Exact diagonalization of the generalized supersymmetric t-J model with boundaries

We study the generalized supersymmetric $t-J$ model with boundaries in three different gradings: FFB, BFF and FBF. Starting from the trigonometric R-matrix, and in the framework of the graded quantum inverse scattering method (QISM), we solve the eigenvalue problems for the supersymmetric $t-J$ model. A detailed calculations are presented to obtain the eigenvalues and Bethe ansatz equations of the supersymmetric $t-J$ model with boundaries in three different backgrounds.Comment: Latex file, 32 page

Valence bond solid formalism for d-level one-way quantum computation

The d-level or qudit one-way quantum computer (d1WQC) is described using the valence bond solid formalism and the generalised Pauli group. This formalism provides a transparent means of deriving measurement patterns for the implementation of quantum gates in the computational model. We introduce a new universal set of qudit gates and use it to give a constructive proof of the universality of d1WQC. We characterise the set of gates that can be performed in one parallel time step in this model.Comment: 26 pages, 9 figures. Published in Journal of Physics A: Mathematical and Genera

Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries

The one-dimensional Hubbard model with open boundary conditions is exactly solved by means of algebraic Bethe ansatz. The eigenvalue of the transfer matrix, the energy spectrum as well as the Bethe ansatz equations are obtained.Comment: Only LaTex file; no figur

Entanglement and Density Matrix of a Block of Spins in AKLT Model

We study a 1-dimensional AKLT spin chain, consisting of spins $S$ in the bulk and $S/2$ at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension $(S+1)^{2}$. This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to $\ln(S+1)^{2}$.Comment: Revised version, typos corrected, references added, 31 page

Quantum Impurity Entanglement

Entanglement in J_1-J_2, S=1/2 quantum spin chains with an impurity is studied using analytic methods as well as large scale numerical density matrix renormalization group methods. The entanglement is investigated in terms of the von Neumann entropy, S=-Tr rho_A log rho_A, for a sub-system A of size r of the chain. The impurity contribution to the uniform part of the entanglement entropy, S_{imp}, is defined and analyzed in detail in both the gapless, J_2 <= J_2^c, as well as the dimerized phase, J_2>J_2^c, of the model. This quantum impurity model is in the universality class of the single channel Kondo model and it is shown that in a quite universal way the presence of the impurity in the gapless phase, J_2 <= J_2^c, gives rise to a large length scale, xi_K, associated with the screening of the impurity, the size of the Kondo screening cloud. The universality of Kondo physics then implies scaling of the form S_{imp}(r/xi_K,r/R) for a system of size R. Numerical results are presented clearly demonstrating this scaling. At the critical point, J_2^c, an analytic Fermi liquid picture is developed and analytic results are obtained both at T=0 and T>0. In the dimerized phase an appealing picure of the entanglement is developed in terms of a thin soliton (TS) ansatz and the notions of impurity valence bonds (IVB) and single particle entanglement (SPE) are introduced. The TS-ansatz permits a variational calculation of the complete entanglement in the dimerized phase that appears to be exact in the thermodynamic limit at the Majumdar-Ghosh point, J_2=J_1/2, and surprisingly precise even close to the critical point J_2^c. In appendices the relation between the finite temperature entanglement entropy, S(T), and the thermal entropy, S_{th}(T), is discussed and and calculated at the MG-point using the TS-ansatz.Comment: 62 pages, 27 figures, JSTAT macro