Uniqueness of the bosonization of the Uq(su(2)k)U_q(su(2)_k) quantum current algebra

Four apparently different bosonizations of the $U_q(su(2)_k)$ quantum current algebra for arbitrary level $k$ have recently been proposed in the literature. However, the relations among them have so far remained unclear except in one case. Assuming a special standard form for the $U_q(su(2)_k)$ quantum currents, we derive a set of general consistency equations that must be satisfied. As particular solutions of this set of equations, we recover two of the four bosonizations and we derive a new and simpler one. Moreover, we show that the latter three, and the remaining two bosonizations which cannot be derived directly from this set of equations since by construction they do not have the standard form, are all related to each other through some redefinitions of their Heisenberg boson oscillators.Comment: 25 page

Optical absorption of spin ladders

We present a theory of phonon-assisted optical two-magnon absorption in two-leg spin-ladders. Based on the strong intra-rung-coupling limit we show that collective excitations of total spin S=0, 1 and 2 exist outside of the two-magnon continuum. It is demonstrated that the singlet collective state has a clear signature in the optical spectrum.Comment: 4 pages, 3 figure

Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet

The exact expression derived by Bougourzi, Couture, and Kacir for the 2-spinon contribution to the dynamic spin structure factor $S_{zz}(q,\omega)$ of he one-dimensional $S$=1/2 Heisenberg antiferromagnet at $T=0$ is evaluated for direct comparison with finite-chain transition rates ($N\leq 28$) and an approximate analytical result previously inferred from finite-$N$ data, sum rules, and Bethe-ansatz calculations. The 2-spinon excitations account for 72.89% of the total intensity in $S_{zz}(q,\omega)$. The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the 2-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and $q$-dependent susceptibility are determined via sum rules.Comment: 6 pages (RevTex) and 5 figures (Postscript

Spectrum and transition rates of the XX chain analyzed via Bethe ansatz

As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the Bethe ansatz solutions for the entire XX spectrum, which include states with real and complex magnon momenta. We discuss the relation between the spinon or magnon quasiparticles (Bethe ansatz) and the lattice fermions (Jordan-Wigner representation). We present determinantal expressions for transition rates of spin fluctuation operators between Bethe wave functions and reduce them to product expressions. We apply the new formulas to two-spinon transition rates for chains with up to N=4096 sites.Comment: 11 pages, 4 figure

Dynamical structure factor of the anisotropic Heisenberg chain in a transverse field

We consider the anisotropic Heisenberg spin-1/2 chain in a transverse magnetic field at zero temperature. We first determine all components of the dynamical structure factor by combining exact results with a mean-field approximation recently proposed by Dmitriev {\it et al}., JETP 95, 538 (2002). We then turn to the small anisotropy limit, in which we use field theory methods to obtain exact results. We discuss the relevance of our results to Neutron scattering experiments on the 1D Heisenberg chain compound ${\rm Cs_2CoCl_4}$.Comment: 13 pages, 14 figure

Jordan-Wigner approach to dynamic correlations in spin-ladders

We present a method for studying the excitations of low-dimensional quantum spin systems based on the Jordan-Wigner transformation. Using an extended RPA-scheme we calculate the correlation function of neighboring spin flips which well approximates the optical conductivity of ${\rm Sr_2CuO_3}$. We extend this approach to the two-leg $S=1/2$--ladder by numbering the spin operators in a meander-like sequence. We obtain good agreement with the optical conductivity of the spin ladder compound (La,Ca)$_{14}$Cu$_{24}$O$_{41}$ for polarization along the rungs. For polarization along the legs higher order correlations are important to explain the weight of high-energy continuum excitations and we estimate the contribution of 4-- and 6--fermion processes.Comment: 15 pages, 16 figure

Charge and spin dynamics in the one-dimensional t−Jzt-J_z and t−Jt-J models

The impact of the spin-flip terms on the (static and dynamic) charge and spin correlations in the Luttinger-liquid ground state of the 1D $t-J$ model is assessed by comparison with the same quantities in the 1D $t-J_z$ model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At $J_z/t=0^+$ we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. The $t-J_z$ charge excitations (but not the spin excitations) at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the $t-J$ model. In the $t-J_z$ model, phase separation is accompanied by N\'eel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration (topological long-range order). In the $t-J$ model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations (dominated by 2-spinon excitations) in the phase-separated state.Comment: 11 pages (RevTex). 14 Figures available from author