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

Journal of the Physical Society of Japan

The Thirring Model at a Finite Fermion Density

Yukio Okwamoto

Published Apr 15, 1983• 3 citations
Publisher

Abstract

The spectrum of the massless Thirring model at a finite fermion density is examined, using the Bethe ansatz, with the momentum cutoff. The cutoff procedure in this letter is valid for the model within the first order of the coupling constant.
DOI
10.1143/jpsj.52.1081

Related papers

One-dimensional backward-scattering fermion model with built-in cutoff

S. Rudin

A built-in cutoff for a fermion model in one dimension is proposed, consisting of (1) a cubic term in the kinetic energy and (2) an "optical potential" counterterm. This model is shown to be soluble by the Bethe ansatz and the mass gap is obtained as a function of coupling constant. This functional dependence reproduces a result obtained by methods other than the Bethe ansatz.

Physical review. B, Condensed matter•Oct 15, 1983•7 citations

Method for Solving the Massive Thirring Model

Hugh Bergknoff, H. B. Thacker

The Hamiltonian of the massive Thirring model is explicitly diagonalized by formulating a Bethe Ansatz for the eigenstates. A general method for computing the energy spectrum is presented.Received 11 August 1978DOI:https://doi.org/10.1103/PhysRevLett.42.135©1979 American Physical Society

Physical Review Letters•Jan 15, 1979•94 citations

Strong Coupling Limit of Bethe Ansatz Solutions in Massive Thirring Model

T. Fujita, T. Kake, H. Takahashi

arXiv:hep-th/9906120•Annals of Physics•May 1, 2000•5 citations

Structure and solution of the massive Thirring model

Hugh Bergknoff, H. B. Thacker

The Hamiltonian of the massive Thirring model is explicitly diagonalized by formulating a Bethe ansatz for the eigenstates. The physical states are described by many-body wave functions representing the vacuum as a filled Fermi-Dirac sea and particle states as excitations built upon it. The spectrum of states is determined by imposing periodic boundary conditions on the wave functions. The energies are calculated by reducing the periodic boundary conditions to linear integral equations. For fermion-antifermion bound states the Dashen-Hasslacher-Neven spectrum is obtained. It is shown that the solution to the massive Thirring model can be understood as the critical limit of Baxter's solution of the eight-vertex model.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jun 15, 1979•159 citations

New Vacuum of Bethe Ansatz Solutions in Thirring Model

Takehisa Fujita, Makoto Hiramoto, Takeshi Homma +1 more

We find a new vacuum of the Bethe ansatz solutions in the massless Thirring model. This vacuum breaks the chiral symmetry and has the lower energy than the well-known symmetric vacuum energy. Further, we evaluate the energy spectrum of the one particle-one hole ($1p-1h$) states, and find that it has a finite gap. The analytical expressions for the true vacuum as well as for the lowest $1p-1h$ excited state are also found. Further, we examine the bosonization of the massless Thirring model and prove that the well-known procedure of bosonization of the massless Thirring model is incomplete because of the lack of the zero mode in the boson field.

arXiv:hep-th/0410221•Journal of the Physical Society of Japan•Apr 1, 2005•10 citations

Commensurate-Incommensurate Transition in the Two-Dimensional Sine-Gordon System: the Bethe Ansatz Calculation

Yukio Okwamoto

Recently Haldane has derived the Bethe ansatz equations describing the ground state properties of the massive Thirring model with finite `hole' density (the quantum sine-Gordon model with finite soliton density). His derivation is explicitly confirmed here using a particular cutoff scheme, and his solutions of the equations in various limits are reviewed with complementary results. The commensurate-incommensurate transition in the two-dimensional sine-Gordon model with a uniaxial misfit is examined at finite temperatures using the results obtained in the massive Thirring model.

Journal of the Physical Society of Japan•Mar 1, 1983•6 citations
The Hamiltonian of the massive Thirring model is explicitly diagonalized by formulating a Bethe ansatz for the eigenstates. The physical states are described by many-body wave functions representing the vacuum as a filled Fermi-Dirac sea and particle states as excitations built upon it. The spectrum of states is determined by imposing periodic boundary conditions on the wave functions. The energies are calculated by reducing the periodic boundary conditions to linear integral equations. For fermion-antifermion bound states the Dashen-Hasslacher-Neven spectrum is obtained. It is shown that the solution to the massive Thirring model can be understood as the critical limit of Baxter's solution of the eight-vertex model.
We find a new vacuum of the Bethe ansatz solutions in the massless Thirring model. This vacuum breaks the chiral symmetry and has the lower energy than the well-known symmetric vacuum energy. Further, we evaluate the energy spectrum of the one particle-one hole (1p−1h1p-1h1p−1h) states, and find that it has a finite gap. The analytical expressions for the true vacuum as well as for the lowest 1p−1h1p-1h1p−1h excited state are also found. Further, we examine the bosonization of the massless Thirring model and prove that the well-known procedure of bosonization of the massless Thirring model is incomplete because of the lack of the zero mode in the boson field.
Recently Haldane has derived the Bethe ansatz equations describing the ground state properties of the massive Thirring model with finite `hole' density (the quantum sine-Gordon model with finite soliton density). His derivation is explicitly confirmed here using a particular cutoff scheme, and his solutions of the equations in various limits are reviewed with complementary results. The commensurate-incommensurate transition in the two-dimensional sine-Gordon model with a uniaxial misfit is examined at finite temperatures using the results obtained in the massive Thirring model.