Related papers: Some aspects of functional Bethe ansatz
We examine the question of whether Bethe's ansatz reproduces all states in the periodic Heisenberg XXZ and XXX spin chains. As was known to Bethe himself, there are states for which the Bethe momenta $k_n$ diverge: these are in fact the…
We construct an integrable physical model of a single particle scattering with impurities spread on a circle. The $S$-matrices of the scattering with the impurities are such that the quantized energies of this system, coming from the Bethe…
This thesis presents an introduction to the class of Richardson-Gaudin integrable models, with special focus on the Bethe ansatz wave function, and investigates ways of applying the properties of Richardson-Gaudin models both in and out of…
We solve the two-channel Anderson impurity model using the Bethe-Ansatz. We determine the ground state and derive the thermodynamics, obtaining the impurity entropy and specific heat over the full range of temperature. We show that the low…
We consider the weakly asymmetric exclusion process with $N=L/2$ particles on a periodic lattice of $L$ sites, and hopping rates $1$ and $q=1-\mu/\sqrt{L}$ respectively in the forward and in the backward direction. Using Bethe ansatz, we…
The Bethe Ansatz equations for the one-dimensional Hubbard model are reexamined. A new procedure is introduced to properly include bound states. The corrected equations lead to new elementary excitations away from half-filling.
A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state…
Integrable Kondo impurities in two cases of the one-dimensional $t-J$ model are studied by means of the boundary ${\bf Z}_2$-graded quantum inverse scattering method. The boundary $K$ matrices depending on the local magnetic moments of the…
The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the…
The small polaron with generic, nondiagonal boundary terms is investigated within the framework of quantum integrability. The fusion hierarchy of the transfer matrices and its truncation for particular values of the anisotropy parameter are…
We consider a generalisation of the p+ip pairing Hamiltonian with external interaction terms. These terms allow for the exchange of particles between the system and its environment. As a result the u(1) symmetry associated with conservation…
The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite dimensional algebra are investigated. Using a suitable functional representation, all eigenfunctions are shown to obey a second-order…
The dynamical fluctuations in approaches such as dynamical mean-field theory (DMFT) allow for the self-consistent optimization of a local fragment, hybridized with a true correlated environment. We show that these correlated environmental…
We develop an exact non-perturbative framework to compute steady-state properties of quantum-impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates…
A Bethe Ansatz solution of a (modified) Hubbard chain with a Kondo impurity of arbitrary spin S at a highly symmetric line of parameter space is proposed and explored. Our results confirm the existence of a strong-coupling (line of)…
We employ a discrete integral-reflection representation of the double affine Hecke algebra of type $C^\vee C$ at the critical level q=1, to endow the open finite $q$-boson system with integrable boundary interactions at the lattice ends. It…
We study the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification allows us to…
Quantum invariants of the orbit dependent pairing problem are identified in the limit where the orbits become degenerate. These quantum invariants are simultaneously diagonalized with the help of the Bethe ansatz method and a symmetry in…
We found the eigenvalues of the transfer matrices for the 1-D Hubbard model and for the coupled XY model with twisted boundary condition by using the analytic Bethe Ansatz method. Under a particular condition the two models have the same…
We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(m|n)$-invariant $R$-matrix. We compute the norm of the Hamiltonian eigenstates. Using the notion of a generalized model we show…