C. J. Hamer

Conformal Anomaly and Surface Energy for Potts and Ashkin-teller Quantum Chains

Exact equivalences between the critical quantum Potts and Ashkin-Teller chains and a modified XXZ Heisenberg chain have recently been derived by Alcaraz et al (1987). The leading finite-size corrections to the ground-state energies of these chains are derived using the methods of de Vega and Woynarovich (1985) and Eckle. Exact results are then obtained for the conformal anomaly of each model, and for the surface energy in the case of free boundaries.

Finite-lattice extrapolations for Z3 and Zs models

A method is presented to accelerate the convergence of finite-lattice sequences to their bulk limit. The calculation of highly accurate estimates of the critical parameters of the bulk system is then possible. Applied to the Hamiltonian version of the Z3 model (three-state Potts model) in (1+1) dimensions, these techniques yield estimates for the exponents gamma =1.444+or-0.0001, nu =0.8333+or-0.0003 and alpha =0.33+or-0.01. For the Z5 model, the presence of a Kosterlitz-Thouless transition is confirmed.

PHASE DIAGRAM OF A HEISENBERG SPIN-PEIERLS MODEL WITH QUANTUM PHONONS

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

Strong-coupling expansions for multiparticle excitations: continuum and bound states

We present a new linked cluster expansion for calculating properties of multiparticle excitation spectra to high orders. We use it to obtain the two-particle spectra for systems of coupled spin-half dimers. We find that even for weakly coupled dimers the spectrum is very rich, consisting of many bound states. The number of bound states depends on both geometry of coupling and frustration. Many of the bound states can only be seen by going to sufficiently high orders in the perturbation theory, showing the extended character of the pair attraction.

Ground-state parameters, finite-size scaling, and low-temperature properties of the two-dimensional S = 1 2 XY model

We present high-precision quantum Monte Carlo results for the

Phase diagram of the one-dimensional Holstein model of spinless fermions

S=\frac{1}{2}

Finite-size corrections for ground states of the XXZ Heisenberg chain

\mathrm{XY}

Finite-lattice methods in quantum Hamiltonian field theory. I. The Ising model

model on a two-dimensional square lattice, in the ground state as well as at finite temperature. The energy, the spin stiffness, the magnetization, and the susceptibility are calculated and extrapolated to the thermodynamic limit. For the ground state, we test a variety of finite-size scaling predictions of effective Lagrangian theory and find good agreement and consistency between the finite-size corrections for different quantities. The low-temperature behavior of the susceptibility and the internal energy is also in good agreement with theoretical predictions.

Density Matrix Renormalisation Group Approach to the Massive Schwinger Model

The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is studied using a new variant of the density matrix renormalization group. By examining various low-energy excitations of finite chains, the metal-insulator phase boundary is determined precisely and agrees with the predictions of strong coupling theory in the antiadiabatic regime and is consistent with renormalization group arguments in the adiabatic regime. The Luttinger liquid parameters, determined by finite-size scaling, are consistent with a Kosterlitz-Thouless transition.