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 Statistical Physics

Bethe ansatz results for Hubbard chains with toroidal boundary conditions

Marcio Jose Martins, Richard M. Fye

Published Jul 1, 1991• 13 citations
Publisher
DOI
10.1007/bf01057877

Related papers

Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions

Junpeng Cao, Wen‐Li Yang, Kangjie Shi +1 more

arXiv:1306.1742•Nuclear Physics B•Jul 4, 2013•110 citations

The spin-S XXZ quantum chain with general toroidal boundary conditions

Francisco Castilho Alcaraz, Marcio Jose Martins

The authors derive the operator content of the spin-S XXZ quantum chain with generalised toroidal boundary conditions compatible with the U(1) symmetry of the model. These results are derived by solving numerically the associated Bethe ansatz equations for finite chains and exploring the consequences of the conformal invariance of the infinite system. They also show that, as in the spin-1/2 case, the conformal anomaly and dimensions of general extended SU(2) algebras can be obtained from these spin-S chains by choosing properly the coupling constant and the boundary condition.

Journal of Physics A Mathematical and General•Apr 21, 1990•26 citations

Relationship between the Bethe-ansatz equations for the Hubbard model with boundary fields

Hitoshi Asakawa

Physics Letters A•Sep 1, 1997•5 citations

Bethe ansatz solution for quantum spin-1 chains with boundary terms

E.C. Fireman, A. Lima-Santos, W. Utiel

arXiv:nlin/0110048•Nuclear Physics B•Apr 1, 2002•28 citations

Bethe equations for the critical three-state Potts spin chain with toroidal boundary conditions

Marcio Jose Martins

In this paper, we consider the parameterization of the spectra of the three-state critical Potts quantum chain with integrable twisted boundary conditions in terms of Bethe ansatz type equations. The Bethe equations are found by investigating the structure of the eigenvalues of the respective twisted transfer matrices, and with the help of certain identities satisfied by the product of transfer matrices operators. We have studied the completeness of the spectrum in terms of the Bethe roots for small lattice sizes and have computed the eigenstate momenta. We found that the spins of the low-lying excitations can have fractional values in accordance with predictions of the underlying conformal field theory. We argue that our framework can be used to build integrable Hamiltonians whose spectra are determined by mixing different toroidal boundary conditions.

Nuclear Physics B•Jan 27, 2026•0 citations

Bethe equations for the critical three-state Potts spin chain with toroidal boundary conditions

Martins, M. J.

In this paper, we consider the parameterization of the spectra of the three-state critical Potts quantum chain with integrable twisted boundary conditions in terms of Bethe ansatz type equations. The Bethe equations are found by investigating the structure of the eigenvalues of the respective twisted transfer matrices, and with the help of certain identities satisfied by the product of transfer matrix operators. We have studied the completeness of the spectrum in terms of the Bethe roots for small lattice sizes and have computed the eigenstate momenta. We found that the spins of the low-lying excitations can have fractional values in accordance with predictions of the underlying conformal field theory. We argue that our framework can be used to build integrable Hamiltonians whose spectra are determined by mixing different toroidal boundary conditions.

arXiv:2512.07763•Dec 8, 2025•0 citations
The authors derive the operator content of the spin-S XXZ quantum chain with generalised toroidal boundary conditions compatible with the U(1) symmetry of the model. These results are derived by solving numerically the associated Bethe ansatz equations for finite chains and exploring the consequences of the conformal invariance of the infinite system. They also show that, as in the spin-1/2 case, the conformal anomaly and dimensions of general extended SU(2) algebras can be obtained from these spin-S chains by choosing properly the coupling constant and the boundary condition.
In this paper, we consider the parameterization of the spectra of the three-state critical Potts quantum chain with integrable twisted boundary conditions in terms of Bethe ansatz type equations. The Bethe equations are found by investigating the structure of the eigenvalues of the respective twisted transfer matrices, and with the help of certain identities satisfied by the product of transfer matrices operators. We have studied the completeness of the spectrum in terms of the Bethe roots for small lattice sizes and have computed the eigenstate momenta. We found that the spins of the low-lying excitations can have fractional values in accordance with predictions of the underlying conformal field theory. We argue that our framework can be used to build integrable Hamiltonians whose spectra are determined by mixing different toroidal boundary conditions.
In this paper, we consider the parameterization of the spectra of the three-state critical Potts quantum chain with integrable twisted boundary conditions in terms of Bethe ansatz type equations. The Bethe equations are found by investigating the structure of the eigenvalues of the respective twisted transfer matrices, and with the help of certain identities satisfied by the product of transfer matrix operators. We have studied the completeness of the spectrum in terms of the Bethe roots for small lattice sizes and have computed the eigenstate momenta. We found that the spins of the low-lying excitations can have fractional values in accordance with predictions of the underlying conformal field theory. We argue that our framework can be used to build integrable Hamiltonians whose spectra are determined by mixing different toroidal boundary conditions.