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

Le Journal de Physique Colloques

DOUBLE SINE-GORDON MODEL FOR THE CLASSICAL AND QUANTUM THERMODYNAMICS OF MAGNETIC CHAINS

R. Giachetti, V. Tognetti, Ruggero Vaia

Published Dec 1, 1988• 1 citation
Publisher

Abstract

The Double Sine-Gordon (DSG) model has been often used for describing anisotropic spin chains. We firstly present classical transfer matrix calculations of thermodynamic quantities. Secondly, the effects of the quantum fluctuations are taken into account by means of an effective potential, which was successfully used for SG models.
DOI
10.1051/jphyscol:19888727

Related papers

Thermodynamic properties of quantum sine-Gordon spin chain system KCuGaF 6

Izumi Umegaki, Hidekazu Tanaka, Toshio Ono +2 more

We investigated the thermodynamic properties of the spin-1/2 one-dimensional Heisenberg antiferromagnet KCuGaF${}_{6}$ by measuring the specific heat in magnetic fields. When this compound is subjected to a uniform magnetic field $\mathbit{H}$, a transverse staggered magnetic field $\mathbit{h}$ is induced in this compound owing to the staggered component of the $\mathbit{g}$ tensor and the Dzyaloshinskii-Moriya interaction with an alternating $\mathbit{D}$ vector. Consequently, the quantum sine-Gordon (SG) model is an effective model of this compound in a uniform magnetic field. In three different field directions, we observed a magnetic-field-induced gap, which increases with $H$. We analyzed experimental results using specific heat theory based on quantum SG theory. The thermodynamic property for $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}c$ is very well described in terms of the elementary excitations characteristic of the quantum SG model, while for the other field directions significant contributions from other excitation modes beyond the framework of the quantum SG model were observed. For $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}b$, a quantum phase transition between gapless and gapped ground states was observed.

arXiv:1112.5531•Physical Review B•Apr 24, 2012•15 citations

QUANTUM SINE-GORDON THERMODYNAMICS

X. Zotos

Using the Bethe ansatz method we analyze the thermodynamics of the quantum sine-Gordon model. We present a finite set of coupled nonlinear integral equations for the thermodynamic equilibrium densities of the various excitations, which we solve numerically. We calculate the specific heat and we compare our results with recent experiments on CsNiF3 and TMMC. The good accord obtained indicates the importance of quantum effects.

Le Journal de Physique Colloques•Jun 1, 1983•3 citations

Critical properties of the double-frequency sine-Gordon model with applications

Michele Fabrizio, Alexander O. Gogolin, A. A. Nersesyan

We study the properties of the double-frequency sine–Gordon model in the vicinity of the Ising quantum phase transition displayed by this model. Using a mapping onto a generalised lattice quantum Ashkin-Teller model, we obtain critical and nearly-off-critical correlation functions of various operators. We discuss applications of the double-sine-Gordon model to one-dimensional physical systems, like spin chains in a staggered external field and interacting electrons in a staggered potential. PACS: 71.10.Pm; 71.10.Fd; 75.10.Jm

•Jan 1, 2008•49 citations

Classical aspects of quantum spin chains (abstract)

L. F. Lemmens, Wim J. M. de Jonge, Klaas Kopinga

A variational estimate of the free energy of a quantum spin chain based on the stochastic behavior of the quantization axes is proposed. It allows a description of the nonlinear excitations and quantum spin waves within the same framework. For an easy-plane ferromagnet with an external field in the plane it reveals that the nonlinear excitations (solitons) are predominantly described by the classical degrees of freedom. Considerable effort has been devoted to the theoretical description1 and experimental verification of the existence of nonlinear excitations. In this field magnetic chain systems have played an important part.2 Chain systems with an easy-plane anisotropy, such as (C6 H11 NH3 )CuBr3 (CHAB) and CsNiF3 , which are subjected to a symmetry breaking field, were found to be soliton bearing.3 Theoretically the description of the nonlinear effect is based on the mapping of the spin dynamics on a sine-Gordon model. Further research4 indicated that the interpretation of the thermodynamical properties of real systems in terms of the sine-Gordon model required however quantum and anisotropy corrections. Since the dipolar interactions between the spins in the chain are considered to be negligible, the direction of the spin chain in configuration space with respect to any preferred direction in spin space does not enter explicitly in the Hamiltonian. This makes it interesting to define a site-dependent z direction in spin space which makes an angle (Θn ,φn ) with the z direction in configuration space. The model Hamiltonian can then be written in terms of the spin operators defined with respect to the site-dependent quantization axis. The representation with equal quantization axis for all the sites is related to the representation with different quantization axes at each site by a rotation in spin space. The unitary transformation that describes the rotation contains the angles (Θn ,φn ), which we have treated as random variables. Based on this observation we have proposed a new variational approach for the quantum spin chain. We will outline the main results here. A full account is published elsewhere.5 In our approach the free energy of the system can be separated in a quantum part and a classical part. The free energy F of the chain is then approximated by an upper bound F<Fcl +Fqm , where βFcl =−ln[E(exp−βVcl )] and βFqm =−ln Tr(exp−β〈Hqm 〉). The first part is a configurational classical free energy, depending on the choice of the probability distribution for the quantization axes via the expectation E. The second contribution is the free energy of a modified quantum chain, whose parameters are classical averages and can be obtained from the configurational classical free energy. For easy-plane ferromagnetic chains, the nonlinear excitations are comprised in the classical part, whereas the quantum part contains predominantly linear excitations. For those thermodynamical quantities that are insensitive to the contribution of the quantum excitations, the chain is thermodynamically equivalent with a classical sine-Gordon system. The out-of-plane corrections are incorporated in the quantum part of the free energy. This behavior is corroborated experimentally by measurements of the excess heat capacity of CHAB for different magnetic fields with the same in-plane component.6 The validity of our approach is, however, not restricted to easy-plane ferromagnetic chains. Also for more complex systems with, for example, an orthorhombic or helical symmetry, the introduction of stochastic quantization axes can shed new light on some of the thermodynamical properties of these quantum systems in terms of their classical equivalent.

Journal of Applied Physics•May 1, 1990•0 citations

NUMERICAL QUANTUM TRANSFER-MATRIX RESULTS FOR A SPIN CHAIN CORRESPONDING TO CHAB

Th. Delica, R. W. Gerling, Hajo Leschke

A variant of the quantum transfer-matrix method is used to obtain numerically accurate results for the specific heat of an easy-plane spin chain with an in-plane field, corresponding to the ferromagnetic compound CHAB. They are contrasted with predictions of the classical sine-Gordon approximation for the chain and with experimental data.

Le Journal de Physique Colloques•Dec 1, 1988•1 citation

Quantum electronic circuit simulation of generalized sine-Gordon models

Ananda Roy, Hubert Saleur

Investigation of strongly interacting, nonlinear quantum field theories (QFTs) remains one of the outstanding challenges of modern physics. Here, we describe analog quantum simulators for nonlinear QFTs using mesoscopic superconducting circuit lattices. Using the Josephson effect as the source of nonlinear interaction, we investigate generalizations of the quantum sine-Gordon model. In particular, we consider a two-field generalization, the double sine-Gordon model. In contrast to the sine-Gordon model, this model can be purely quantum integrable, when it does not admit a semiclassical description---a property that is generic to many multifield QFTs. The primary goal of this work is to investigate different thermodynamic properties of the double sine-Gordon model and propose experiments that can capture its subtle quantum integrability. First, we analytically compute the mass spectrum and the ground-state energy in the presence of an external ``magnetic'' field using Bethe ansatz and conformal perturbation theory. Second, we calculate the thermodynamic Bethe ansatz equations for the model and analyze its finite temperature properties. Third, we propose experiments to verify the theoretical predictions.

arXiv:1902.09530•Physical review. B./Physical review. B•Oct 23, 2019•27 citations
We investigated the thermodynamic properties of the spin-1/2 one-dimensional Heisenberg antiferromagnet KCuGaF6{}_{6}6​ by measuring the specific heat in magnetic fields. When this compound is subjected to a uniform magnetic field $\mathbit{H}$, a transverse staggered magnetic field $\mathbit{h}$ is induced in this compound owing to the staggered component of the $\mathbit{g}$ tensor and the Dzyaloshinskii-Moriya interaction with an alternating $\mathbit{D}$ vector. Consequently, the quantum sine-Gordon (SG) model is an effective model of this compound in a uniform magnetic field. In three different field directions, we observed a magnetic-field-induced gap, which increases with HHH. We analyzed experimental results using specific heat theory based on quantum SG theory. The thermodynamic property for $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}c$ is very well described in terms of the elementary excitations characteristic of the quantum SG model, while for the other field directions significant contributions from other excitation modes beyond the framework of the quantum SG model were observed. For $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}b$, a quantum phase transition between gapless and gapped ground states was observed.
We study the properties of the double-frequency sine–Gordon model in the vicinity of the Ising quantum phase transition displayed by this model. Using a mapping onto a generalised lattice quantum Ashkin-Teller model, we obtain critical and nearly-off-critical correlation functions of various operators. We discuss applications of the double-sine-Gordon model to one-dimensional physical systems, like spin chains in a staggered external field and interacting electrons in a staggered potential. PACS: 71.10.Pm; 71.10.Fd; 75.10.Jm
A variational estimate of the free energy of a quantum spin chain based on the stochastic behavior of the quantization axes is proposed. It allows a description of the nonlinear excitations and quantum spin waves within the same framework. For an easy-plane ferromagnet with an external field in the plane it reveals that the nonlinear excitations (solitons) are predominantly described by the classical degrees of freedom. Considerable effort has been devoted to the theoretical description1 and experimental verification of the existence of nonlinear excitations. In this field magnetic chain systems have played an important part.2 Chain systems with an easy-plane anisotropy, such as (C6 H11 NH3 )CuBr3 (CHAB) and CsNiF3 , which are subjected to a symmetry breaking field, were found to be soliton bearing.3 Theoretically the description of the nonlinear effect is based on the mapping of the spin dynamics on a sine-Gordon model. Further research4 indicated that the interpretation of the thermodynamical properties of real systems in terms of the sine-Gordon model required however quantum and anisotropy corrections. Since the dipolar interactions between the spins in the chain are considered to be negligible, the direction of the spin chain in configuration space with respect to any preferred direction in spin space does not enter explicitly in the Hamiltonian. This makes it interesting to define a site-dependent z direction in spin space which makes an angle (Θn ,φn ) with the z direction in configuration space. The model Hamiltonian can then be written in terms of the spin operators defined with respect to the site-dependent quantization axis. The representation with equal quantization axis for all the sites is related to the representation with different quantization axes at each site by a rotation in spin space. The unitary transformation that describes the rotation contains the angles (Θn ,φn ), which we have treated as random variables. Based on this observation we have proposed a new variational approach for the quantum spin chain. We will outline the main results here. A full account is published elsewhere.5 In our approach the free energy of the system can be separated in a quantum part and a classical part. The free energy F of the chain is then approximated by an upper bound F<Fcl +Fqm , where βFcl =−ln[E(exp−βVcl )] and βFqm =−ln Tr(exp−β〈Hqm 〉). The first part is a configurational classical free energy, depending on the choice of the probability distribution for the quantization axes via the expectation E. The second contribution is the free energy of a modified quantum chain, whose parameters are classical averages and can be obtained from the configurational classical free energy. For easy-plane ferromagnetic chains, the nonlinear excitations are comprised in the classical part, whereas the quantum part contains predominantly linear excitations. For those thermodynamical quantities that are insensitive to the contribution of the quantum excitations, the chain is thermodynamically equivalent with a classical sine-Gordon system. The out-of-plane corrections are incorporated in the quantum part of the free energy. This behavior is corroborated experimentally by measurements of the excess heat capacity of CHAB for different magnetic fields with the same in-plane component.6 The validity of our approach is, however, not restricted to easy-plane ferromagnetic chains. Also for more complex systems with, for example, an orthorhombic or helical symmetry, the introduction of stochastic quantization axes can shed new light on some of the thermodynamical properties of these quantum systems in terms of their classical equivalent.
Investigation of strongly interacting, nonlinear quantum field theories (QFTs) remains one of the outstanding challenges of modern physics. Here, we describe analog quantum simulators for nonlinear QFTs using mesoscopic superconducting circuit lattices. Using the Josephson effect as the source of nonlinear interaction, we investigate generalizations of the quantum sine-Gordon model. In particular, we consider a two-field generalization, the double sine-Gordon model. In contrast to the sine-Gordon model, this model can be purely quantum integrable, when it does not admit a semiclassical description---a property that is generic to many multifield QFTs. The primary goal of this work is to investigate different thermodynamic properties of the double sine-Gordon model and propose experiments that can capture its subtle quantum integrability. First, we analytically compute the mass spectrum and the ground-state energy in the presence of an external ``magnetic'' field using Bethe ansatz and conformal perturbation theory. Second, we calculate the thermodynamic Bethe ansatz equations for the model and analyze its finite temperature properties. Third, we propose experiments to verify the theoretical predictions.