Spinon excitations in the XX chain: spectra, transition rates, observability

The exact one-to-one mapping between (spinless) Jordan-Wigner lattice fermions and (spin-1/2) spinons is established for all eigenstates of the one-dimensional s = 1=2 XX model on a lattice with an even or odd number N of lattice sites and periodic boundary conditions. Exact product formulas for the transition rates derived via Bethe ansatz are used to calculate asymptotic expressions of the 2-spinon and 4-spinon parts (for large even N) as well as of the 1-spinon and 3-spinon parts (for large odd N) of the dynamic spin structure factors. The observability of these spectral contributions is assessed for finite and infinite N.Comment: 19 pages, 10 figure

Domain wall dynamics in integrable and chaotic spin-1/2 chains

We study the time evolution of correlation functions, spin current, and local magnetization in an isolated spin-1/2 chain initially prepared in a sharp domain wall state. The results are compared with the level of spatial delocalization of the eigenstates of the system which is measured using the inverse participation ratio. Both integrable and non-integrable regimes are considered. Non-integrability is introduced to the integrable Hamiltonian with nearest neighbor couplings by adding a single site impurity field or by adding next-nearest-neighbor couplings. A monotonic correspondence between the enhancement of the level of delocalization, spin current and magnetization dynamics occurs in the integrable domain. This correspondence is however lost for chaotic models with weak Ising interactions.Comment: 9 pages, 5 figures, 1 tabl

The Algebraic Bethe Ansatz and Tensor Networks

We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a conserved number of down-spins. The tensor network formulation suggestes possible extensions of the Algebraic Bethe Ansatz to two dimensions

Line shapes of dynamical correlation functions in Heisenberg chains

We calculate line shapes of correlation functions by use of complete diagonalization data of finite chains and analytical implications from conformal field theory, density of states, and Bethe ansatz. The numerical data have different finite size accuracy in case of the imaginary and real parts in the frequency and time representations of spin-correlation functions, respectively. The low temperature, conformally invariant regime crosses over at $T^*\approx 0.7J$ to a diffusive regime that in turn connects continuously to the high temperature, interacting fermion regime. The first moment sum rule is determined.Comment: 13 pages REVTEX, 18 figure

The twisted XXZ chain at roots of unity revisited

The symmetries of the twisted XXZ spin-chain (alias the twisted six-vertex model) at roots of unity are investigated. It is shown that when the twist parameter is chosen to depend on the total spin an infinite-dimensional non-abelian symmetry algebra can be explicitly constructed for all spin sectors. This symmetry algebra is identified to be the upper or lower Borel subalgebra of the sl_2 loop algebra. The proof uses only the intertwining property of the six-vertex monodromy matrix and the familiar relations of the six-vertex Yang-Baxter algebra.Comment: 10 pages, 2 figures. One footnote and some comments in the conclusions adde

Taxonomy of particles in Ising spin chains

The statistical mechanics of particles with shapes on a one-dimensional lattice is investigated in the context of the $s=1$ Ising chain with uniform nearest-neighbor coupling, quadratic single-site potential, and magnetic field, which supports four distinct ground states: $|\uparrow\downarrow\uparrow\downarrow...>$, $|\circ\circ...>$, $|\uparrow\uparrow...>$, $|\uparrow\circ\uparrow\circ...>$. The complete spectrum is generated from each ground state by particles from a different set of six or seven species. Particles and elements of pseudo-vacuum are characterized by motifs (patterns of several consecutive site variables). Particles are floating objects that can be placed into open slots on the lattice. Open slots are recognized as permissible links between motifs. The energy of a particle varies between species but is independent of where it is placed. Placement of one particle changes the open-slot configuration for particles of all species. This statistical interaction is encoded in a generalized Pauli principle, from which the multiplicity of states for a given particle combination is determined and used for the exact statistical mechanical analysis. Particles from all species belong to one of four categories: compacts, hosts, tags, or hybrids. Compacts and hosts find open slots in segments of pseudo-vacuum. Tags find open slots inside hosts. Hybrids are tags with hosting capability. In the taxonomy of particles proposed here, `species' is indicative of structure and `category' indicative of function. The hosting function splits the Pauli principle into exclusion and accommodation parts. Near phase boundaries, the state of the Ising chain at low temperature is akin to that of miscible or immiscible liquids with particles from one species acting as surfactant molecules.Comment: 12 pages, 6 tables, 6 figure

Statistically interacting quasiparticles in Ising chains

The exclusion statistics of two complementary sets of quasiparticles, generated from opposite ends of the spectrum, are identified for Ising chains with spin s=1/2,1. In the s=1/2 case the two sets are antiferromagnetic domain walls (solitons) and ferromagnetic domains (strings). In the s=1 case they are soliton pairs and nested strings, respectively. The Ising model is equivalent to a system of two species of solitons for s=1/2 and to a system of six species of soliton pairs for s=1. Solitons exist on single bonds but soliton pairs may be spread across many bonds. The thermodynamics of a system of domains spanning up to $M$ lattice sites is amenable to exact analysis and shown to become equivalent, in the limit M -> infinity, to the thermodynamics of the s=1/2 Ising chain. A relation is presented between the solitons in the Ising limit and the spinons in the XX limit of the s=1/2 XXZ chain.Comment: 18 pages and 4 figure

Computation of Dynamical Structure Factors with the Recursion Method

We compute the energies and transition probabilities for low excitations in the one dimensional antiferromagnetic spin-1/2 Heisenberg model by means of the recursion method. We analyse finite size effects in the euclidian time ($\tau$)-representation and compare the resulting estimate for the thermodynamical limit with two parametrizations for the dynamical structure factors in the spectral ($\omega$)-representation.Comment: PostScript file with 13 pages + 5 figures, uuencoded compresse

Thermodynamics of statistically interacting quantum gas in D dimensions

We present the exact thermodynamics (isochores, isotherms, isobars, response functions) of a statistically interacting quantum gas in D dimensions. The results in D=1 are those of the thermodynamic Bethe ansatz for the nonlinear Schroedinger model, a gas with repulsive two-body contact potential. In all dimensions the ideal boson and fermion gases are recovered in the weak-coupling and strong-coupling limits, respectively. For all nonzero couplings ideal fermion gas behavior emerges for D>>1 and, in the limit D->infinity, a phase transition occurs at T>0. Significant deviations from ideal quantum gas behavior are found for intermediate coupling and finite D.Comment: 12 pages and 19 figure

Density matrix algorithm for the calculation of dynamical properties of low dimensional systems

I extend the scope of the density matrix renormalization group technique developed by White to the calculation of dynamical correlation functions. As an application and performance evaluation I calculate the spin dynamics of the 1D Heisenberg chain.Comment: 4 pages + 4 figures in one Latex + 4 postscript file