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

arXiv:1503.07885 · Physics Letters B

Bethe states for the two-site Bose–Hubbard model: A binomial approach

Gilberto N. Santos Filho, Changrim Ahn, Angela Foerster, I. Roditi

Published May 5, 2015• 5 citations
arXivHTMLPDF

Abstract

We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl(2)-invariant R-matrix for the two-site Bose–Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.

DOI
10.1016/j.physletb.2015.05.003

Related papers

Exact solution of a generalized two-sites Bose-Hubbard model

Gilberto N. Santos Filho

I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the gl(2)-invariant R-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a SN−1 sphere, where N is the total number of atoms in the condensate.

Notas de Física•Apr 10, 2016•0 citations

Exact solution of a generalized two-sites Bose-Hubbard model

Gilberto N. Santos Filho

I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a $S^{N-1}$ sphere, where $N$ is the total number of atoms in the condensate.

arXiv:1610.07111•Oct 23, 2016•0 citations

Exactly Solvable Bose and Fermi many-body Hamiltonian with higher order terms based on the S2 symmetry

Feng Pan, L. R. Dai

It is shown that the two component Fermi or Bose many-body Hamiltonian, such as the two-orbit fermion pairing and two-site Bose-Hubbard model with arbitrary finite higher order terms can always be solved exactly by using Bethe ansatz vector construction based on the permutation of two components of bosons or fermions involved. As examples of the solution, the extended one-dimensional dimer Bose -Hubbard model with multi-body interactions and the mean-fifield plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits are demonstrated with the eigenstates and the eigen-energy and the related Bethe ansatz equations. It is shown that the main feature of the solutions lies in the fact that the Bethe ansatz vectors can be expressed in terms of binomials of the boson or fermion operators times the related symmetric functions. As the consequence, two-component quantum many-body systems , such as the extended Lipkin-Meshkov-Glick model with higher-order interactions, can be solved in a similar way.

•Aug 3, 2021•0 citations

High-accuracy energy formulas for the attractive two-site Bose-Hubbard model

Igor Ermakov, Tim Byrnes, N. M. Bogoliubov

The attractive two-site Bose-Hubbard model is studied within the framework of the analytical solution obtained by the application of the quantum inverse scattering method. The structure of the ground and excited states is analyzed in terms of solutions of Bethe equations, and an approximate solution for the Bethe roots is given. This yields approximate formulas for the ground-state energy and for the first excited-state energy. The obtained formulas work with remarkable precision for a wide range of parameters of the model, and are confirmed numerically. An expansion of the Bethe state vectors into a Fock space is also provided for evaluation of expectation values, although this does not have accuracy similar to that of the energies.

arXiv:1708.08696•Physical Review A•Feb 20, 2018•2 citations

Current algebra for a generalized two-site Bose-Hubbard model

Gilberto N. Santos Filho

We present a current algebra for a generalized two-site Bose-Hubbard model and use it to get the quantum dynamics of the currents. For different choices of the Hamiltonian parameters we get different currents dynamics. We generalize the Heisenberg equation of motion to write the n-th time derivative of any operator.

arXiv:1511.05026•Nov 16, 2015•2 citations

Current algebra for the two-site Bose-Hubbard model

Gilberto N. Santos Filho

We present a current algebra for the two-site Bose-Hubbard model and use it to get the quantum dynamics of the currents. For different choices of the Hamiltonian parameters we get different currents dynamics. We generalize the Heisenberg equation of motion to write the second derivative of an operator.

•May 26, 2015•0 citations
We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl(2)-invariant R-matrix for the two-site Bose–Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the gl(2)gl(2)gl(2)-invariant RRR-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a SN−1S^{N-1}SN−1 sphere, where NNN is the total number of atoms in the condensate.
It is shown that the two component Fermi or Bose many-body Hamiltonian, such as the two-orbit fermion pairing and two-site Bose-Hubbard model with arbitrary finite higher order terms can always be solved exactly by using Bethe ansatz vector construction based on the permutation of two components of bosons or fermions involved. As examples of the solution, the extended one-dimensional dimer Bose -Hubbard model with multi-body interactions and the mean-fifield plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits are demonstrated with the eigenstates and the eigen-energy and the related Bethe ansatz equations. It is shown that the main feature of the solutions lies in the fact that the Bethe ansatz vectors can be expressed in terms of binomials of the boson or fermion operators times the related symmetric functions. As the consequence, two-component quantum many-body systems , such as the extended Lipkin-Meshkov-Glick model with higher-order interactions, can be solved in a similar way.
The attractive two-site Bose-Hubbard model is studied within the framework of the analytical solution obtained by the application of the quantum inverse scattering method. The structure of the ground and excited states is analyzed in terms of solutions of Bethe equations, and an approximate solution for the Bethe roots is given. This yields approximate formulas for the ground-state energy and for the first excited-state energy. The obtained formulas work with remarkable precision for a wide range of parameters of the model, and are confirmed numerically. An expansion of the Bethe state vectors into a Fock space is also provided for evaluation of expectation values, although this does not have accuracy similar to that of the energies.