The SLAC real-space renormalization group method is used to study one-dimensional antiferromagnetic chains at zero temperature. Calculations using three-site blocks (for the Heisenberg-Ising model) and two-site blocks (for the isotropic Heisenberg model) are compared with exact results. In connection with the two-site calculation a duality transformation is introduced under which the isotropic ...

We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMA-completeness for approximating the ground energy of the Bose-Hubbard model on simple graphs. Using a connection between the XY and Bose-Hubbard mod...

We consider the spin1 2 XY chain in a transverse field with regularly varying exchange interactions and on-site fields. In two limiting cases of the isotropic (XX) and extremely anisotropic (Ising) exchange interaction the thermodynamic quantities are calculated rigorously with the help of continued fractions. We discuss peculiarities of the low-temperature magnetic properties and a possibility...