Bill Sutherland

Exact ground state of a quantum mechanical antiferromagnet

We present some exact results for the ground state of a quantum mechanical antiferromagnetic model in the two dimensions with next-nearest neighbor interactions.

Nondiffractive scattering: Scattering from kaleidoscopes

We introduce and exactly solve a series of multidimensional scattering problems. The potential is a generalization of the delta function potential and has the symmetry of a kaleidoscope. The solution demonstrates the property of nondiffractive scattering. The bound state energies are calculated exactly for all cases. We prove a remarkable identity for certain finite groups.

Exciton, spinon, and spin wave modes in a soluble one-dimensional many-body system

In this paper, we present the exact solution (in the thermodynamic limit) to a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential s(s+1)/sinh 2 (r), while unlike particles interact with a pair potential -s(s+1)/cosh 2 (r). We first give a proof of integrability, then derive the coupled equations determining the complete spectrum. All singularities occur in the ground state when there are equal numbers of the two components; we give explicit results for the ground state and low-lying states in this case

Exact Solution of a Large Class of Interacting Quantum Systems Exhibiting Ground State Singularities

We demonstrate how to construct a large class of interacting quantum systems for which an exact solution may be found for the ground state wave function and ground state energy for some range of interaction parameters. It is shown that the ground state exhibits singularities in these cases, and in some simple instances the exact ground state phase diagram and critical indices are also found.

Critical exponents for the sinh-cosh interaction model in the zero sector.

In this paper, we continue our investigation of a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential {ital s}({ital s}+1)/sinh{sup 2}({ital r}), while unlike particles interact with a pair potential {minus}{ital s}({ital s}+1)/cosh{sup 2}({ital r}). For an equal number of particles of the two components, the ground state for {ital s}{gt}0 corresponds to an antiferromagnet/insulator. Excitations consist of a gapless pair-hole--pair continuum, a two-particle continuum with gap and excitons with gap. For {minus}1{lt}{ital s}{lt}0, the system has two gapless excitations---a particle-hole continuum and a two-spin-wave continuum. Using finite-size scaling methods of conformal field theory, we calculate the asymptotic expressions and critical exponents for correlation functions of these gapless excitations at zero temperature. The conformal structure is closely related to the Hubbard model with repulsive on-site interaction.

Gaps in the Heisenberg-Ising model.

We report on the closing of gaps in the ground state of the critical Heisenberg-Ising chain at momentum

Survey of exactly solved models for conducting polymers

\pi

Test of conformal invariance in a one-dimensional quantum liquid with long-range interactions

. For half-filling, the gap closes at special values of the anisotropy

Conservation laws in the continuum systems

\Delta= \cos(\pi/Q)

Exact solution of a one-dimensional multicomponent lattice gas with hyperbolic interaction.

,