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The recently introduced two-parameter eight-state $U_q[gl(3|1)]$ supersymmetric fermion model is extended to include boundary terms. Nine classes of boundary conditions are constructed, all of which are shown to be integrable via the graded…

Statistical Mechanics · Physics 2007-05-23 A. J. Bracken , X. -Y. Ge , Y. -Z. Zhang , H. -Q. Zhou

I present a currents algebra for the two-sites Bose-Hubbard model, generalize the Heisenberg equation of motion to write the second time derivative of the currents operators and use it to get the quantum dynamics of the currents. For…

Quantum Gases · Physics 2016-05-06 Gilberto N. Santos Filho

We present a deep neural network (DNN)-based model (HubbardNet) to variationally find the ground state and excited state wavefunctions of the one-dimensional and two-dimensional Bose-Hubbard model. Using this model for a square lattice with…

Strongly Correlated Electrons · Physics 2023-09-04 Ziyan Zhu , Marios Mattheakis , Weiwei Pan , Efthimios Kaxiras

We study a matrix product representation of the Bethe ansatz state for the Lieb-Linger model describing the one-dimensional Bose gas with delta-function interaction. We first construct eigenstates of the discretized model in the form of…

Statistical Mechanics · Physics 2014-11-20 Isao Maruyama , Hosho Katsura

We implement the Bethe anstaz method for the elliptic quantum group $E_{\tau,\eta}(A_2^{(2)})$. The Bethe creation operators are constructed as polynomials of the Lax matrix elements expressed through a recurrence relation. We also give the…

Quantum Algebra · Mathematics 2009-11-13 Nenad Manojlovic , Zoltan Nagy

We consider open XXX spins chain with two general boundary matrices submitted to one constraint, which is equivalent to the possibility to put the two matrices in a triangular form. We construct Bethe vectors from a generalized algebraic…

Mathematical Physics · Physics 2015-06-11 S. Belliard , N. Crampe , E. Ragoucy

The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site…

Strongly Correlated Electrons · Physics 2007-05-23 M. M. Sanchez , A. Avella , F. Mancini

The one-dimensional Bose-Hubbard model in large-$U$ limit has been studied via reducing and mapping the Hamiltonian to a simpler one. The eigenstates and eigenvalues have been obtained exactly in the subspaces with fixed numbers of single-…

Strongly Correlated Electrons · Physics 2021-12-21 Yong Zheng

The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their…

Condensed Matter · Physics 2009-10-31 J. Gruneberg

The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct…

We investigate bound states in the one-dimensional two-particle Bose-Hubbard model with an attractive ($V> 0$) impurity potential. This is a one-dimensional, discrete analogy of the hydrogen negative ion H$^-$ problem. There are several…

Quantum Gases · Physics 2013-02-19 J. M. Zhang , Daniel Braak , Marcus Kollar

We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra $U_q(\widehat{\mathfrak{gl}}_{n})$. We also present a sum…

Mathematical Physics · Physics 2018-03-01 A. Hutsalyuk , A. Liashyk , S. Z. Pakuliak , E. Ragoucy , N. A. Slavnov

An improved variational ansatz is proposed to capture the most striking properties of the ground state of a slightly biased attractive two-site Bose-Hubbard Hamiltonian. Our ansatz, albeit its simplicity, is found to capture well the exact…

Quantum Gases · Physics 2015-05-30 Marina Melé-Messeguer , Bruno Juliá-Díaz , Artur Polls

We found the eigenvalues of the transfer matrix for the 2-D inhomogeneous statistical model with twisted boundary condition by using the analytic Bethe Ansatz method. In the uniform case, the derived hamiltonian generalizes the 1-D Hubbard…

Statistical Mechanics · Physics 2008-02-03 Ruihong Yue , Tetsuo Deguchi

In this work we have developed the essential tools for the algebraic Bethe ansatz solution of integrable vertex models invariant by a unique U(1) charge symmetry. The formulation is valid for arbitrary statistical weights and respective…

Mathematical Physics · Physics 2009-11-13 C. S. Melo , M. J. Martins

The form factor equations are solved for an SU(N) invariant S-matrix under the assumption that the anti-particle is identified with the bound state of N-1 particles. The solution is obtained explicitly in terms of the nested off-shell Bethe…

High Energy Physics - Theory · Physics 2008-11-26 Hratchia M. Babujian , Angela Foerster , Michael Karowski

We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. Using the…

Mathematical Physics · Physics 2007-05-23 N. Crampe , C. A. S. Young

This paper continues our recent studies on the algebraic Bethe ansatz for the RTT-algebras of sp($2n$) and o($2n$) types. In these studies, we encountered the RTT-algebras which we called An. The next step in our construction of the Bethe…

Mathematical Physics · Physics 2020-08-12 C. Burdik , O. Navratil

Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where…

Quantum Physics · Physics 2017-02-09 Feng Pan , Yao-Zhong Zhang , Jerry P. Draayer

We study quantum integrable models with GL(3) trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz. Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the…

Mathematical Physics · Physics 2013-10-08 Samuel Belliard , Stanislav Pakuliak , Eric Ragoucy , Nikita A. Slavnov