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 de Physique I

Zero modes and commensurate-incommensurate transitions

C. Mantea, A. Corciovei, A. Stepanescu, Aldo MASOERO

Published Jan 1, 1992• 0 citations
Publisher

Abstract

There are two different results concerning the functional relationship between the chemical potential of the 1D massive Thirring model and the misfit parameter of the 1D quantum sine-Gordon model which have been reported [4-7]. In order to investigate this problem, the Jordan boson representation of fermion field operators is used to obtain the bosonized expression of the 1D massive Thirring model. The equivalence of this model with the 1D quantum sine-Gordon model is proved, all zero-mode contributions taken into account. The problem of controversial results previously reported is solved. Thereafter, by means of Bethe-Ansatz method, a new expression for the critical curve of the commensurate-incommensurate transition in the two-dimensional sine-Gordon model is found.

DOI
10.1051/jp1:1992121

Related papers

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

Commensurate-incommensurate phase transition in one-dimensional quantum sine-Gordon model based on a lattice massive thirring model

Shuichi lwabuchi

The commensurate-incommensurate (C-IC) phase transition in the one dimensional quantum sineGordon model at zero temperature is exactly solved with the use of the Bethe ansatz technique for the lattice massive Thirring model. The energy difference between C and IC phases is derived based on the same ground state which is valid in the whole parameter region. It is due to the fact that there is no change in the ground state of the lattice massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model. It is proved in the whole parameter region that the IC phase can be realized with the soliton density proportional to x f E s (Es: formation energy of soliton), when Es becomes negative.

•Jan 1, 2005•0 citations

Commensurate-incommensurate phase transition in one-dimensional quantum sine-Gordon model based on a lattice massive thirring model

Shuichi Iwabuchi

The European Physical Journal B•Sep 1, 1995•1 citation

Commensurate-Incommensurate Cross-Over in the One-Dimensional Quantum Sine-Gordon System (g2=4 ). II: Dynamical Properties

H. Yamamoto, A. D. S. Nagi

The dynamical behavior of the one-dimensional quantum sine-Gordon system with a misfit parameter is investigated at a particular value of the quantum parameter g2=4π. For this purpose the dynamical correlation functions are calculated by using the Fermi-Bose relation. From the behavior of the displacement correlation function we find that the thermal velocity is given by ∼√T/m0 in the commensurate state (m0-| µ 8730|≫T) or in the cross-over region (m0≃| µ \tilde |≫T) and approaches value 1 as T or | µ \tilde | is increased. Here m0 and µ \tilde, respectively, are the gap and the chemical potential in the corresponding fermion system. For the case of denity-density correlation function, we give in the commensurate state expressions which are similar to those derived on the basis of the soliton phenomenology in the classical system. A particular case of the density-density correlation function is discussed in detail by following another route.

Progress of Theoretical Physics•Sep 1, 1984•0 citations

Scaling exponents in the incommensurate phase of the sine-Gordon and U(1) Thirring models

Emiliano Papa, Alexei M. Tsvelik

In this paper we study the critical exponents of the quantum sine-Gordon model and U(1) Thirring models in the incommensurate phase. This phase appears when the chemical potential h exceeds a critical value and is characterized by a finite density of solitons. The low-energy sector of this phase is critical and is described by the Gaussian model (Tomonaga-Luttinger liquid) with the compactification radius dependent on the soliton density and the sine-Gordon model coupling constant $\ensuremath{\beta}.$ For a fixed value of $\ensuremath{\beta},$ we find that the Luttinger parameter K is equal to 1/2 at the commensurate-incommensurate transition point and approaches the asymptotic value ${\ensuremath{\beta}}^{2}/8\ensuremath{\pi}$ away from it. We describe a possible phase diagram of the model consisting of an array of weakly coupled chains. The possible phases are Fermi liquid, spin density wave, spin-Peierls, and Wigner crystal.

arXiv:cond-mat/0006422•Physical review. B, Condensed matter•Feb 6, 2001•15 citations

Thermodynamics of the massive Thirring-sine-Gordon model: the Bethe ansatz variational method

S. G. Chung, Y -C Chang

The Bethe ansatz variational approach to the thermodynamics of the massive Thirring-sine-Gordon model in the attractive coupling regime and in the zero-change sector is discussed in detail.

Journal of Physics A Mathematical and General•Jul 11, 1987•13 citations
There are two different results concerning the functional relationship between the chemical potential of the 1D massive Thirring model and the misfit parameter of the 1D quantum sine-Gordon model which have been reported [4-7]. In order to investigate this problem, the Jordan boson representation of fermion field operators is used to obtain the bosonized expression of the 1D massive Thirring model. The equivalence of this model with the 1D quantum sine-Gordon model is proved, all zero-mode contributions taken into account. The problem of controversial results previously reported is solved. Thereafter, by means of Bethe-Ansatz method, a new expression for the critical curve of the commensurate-incommensurate transition in the two-dimensional sine-Gordon model is found.
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.
The commensurate-incommensurate (C-IC) phase transition in the one dimensional quantum sineGordon model at zero temperature is exactly solved with the use of the Bethe ansatz technique for the lattice massive Thirring model. The energy difference between C and IC phases is derived based on the same ground state which is valid in the whole parameter region. It is due to the fact that there is no change in the ground state of the lattice massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model. It is proved in the whole parameter region that the IC phase can be realized with the soliton density proportional to x f E s (Es: formation energy of soliton), when Es becomes negative.
The dynamical behavior of the one-dimensional quantum sine-Gordon system with a misfit parameter is investigated at a particular value of the quantum parameter g2=4π. For this purpose the dynamical correlation functions are calculated by using the Fermi-Bose relation. From the behavior of the displacement correlation function we find that the thermal velocity is given by ∼√T/m0 in the commensurate state (m0-| µ 8730|≫T) or in the cross-over region (m0≃| µ \tilde |≫T) and approaches value 1 as T or | µ \tilde | is increased. Here m0 and µ \tilde, respectively, are the gap and the chemical potential in the corresponding fermion system. For the case of denity-density correlation function, we give in the commensurate state expressions which are similar to those derived on the basis of the soliton phenomenology in the classical system. A particular case of the density-density correlation function is discussed in detail by following another route.
In this paper we study the critical exponents of the quantum sine-Gordon model and U(1) Thirring models in the incommensurate phase. This phase appears when the chemical potential h exceeds a critical value and is characterized by a finite density of solitons. The low-energy sector of this phase is critical and is described by the Gaussian model (Tomonaga-Luttinger liquid) with the compactification radius dependent on the soliton density and the sine-Gordon model coupling constant $\ensuremath{\beta}.$ For a fixed value of $\ensuremath{\beta},$ we find that the Luttinger parameter K is equal to 1/2 at the commensurate-incommensurate transition point and approaches the asymptotic value ${\ensuremath{\beta}}^{2}/8\ensuremath{\pi}$ away from it. We describe a possible phase diagram of the model consisting of an array of weakly coupled chains. The possible phases are Fermi liquid, spin density wave, spin-Peierls, and Wigner crystal.