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 the Physical Society of Japan

Bethe Ansatz Equation for the Hubbard Model with Boundary Fields

Masahiro Shiroishi, Miki Wadati

Published Jan 15, 1997• 62 citations
Publisher

Abstract

We apply the coordinate Bethe ansatz method to the one-dimensional Hubbard model with boundary fields. We find two integrable boundaries, that is, the boundary chemical potential and the boundary magnetic field. In total, four possible boundary conditions are explicitly presented. Using the Bethe ansatz equations, the finite size corrections and the low-lying excitation spectrum are evaluated.

DOI
10.1143/jpsj.66.1

Related papers

Spectrum of boundary states in the open Hubbard chain

Gerald Bedürftig, Holger Frahm

We use the Bethe ansatz solution for the one-dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials, one finds that the true ground state contains a single charge or, for boundary potentials comparable with the Hubbard interaction, a pair of electrons in a bound state. If these are left unoccupied one finds holon and spinon bound states. We compute the finite size corrections to the low-lying energies in this system and use the predictions of boundary conformal field theory to study the exponents related to the orthogonality catastrophe.

arXiv:cond-mat/9702227•Journal of Physics A Mathematical and General•Jun 21, 1997•42 citations

Spectrum of boundary states in the open Hubbard chain

Gerald Bedürftig, Holger Frahm

We use the Bethe Ansatz solution for the one dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials one finds that the true ground state contains a single charge or, for boundary potentials comparable to the Hubbard interaction, a pair of electrons in a bound state. If these are left unoccupied one finds holon and spinon bound states. We compute the finite size corrections to the low lying energies in this system and use the predictions of boundary conformal field theory to study the exponents related to the orthogonality catastrophe.

•Jan 1, 1997•20 citations

Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields

Yuanyuan Li, Junpeng Cao, Wen‐Li Yang +2 more

The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.

arXiv:1311.0432•Nuclear Physics B•Dec 11, 2013•36 citations

Exact Solution of a New Class of Hubbard-Type Models with Open Boundary Conditions

Cao Li

A new class of Hubbard-type models with open boundary conditions in one dimension is studied in the frame- work of coordinate Bethe ansatz method.The energy spectrum,integrable boundary conditions and the corresponding Bethe ansatz equations are derived.

Chinese Physics C•Jan 1, 2007•0 citations

Coordinate Bethe ansatz for the one-dimensional SU(n) Hubbard model with open boundary conditions

Guang-Liang Li, Rui‐Hong Yue, Kangjie Shi

The one-dimensional (1D) SU(n) Hubbard model with open boundary condition is solved by using the coordinate Bethe ansatz method. The energy and integrable boundary conditions are obtained. At the same time, the corresponding Bethe ansatz equations are achieved by diagonalizing the inhomogeneous transfer matrix of the open SU(2n−2) XXX vertex model. When n=2, our result comes back to that of the 1D Hubbard model given by Deguchi and Yue (con-mat/9704138).

Journal of Mathematical Physics•Jun 1, 2001•0 citations

Exact solutions of 1-D Hubbard model with open boundary conditions and the conformal dimensions under boundary magnetic fields

Tetsuo Deguchi, Rui‐Hong Yue

The Bethe ansatz equations of the 1-D Hubbard model under open boundary conditions are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model with open boundaries. Through the finite-size correction, we obtain the energy spectrum of the open chain and discuss the effects of boundary magnetic fields applied only at the edges of the chain. Several physical implications of the finite-size spectrum are discussed from the viewpoint of the boundary conformal field theories (BCFT); the conformal dimension of the spin excitation is quite sensitive to the boundary magnetic fields, and this sensitivity can be explained in terms of the $π/2$-phase shift of the BCFT. For several limiting cases such as for the half-filling case, the conformal dimensions are explicitly calculated.

arXiv:cond-mat/9704138•Apr 16, 1997•7 citations
We apply the coordinate Bethe ansatz method to the one-dimensional Hubbard model with boundary fields. We find two integrable boundaries, that is, the boundary chemical potential and the boundary magnetic field. In total, four possible boundary conditions are explicitly presented. Using the Bethe ansatz equations, the finite size corrections and the low-lying excitation spectrum are evaluated.
We use the Bethe ansatz solution for the one-dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials, one finds that the true ground state contains a single charge or, for boundary potentials comparable with the Hubbard interaction, a pair of electrons in a bound state. If these are left unoccupied one finds holon and spinon bound states. We compute the finite size corrections to the low-lying energies in this system and use the predictions of boundary conformal field theory to study the exponents related to the orthogonality catastrophe.
We use the Bethe Ansatz solution for the one dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials one finds that the true ground state contains a single charge or, for boundary potentials comparable to the Hubbard interaction, a pair of electrons in a bound state. If these are left unoccupied one finds holon and spinon bound states. We compute the finite size corrections to the low lying energies in this system and use the predictions of boundary conformal field theory to study the exponents related to the orthogonality catastrophe.
The Bethe ansatz equations of the 1-D Hubbard model under open boundary conditions are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model with open boundaries. Through the finite-size correction, we obtain the energy spectrum of the open chain and discuss the effects of boundary magnetic fields applied only at the edges of the chain. Several physical implications of the finite-size spectrum are discussed from the viewpoint of the boundary conformal field theories (BCFT); the conformal dimension of the spin excitation is quite sensitive to the boundary magnetic fields, and this sensitivity can be explained in terms of the π/2π/2π/2-phase shift of the BCFT. For several limiting cases such as for the half-filling case, the conformal dimensions are explicitly calculated.