously monomer-doped QDM this model suffers from the well-known "minus sign" problem) small cluster calculations have revealed a rich phase diagram : a d-wave hole-pair unconventional superconductor appears at small enough doping and a bosonic superfluid is stable at large doping. The hole kinetic energy is shown to favor binding of topological defects to the bare fermionic holons turning them into bosons, in agreement with earlier qualittive arguments based on RVB wave-functions.

Post-scriptum :

Details and references are given in the corresponding paper "Properties of holons in the Quantum Dimer Models" published in :

D. Poilblanc, Physical Review Letters 100, 157206 (2008).