Static and dynamic properties of a one-dimensional spin-1/2 system

Isaías Vallejo-Fabila, Germán A. Luna-Acosta, E. Jonathan Torres Herrera

J. A. Plascak

The mean field renormalisation group approach is applied to the study of the static and dynamical critical properties of the spin- 1 / 2 anisotropic Heisenberg model in a transverse field. The critical surface and estimates of static and dynamical critical exponents are obtained for the one-, two-, and three-dimensional models.

Stanislav Alekseevich Molchanov, Nguyen The Long

S. Glocke, Andreas Klümper, Jesko Sirker

The density-matrix renormalization group (DMRG) applied to transfer matrices allows it to calculate static as well as dynamical properties of one-dimensional quantum systems at finite temperature in the thermodynamic limit. To this end the quantum system is mapped onto a two-dimensional classical system by a Trotter-Suzuki decomposition. Here we discuss two different mappings: The standard mapping onto a two-dimensional lattice with checkerboard structure as well as an alternative mapping introduced by two of us. For the classical system an appropriate quantum transfer matrix is defined which is then treated using a DMRG scheme. As applications, the calculation of thermodynamic properties for a spin-1/2 Heisenberg chain in a staggered magnetic field and the calculation of boundary contributions for open spin chains are discussed. Finally, we show how to obtain real time dynamics from a classical system with complex Boltzmann weights and present results for the autocorrelation function of the XXZ-chain.

James D. Johnson

Abel Rojo-Francàs, A. Polls, Bruno Juliá-Díaz

We provide a detailed study of the properties of a few interacting spin 1 / 2 fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of direct diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime. The N = 2 case is used to benchmark our numerical techniques with the known exact solution of the problem. After a detailed description of the numerical methods, in a tutorial-like manner, we present the static properties of the system for N = 2 , 3 , 4 and 5 particles, e.g., low-energy spectrum, one-body density matrix, ground-state densities. Then, we consider dynamical properties of the system exploring first the excitation of the breathing mode, using the dynamical structure function and corresponding sum-rules, and then a sudden quench of the interaction strength.