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Physical review. B, Solid state

Quantum solitons in one-dimensional conductors

Alan H. Luther

Published Jan 1, 1977• 55 citations
Publisher

Abstract

The excitation spectrum in several models of the one-dimensional electron gas is calculated. The models studied are the backward scattering model, charge transfer model, and strong-coupling spinless fermion model, with no restrictions on the interaction strengths. All can exhibit new types of elementary excitations which are identified as quantum solitons and bound solitons. These excitations can participate in transport, and are exponentially activated at low temperatures. The gap energy is calculated for arbitrary coupling strengths in the various models, using a procedure which exactly solves the quantum sine-Gordon equation in one dimension.

DOI
10.1103/physrevb.15.403

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Backward Scattering in the One-Dimensional Electron Gas

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Physical Review Letters•Sep 2, 1974•749 citations
The excitation spectrum in several models of the one-dimensional electron gas is calculated. The models studied are the backward scattering model, charge transfer model, and strong-coupling spinless fermion model, with no restrictions on the interaction strengths. All can exhibit new types of elementary excitations which are identified as quantum solitons and bound solitons. These excitations can participate in transport, and are exponentially activated at low temperatures. The gap energy is calculated for arbitrary coupling strengths in the various models, using a procedure which exactly solves the quantum sine-Gordon equation in one dimension.
The energy spectrum of the one-dimensional Fermi gas and the one-particle Green's functions are calculated within the one-body (soliton) approximation by perturbation expansion from the particular limit solved by Luther and Emery. Fermion properties, in particular the Ward identity, of the Luttinger model are explicitly used to calculate the backward scattering amplitude. The gap in the excitation spectrum is in agreement with the results of other authors. At nonzero temperature the quasiparticles have a lifetime. As a consequence, for instance, the specific heat at low temperatures is linear in TTT and not exponentially activated.
The excitation spectrum of massive fermions with self-interaction moving in one space dimension is calculated, using exact solutions for the spin-1/2 chain problem. This spectrum is shown to be the same as in the massive Thirring model, sine-Gordon equation, and Tomonaga-Luttinger with gap, with suitable relations between coupling constants. Solitons and bound solitons occur, corresponding to magnons and bound magnons in the spin chain. The soliton mass is calculated as a function of lattice spacing, and the ratio of binding energy to soliton mass is shown to be given correctly by the WKB approximation.
The energy spectrum of the one-dimensional electron gas, solved by Luther and Emery for a particular attractive interaction strength UUU of the backward scattering across the Fermi surface, has been calculated for small deviations from this particular limit. The energy spectrum shows a gap at the Fermi energy, whose magnitude is very sensitive to the interaction UUU. The density of states shows a gap at zero temperature, which is smeared out by the quasiparticle lifetime for $T\ensuremath{\ne}0$.