© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2605.07745 · Physical Review C

Massive Thirring / sine-Gordon model with nonzero current density

Eric Oevermann, Thomas D. Cohen

Published Sep 3, 2026• 0 citations

Abstract

This paper determines the zero-temperature equation of state for the massive Thirring / sine-Gordon model. This demonstrates recently derived model-independent upper and lower bounds on the zero-temperature equation of state with fixed number density from systems with a nonzero current density. That approach is potentially valuable as Monte Carlo calculations with a current density avoid the sign problem in the Euclidean formulation. An advantage to illustrating these bounds in the massive Thirring/sine-Gordon model is that the relevant calculations with both a number density and a current density can be done using a Bethe ansatz. For this model, optimal bounds constrain the energy density as a function of number density by a factor of two from above and below at high densities for all choices of couplings. The lower bound becomes exact at low densities, while the upper bound approaches the worst constraint of a factor of 4.90 .

DOI: 10.1103/vyq7-6hxx

Related papers

Classical sine-Gordon limit of massive-Thirring-model thermodynamics

Michael Fowler

It has been shown numerically by Chung that in the classical sine-Gordon limit the low-temperature thermodynamic properties of the massive Thirring model, as calculated using the Bethe ansatz, correspond to those of a free-phonon gas. We give an analytic derivation of this result and find simple expressions for the finite-temperature "excitation-spectrum" functions, and discuss their physical significance.

Physical review. B, Condensed matter•Sep 1, 1982•36 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

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

Finite temperature excitations of the quantum sine-Gordon–massive Thirring model: Variation of the soliton mass with coupling constant and temperature

Michael Durnan Johnson, Michael Fowler

For the quantum sine-Gordon--massive Thirring model at finite temperature, the relationship between the Bethe ansatz ``elementary excitations'' and physical excitations of the system is examined. The thermodynamic equations are written in terms of a set of dressed particles in the general case. We find that the recently predicted soliton mass discontinuity (on varying coupling strength at finite temperature) is not a real effect--the function exhibiting the discontinuity does not correspond to the mass of the soliton.

Physical review. B, Condensed matter•Jan 1, 1985•9 citations

Quantum field ground state of the sine-Gordon model with finite soliton density: exact results

F. D. M. Haldane

The Bethe ansatz solutions of the massive Thirring model are renormalised and used to obtain exactly the ground-state properties of the sine-Gordon model with a finite density of topological solitons. Using a theory of 1D quantum fluids, the correlation function exponents and low-energy excitation spectrum are obtained. Expansions in various limits are given, and various crossovers described.

Journal of Physics A Mathematical and General•Feb 1, 1982•55 citations

The finite temperature properties of the massive Thirring model and the quantum sine-Gordon model

Masatoshi Imada, Kazuo Hida, M. Ishikawa

The thermodynamics of the massive Thirring model is discussed with the help of the Bethe Ansatz approach in a way different from Fowler and Zotos (1982). In particular a finite Debye cut-off is introduced to investigate effects of the lattice discreteness. The specific heat seems to have a structure as a sum of the Debye-type specific heat and a 'soliton' peak, when the authors take into account the relation of the massive Thirring model to the quantum sine-Gordon model. The finite temperature excitations are calculated. The excitation energy proposed by Fowler and Zotos is shown to have significance which is insensitive to the way of formulation.

Journal of Physics C Solid State Physics•Jan 10, 1983•27 citations

This paper determines the zero-temperature equation of state for the massive Thirring / sine-Gordon model. This demonstrates recently derived model-independent upper and lower bounds on the zero-temperature equation of state with fixed number density from systems with a nonzero current density. That approach is potentially valuable as Monte Carlo calculations with a current density avoid the sign problem in the Euclidean formulation. An advantage to illustrating these bounds in the massive Thirring/sine-Gordon model is that the relevant calculations with both a number density and a current density can be done using a Bethe ansatz. For this model, optimal bounds constrain the energy density as a function of number density by a factor of two from above and below at high densities for all choices of couplings. The lower bound becomes exact at low densities, while the upper bound approaches the worst constraint of a factor of 4.90 .

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.

For the quantum sine-Gordon--massive Thirring model at finite temperature, the relationship between the Bethe ansatz ``elementary excitations'' and physical excitations of the system is examined. The thermodynamic equations are written in terms of a set of dressed particles in the general case. We find that the recently predicted soliton mass discontinuity (on varying coupling strength at finite temperature) is not a real effect--the function exhibiting the discontinuity does not correspond to the mass of the soliton.

The thermodynamics of the massive Thirring model is discussed with the help of the Bethe Ansatz approach in a way different from Fowler and Zotos (1982). In particular a finite Debye cut-off is introduced to investigate effects of the lattice discreteness. The specific heat seems to have a structure as a sum of the Debye-type specific heat and a 'soliton' peak, when the authors take into account the relation of the massive Thirring model to the quantum sine-Gordon model. The finite temperature excitations are calculated. The excitation energy proposed by Fowler and Zotos is shown to have significance which is insensitive to the way of formulation.