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arXiv:cond-mat/9805232

Non-abelian Electrons

Peter Bouwknegt, Kareljan Schoutens

Published May 19, 1998• 1 citation
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Abstract

We analyze critical and massive SO(5) superspin regimes for correlated electrons on a two-chain ladder. We identify fundamental low energy excitations, which carry the quantum numbers of a free electron, and can be probed in (inverse) photo-emission experiments. These excitations do not obey the usual Pauli Principle, but are governed by specific forms of so-called non-abelian exclusion statistics.

DOI
10.48550/arxiv.cond-mat/9805232

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We analyze critical and massive SO(5) superspin regimes for correlated electrons on a two-chain ladder. We identify fundamental low energy excitations, which carry the quantum numbers of a free electron, and can be probed in (inverse) photo-emission experiments. These excitations do not obey the usual Pauli Principle, but are governed by specific forms of so-called non-abelian exclusion statistics.
We determine the exclusion statistics properties of the fundamental edge quasiparticles over a specific $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}$ non-Abelian quantum Hall state known as the q=2q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2q=2 Pfaffian state. The fundamental excitations are the edge electrons of charge $\ensuremath{-}e$ and the edge quasiholes of charge +e/4+e/4+e/4. We explicitly determine thermodynamic distribution functions and establish a duality which generalizes the duality for fractional exclusion statistics as described by F. D. M. Haldane.
The Hubbard Hamiltonian on a two-leg ladder is studied numerically using quantum Monte Carlo and Exact Diagonalization techniques. A rung interaction, VVV, is turned on such that the resulting model has an exact SO(5) symmetry when V=−UV=-UV=−U. The evolution of the low energy excitation spectrum is presented from the pure Hubbard ladder to the SO(5) ladder. It is shown that the low energy excitations in the pure Hubbard ladder have an approximate SO(5) symmetry.
We study a system of two Tomonaga-Luttinger models coupled by a small transverse hopping (a two-chain ladder). We use Abelian and non-Abelian bosonisation to show that the strong coupling regime at low energies can be described by an SO(5)1_11​ WZW model (or equivalently 5 massless Majorana fermions) deformed by symmetry breaking terms that nonetheless leave the theory critical at T=0. The SO(5) currents of the theory comprise the charge and spin currents and linear combinations of the so-called pi operators (S.C. Zhang, Science 275, 1089 (1997)) which are local in terms both of the original fermions and those of the effective theory. Using bosonisation we obtain the asymptotic behaviour of all correlation functions. We find that the 5 component ``superspin'' vector has power law correlations at T=0; other fermion bilinears have exponentially decaying correlations and the corresponding tendencies are suppressed. Conformal field theory also allows us to obtain the energies, quantum numbers, and degeneracies of the low-lying states and fit them into deformed SO(5) multiplets.