We investigate properties of the entropy density related to a generalized extensive statistics and derive the thermodynamic Bethe ansatz equation for a system of relativistic particles obeying such a statistics. We investigate the conformal limit of such a system. We also derive a generalized Y-system. The Gentile intermediate statistics and the statistics of gamma-ons are considered in detail. In particular, we observe that certain thermodynamic quantities for the Gentile statistics majorize those for the Haldane-Wu statistics. Specifically, for the effective central charges related to affine Toda models we obtain nontrivial inequalities in terms of dilogarithms.We investigate properties of the entropy density related to a generalized extensive statistics and derive the thermodynamic Bethe ansatz equation for a system of relativistic particles obeying such a statistics. We investigate the conformal limit of such a system. We also derive a generalized Y-system. The Gentile intermediate statistics and the statistics of gamma-ons are considered in detail. In particular, we observe that certain thermodynamic quantities for the Gentile statistics majorize those for the Haldane-Wu statistics. Specifically, for the effective central charges related to affine Toda models we obtain nontrivial inequalities in terms of dilogarithms.

Jan 1, 20015 citations

A Note on Statistical Interactions and the Thermodynamic Bethe Ansatz

Denis Bernard, Yong-Shi Wu

We show that the thermodynamic Bethe ansatz equations for one-dimensional integrable many-body systems can be reinterpreted in such a way that they only code the statistical interactions, in the sense of Haldane, between particles of identical or different momenta. Thus, the thermodynamic properties of these systems can be characterized by the generalized ideal gases recently proposed by one of us. For example, the Yang-Yang $δ$ -function gas is a gas with specific statistical interactions between particles of different momenta, while the Calogero-Sutherland system provides a model for an ideal gas of particles with a fractional statistics.We show that the thermodynamic Bethe ansatz equations for one-dimensional integrable many-body systems can be reinterpreted in such a way that they only code the statistical interactions, in the sense of Haldane, between particles of identical or different momenta. Thus, the thermodynamic properties of these systems can be characterized by the generalized ideal gases recently proposed by one of us. For example, the Yang-Yang $δ$-function gas is a gas with specific statistical interactions between particles of different momenta, while the Calogero-Sutherland system provides a model for an ideal gas of particles with a fractional statistics.

arXiv:cond-mat/9404025Apr 12, 199415 citations

Discrete thermodynamic Bethe ansatz

M. C. Bergère, Ken‐Ichiro Imura, Stéphane Ouvry

arXiv:cond-mat/0104107Nuclear Physics BAug 1, 20010 citations

Haldane fractional statistics for a one-dimensional Heisenberg spin X X X chain

Wei-Jia Liu, Jiajia Luo, Xi-Wen Guan

Haldane's fractional exclusion statistics (FES) describe generalized Pauli exclusion statistics, which can be regarded as emergent quantum statistics induced by the intrinsic dynamical interaction. Nonmutual FES have been identified at the quantum criticality of the one-dimensional (1D) and 2D interacting Bose gas [Nat. Sci. Rev. 9, nwac027 (2022)]. It is naturally asked if such nonmutual FES can be induced by the spin-spin interaction in the antiferromagnetic spin-1/2 $XXX$ chain. In this article, we first represent the Bethe ansatz equations of spin strings in terms of the FES equations of different species. Then we show that the 1D spin $XXX$ chain remarkably possesses nonmutual FES in the critical region. We observe that the equation of state in terms of the FES gives rises to full statistical properties of the model at quantum criticality, which are in good agreement with the results obtained from the thermodynamic Bethe ansatz (TBA) equations of the model. From the nonmutual FES, we also precisely determine the quantum scaling functions, which further agree well with the previous TBA results [Phys. Rev. B 96, 220401(R) (2017)]. Finally, we also establish an exact mapping between the scaling functions of the Lieb-Liniger model and the spin Heisenberg spin chain at quantum criticality. Our method provides deep insights into the critical phase of matter from a quantum FES point of view.Haldane's fractional exclusion statistics (FES) describe generalized Pauli exclusion statistics, which can be regarded as emergent quantum statistics induced by the intrinsic dynamical interaction. Nonmutual FES have been identified at the quantum criticality of the one-dimensional (1D) and 2D interacting Bose gas [Nat. Sci. Rev. 9, nwac027 (2022)]. It is naturally asked if such nonmutual FES can be induced by the spin-spin interaction in the antiferromagnetic spin-1/2 $XXX$ chain. In this article, we first represent the Bethe ansatz equations of spin strings in terms of the FES equations of different species. Then we show that the 1D spin $XXX$ chain remarkably possesses nonmutual FES in the critical region. We observe that the equation of state in terms of the FES gives rises to full statistical properties of the model at quantum criticality, which are in good agreement with the results obtained from the thermodynamic Bethe ansatz (TBA) equations of the model. From the nonmutual FES, we also precisely determine the quantum scaling functions, which further agree well with the previous TBA results [Phys. Rev. B 96, 220401(R) (2017)]. Finally, we also establish an exact mapping between the scaling functions of the Lieb-Liniger model and the spin Heisenberg spin chain at quantum criticality. Our method provides deep insights into the critical phase of matter from a quantum FES point of view.

Physical Review AMar 21, 20250 citations

Thermodynamical bethe ansatz and condensed matter

Minoru Takahashi

arXiv:cond-mat/9708087Springer eBooksApr 7, 200831 citations

δ

-function gas is a gas with specific statistical interactions between particles of different momenta, while the Calogero-Sutherland system provides a model for an ideal gas of particles with a fractional statistics.

XXX

chain. In this article, we first represent the Bethe ansatz equations of spin strings in terms of the FES equations of different species. Then we show that the 1D spin

XXX

chain remarkably possesses nonmutual FES in the critical region. We observe that the equation of state in terms of the FES gives rises to full statistical properties of the model at quantum criticality, which are in good agreement with the results obtained from the thermodynamic Bethe ansatz (TBA) equations of the model. From the nonmutual FES, we also precisely determine the quantum scaling functions, which further agree well with the previous TBA results [Phys. Rev. B 96, 220401(R) (2017)]. Finally, we also establish an exact mapping between the scaling functions of the Lieb-Liniger model and the spin Heisenberg spin chain at quantum criticality. Our method provides deep insights into the critical phase of matter from a quantum FES point of view.