Exact Results for One-Dimensional Systems

Michael Fowler

Bill Sutherland, Joel F. Campbell

We investigate solitons in the one-dimensional classical many-body system of particles interacting by an inverse-square pair potential. We use a combination of numerical results for finite systems, and exact results for the continuum limit, to deduce properties of solitons in the thermodynamic limit. Two remarkable conjectures are supported by these results, and the correspondence with the exact results for the quantum system is established.

James Murray Hill

Salvatore R. Manmana

The level of current understanding of the physics of time‐dependent strongly correlated quantum systems is far from complete, principally due to the lack of effective controlled approaches. Recently, there has been progress in the development of approaches for one‐dimensional systems. We describe recent developments in the construction of numerical schemes for general (one‐dimensional) Hamiltonians: in particular, schemes based on exact diagonalization techniques and on the density matrix renormalization group method (DMRG). We present preliminary results for spinless fermions with nearest‐neighbor‐interaction and investigate their accuracy by comparing with exact results.

Edgard Elbaz