Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Solid state

Eigenvalue spectrum of interacting massive fermions in one dimension

Alan H. Luther

Published Sep 1, 1976• 310 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.14.2153

Related papers

Quantum solitons in one-dimensional conductors

Alan H. Luther

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.

Physical review. B, Solid state•Jan 1, 1977•55 citations

Interacting fermions in one dimension: The Tomonaga-Luttinger model

Kurt Schönhammer

The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low energy spectrum of noniteracting fermions is identical to the one of a harmonic chain. This fermion-boson transmutation allows to describe interacting fermions as a system of coupled oscillators. Tomonaga's model of interacting nonrelativistic fermions on a ring is presented and first discussed in low order perturbation theory. After introducing the concept of two independent species of right and left moving fermions the exact solution of the Tomonaga-Luttinger model is discussed in detail. The momentum distribution and spectral functions are calculated using the method of the bosonization of the field operator. The general Luttinger liquid phenomenology is shortly discussed.

arXiv:cond-mat/9710330•Oct 30, 1997•12 citations

Solitons and magnons in quantum spin chains

M. W. Puga, H Beck

The z-component dynamical spin correlation function S zz (q,w) of the s= 1 / 2 anisotropic XY chain is calculated exactly in the fermion representation. S zz consists of two parts: one (S m ) represents two fermion excitations and the other (S s ) describes scattering from thermally excited fermions. In the continuum limit, S s has the structure of the solitonic part of a classical sine-Gordon correlation function, but the soliton form factor is modified by quantum effects. S m has similarities with the spin-wave continuum form of S zz an isotropic spin chains. The continuum results are compared with those for a discrete chain.

Journal of Physics C Solid State Physics•Apr 20, 1982•16 citations

Interacting Fermions in One Dimension. II. Attractive Potential

James McGuire

The exact energies and wavefunctions for a system of (N − 1) one-dimensional fermions all of the same spin and one fermion of the opposite spin are calculated in the large volume, finite density limit, when the particles interact via an attractive delta function potential. It is found that the attractive potential gives rise to a bound state, but, in spite of the presence of this bound state, all of the physical properties which are calculated (ground-state energy, effective mass of a certain class of excitations, etc.) are analytic continuations in the coupling constant of the corresponding results in the repulsive case. In addition, it is possible to have eigenstates which do not have the bound state present. These excited states are also discussed and are found to exhibit a negative effective mass and to modify the particle density at very large distances from the different particle.

Journal of Mathematical Physics•Jan 1, 1966•160 citations

The Luttinger liquid concept for interacting electrons in one dimension

K Sch nhammer

The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low-energy spectrum of noninteracting fermions is identical to the one for a harmonic chain. This allows us to describe interacting fermions as a system of coupled oscillators. The exact solution of the Tomonaga–Luttinger model is discussed and results for the momentum distribution and spectral functions are presented. The general Luttinger liquid phenomenology is briefly discussed and various attempts at the experimental verification of the theoretical predictions are examined. Extended defects in semiconductors might also be candidate systems.

Journal of Physics Condensed Matter•Nov 22, 2002•21 citations

The Luttinger liquid concept for interacting electrons in one dimension

Kurt Schönhammer

The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low-energy spectrum of noninteracting fermions is identical to the one for a harmonic chain. This allows us to describe interacting fermions as a system of coupled oscillators. The exact solution of the Tomonaga-Luttinger model is discussed and results for the momentum distribution and spectral functions are presented. The general Luttinger liquid phenomenology is briefly discussed and various attempts at the experimental verification of the theoretical predictions are examined. Extended defects in semiconductors might also be candidate systems.

•Jan 1, 2002•0 citations
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 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 theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low energy spectrum of noniteracting fermions is identical to the one of a harmonic chain. This fermion-boson transmutation allows to describe interacting fermions as a system of coupled oscillators. Tomonaga's model of interacting nonrelativistic fermions on a ring is presented and first discussed in low order perturbation theory. After introducing the concept of two independent species of right and left moving fermions the exact solution of the Tomonaga-Luttinger model is discussed in detail. The momentum distribution and spectral functions are calculated using the method of the bosonization of the field operator. The general Luttinger liquid phenomenology is shortly discussed.
The z-component dynamical spin correlation function S zz (q,w) of the s= 1 / 2 anisotropic XY chain is calculated exactly in the fermion representation. S zz consists of two parts: one (S m ) represents two fermion excitations and the other (S s ) describes scattering from thermally excited fermions. In the continuum limit, S s has the structure of the solitonic part of a classical sine-Gordon correlation function, but the soliton form factor is modified by quantum effects. S m has similarities with the spin-wave continuum form of S zz an isotropic spin chains. The continuum results are compared with those for a discrete chain.
The exact energies and wavefunctions for a system of (N − 1) one-dimensional fermions all of the same spin and one fermion of the opposite spin are calculated in the large volume, finite density limit, when the particles interact via an attractive delta function potential. It is found that the attractive potential gives rise to a bound state, but, in spite of the presence of this bound state, all of the physical properties which are calculated (ground-state energy, effective mass of a certain class of excitations, etc.) are analytic continuations in the coupling constant of the corresponding results in the repulsive case. In addition, it is possible to have eigenstates which do not have the bound state present. These excited states are also discussed and are found to exhibit a negative effective mass and to modify the particle density at very large distances from the different particle.
The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low-energy spectrum of noninteracting fermions is identical to the one for a harmonic chain. This allows us to describe interacting fermions as a system of coupled oscillators. The exact solution of the Tomonaga–Luttinger model is discussed and results for the momentum distribution and spectral functions are presented. The general Luttinger liquid phenomenology is briefly discussed and various attempts at the experimental verification of the theoretical predictions are examined. Extended defects in semiconductors might also be candidate systems.
The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low-energy spectrum of noninteracting fermions is identical to the one for a harmonic chain. This allows us to describe interacting fermions as a system of coupled oscillators. The exact solution of the Tomonaga-Luttinger model is discussed and results for the momentum distribution and spectral functions are presented. The general Luttinger liquid phenomenology is briefly discussed and various attempts at the experimental verification of the theoretical predictions are examined. Extended defects in semiconductors might also be candidate systems.