Exact form factors for the Josephson tunneling current and relative particle number fluctuations in a model of two coupled Bose-Einstein condensates

Form factors are derived for a model describing the coherent Josephson tunneling between two coupled Bose-Einstein condensates. This is achieved by studying the exact solution of the model in the framework of the algebraic Bethe ansatz. In this approach the form factors are expressed through determinant representations which are functions of the roots of the Bethe ansatz equations.Comment: 11 pages, latex, no figures, final version to appear in Lett. Math. Phy

Exact solvability in contemporary physics

We review the theory for exactly solving quantum Hamiltonian systems through the algebraic Bethe ansatz. We also demonstrate how this theory applies to current studies in Bose-Einstein condensation and metallic grains which are of nanoscale size.Comment: 23 pages, no figures, to appear in ``Classical and Quantum Nonlinear Integrable Systems'' ed. A. Kund

Ground-State Fidelity and Kosterlitz-Thouless Phase Transition for Spin 1/2 Heisenberg Chain with Next-to-the-Nearest-Neighbor Interaction

The Kosterlitz-Thouless transition for the spin 1/2 Heisenberg chain with the next-to-the-nearest-neighbor interaction is investigated in the context of an infinite matrix product state algorithm, which is a generalization of the infinite time-evolving block decimation algorithm [G. Vidal, Phys. Rev. Lett. \textbf{98}, 070201 (2007)] to accommodate both the next-to-the-nearest-neighbor interaction and spontaneous dimerization. It is found that, in the critical regime, the algorithm automatically leads to infinite degenerate ground-state wave functions, due to the finiteness of the truncation dimension. This results in \textit{pseudo} symmetry spontaneous breakdown, as reflected in a bifurcation in the ground-state fidelity per lattice site. In addition, this allows to introduce a pseudo-order parameter to characterize the Kosterlitz-Thouless transition.Comment: 4 pages, 4 figure

Quantum fluctuations in the spiral phase of the Hubbard model

We study the magnetic excitations in the spiral phase of the two--dimensional Hubbard model using a functional integral method. Spin waves are strongly renormalized and a line of near--zeros is observed in the spectrum around the spiral pitch $\pm{\bf Q}$. The possibility of disordered spiral states is examined by studying the one--loop corrections to the spiral order parameter. We also show that the spiral phase presents an intrinsic instability towards an inhomogeneous state (phase separation, CDW, ...) at weak doping. Though phase separation is suppressed by weak long--range Coulomb interactions, the CDW instability only disappears for sufficiently strong Coulomb interaction.Comment: Figures are NOW appended via uuencoded postscript fil

Critical domain-wall dynamics of model B

With Monte Carlo methods, we simulate the critical domain-wall dynamics of model B, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, a dynamic scaling form is revealed. Due to the existence of the quasi-random walkers, the magnetization shows intrinsic dependence on the lattice size $L$. A new exponent which governs the $L$-dependence of the magnetization is measured to be $\sigma=0.243(8)$.Comment: 10pages, 4 figure