Integro-Difference Equation for a correlation function of the spin-12{1\over2} Heisenberg XXZ chain

We consider the Ferromagnetic-String-Formation-Probability correlation function (FSFP) for the spin-$1\over 2$ Heisenberg XXZ chain. We construct a completely integrable system of integro-difference equations (IDE), which has the FSFP as a $\tau$-function. We derive the associated Riemann-Hilbert problem and obtain the large distance asymptotics of the FSFP correlator in some limiting cases.Comment: 14 pages, latex+epsf, 1 figur

The Crab pulsar light curve in the soft gamma ray range: FIGARO II results

The FIGARO II experiment (a large area, balloon borne, crystal scintillator detector working from 0.15 to 4.3 MeV) observed the Crab pulsar on 1990 Jul. 9 for about seven hours. The study of the pulse profile confirms some structures detected with a low significance during the shorter observation of 1986, and adds new important elements to the picture. In particular, between the two main peaks, two secondary peaks appear centered at phase values 0.1 and 0.3, in the energy range 0.38 to 0.49 MeV; in the same energy range, a spectral feature at 0.44 MeV, interpreted as a redshifted positron annihilation line, was observed during the same balloon flight in the phase interval including the second main peak and the neighboring secondary peak. If the phase interval considered is extended to include also the other secondary peak, the significance of the spectral line appears to increase

Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations

We calculate exactly matrix elements between states that are not eigenstates of the quantum XY model for general anisotropy. Such quantities therefore describe non equilibrium properties of the system; the Hamiltonian does not contain any time dependence. These matrix elements are expressed as a sum of Pfaffians. For single particle excitations on the ground state the Pfaffians in the sum simplify to determinants.Comment: 11 pages, no figures; revtex. Minor changes in the text; list of refs. modifie

A solvable model of a random spin-1/2 XY chain

The paper presents exact calculations of thermodynamic quantities for the spin-1/2 isotropic XY chain with random lorentzian intersite interaction and transverse field that depends linearly on the surrounding intersite interactions.Comment: 14 pages (Latex), 2 tables, 13 ps-figures included, (accepted for publication in Phys.Rev.B

Multicritical crossovers near the dilute Bose gas quantum critical point

Many zero temperature transitions, involving the deviation in the value of a $U(1)$ conserved charge from a quantized value, are described by the dilute Bose gas quantum critical point. On such transitions, we study the consequences of perturbations which break the symmetry down to $Z_N$ in $d$ spatial dimensions. For the case $d=1$, $N=2$, we obtain exact, finite temperature, multicritical crossover functions by a mapping to an integrable lattice model.Comment: 10 pages, REVTEX 3.0, 2 EPS figure

Exact solution of Markovian master equations for quadratic fermi systems: thermal baths, open XY spin chains, and non-equilibrium phase transition

We generalize the method of third quantization to a unified exact treatment of Redfield and Lindblad master equations for open quadratic systems of n fermions in terms of diagonalization of 4n x 4n matrix. Non-equilibrium thermal driving in terms of the Redfield equation is analyzed in detail. We explain how to compute all physically relevant quantities, such as non-equilibrium expectation values of local observables, various entropies or information measures, or time evolution and properties of relaxation. We also discuss how to exactly treat explicitly time dependent problems. The general formalism is then applied to study a thermally driven open XY spin 1/2 chain. We find that recently proposed non-equilibrium quantum phase transition in the open XY chain survives the thermal driving within the Redfield model. In particular, the phase of long-range magnetic correlations can be characterized by hypersensitivity of the non-equilibrium-steady state to external (bath or bulk) parameters. Studying the heat transport we find negative thermal conductance for sufficiently strong thermal driving, as well as non-monotonic dependence of the heat current on the strength of the bath coupling.Comment: 24 pages, 12 figures, submitted to New Journal of Physics, Focus issue "Quantum Information and Many-Body Theory

Integrable generalizations of Schrodinger maps and Heisenberg spin models from Hamiltonian flows of curves and surfaces

A moving frame formulation of non-stretching geometric curve flows in Euclidean space is used to derive a 1+1 dimensional hierarchy of integrable SO(3)-invariant vector models containing the Heisenberg ferromagnetic spin model as well as a model given by a spin-vector version of the mKdV equation. These models describe a geometric realization of the NLS hierarchy of soliton equations whose bi-Hamiltonian structure is shown to be encoded in the Frenet equations of the moving frame. This derivation yields an explicit bi-Hamiltonian structure, recursion operator, and constants of motion for each model in the hierarchy. A generalization of these results to geometric surface flows is presented, where the surfaces are non-stretching in one direction while stretching in all transverse directions. Through the Frenet equations of a moving frame, such surface flows are shown to encode a hierarchy of 2+1 dimensional integrable SO(3)-invariant vector models, along with their bi-Hamiltonian structure, recursion operator, and constants of motion, describing a geometric realization of 2+1 dimensional bi-Hamiltonian NLS and mKdV soliton equations. Based on the well-known equivalence between the Heisenberg model and the Schrodinger map equation in 1+1 dimensions, a geometrical formulation of these hierarchies of 1+1 and 2+1 vector models is given in terms of dynamical maps into the 2-sphere. In particular, this formulation yields a new integrable generalization of the Schrodinger map equation in 2+1 dimensions as well as a mKdV analog of this map equation corresponding to the mKdV spin model in 1+1 and 2+1 dimensions.Comment: Published version with typos corrected. Significantly expanded version of a talk given by the first author at the 2008 BIRS workshop on "Geometric Flows in Mathematics and Physics

Density-Matrix Spectra of Solvable Fermionic Systems

We consider non-interacting fermions on a lattice and give a general result for the reduced density matrices corresponding to parts of the system. This allows to calculate their spectra, which are essential in the DMRG method, by diagonalizing small matrices. We discuss these spectra and their typical features for various fermionic quantum chains and for the two-dimensional tight-binding model.Comment: 12 pages and 9 figure