While Ising-type interactions are ideal for implementing controlled phase flip gates in one-way quantum computing, natural interactions between solid-state qubits are most often described by either the XY or the Heisenberg models. We show an efficient way of generating cluster states directly using either the imaginary SWAP (iSWAP) gate for the XY model, or the sqrt[SWAP] gate for the Heisenber...

We present an investigation of the sinh-cosh (SC) interaction model with twisted boundary conditions. We argue that, when unlike particles repel, the SC model may be usefully viewed as a Heisenberg-Ising fluid with moving Heisenberg-Ising spins. We derive the Luttinger liquid relation for the stiffness and the susceptibility, both from conformal arguments, and directly from the integral equatio...

We present a simple method, combining the density-matrix renormalization-group (DMRG) algorithm with finite-size scaling, which permits the study of critical behavior in quantum spin chains. Spin moments and dimerization are induced by boundary conditions at the chain ends and these exhibit power-law decay at critical points. Results are presented for the spin-1/2 Heisenberg antiferromagnet; an...

An upper bound Te for the critical temperature of a class of spin systems which includes the Heisenberg ferromagnet is derived. The analyticity of the free energy as a function of the temperature, the external magnetic field, and the interaction potentials, is demonstrated in a domain which includes all temperatures T > Tc For the isotropic Heisenberg ferromagnet in v dimensions we find the poo...