A Three-Dimensional Solvable Model

Vladimir V. Bazhanov, R. J. Baxter

Vladislav Popkov

We review the method of constructing solvable models in three dimensions, by starting from two-dimensional solvable models. The solvable three-dimensional models thus constructed do possess positive Boltzmann weights. These are multilayer two-dimensional systems with interactions in the third direction which can be interpreted as nearest-neighbour interactions. The set of conditions corresponding to the general 3D multilayer extension of solvable 2D models is derived.

Ashok Kumar Kapoor, Prasanta Kumar Panigrahi, S. Sree Ranjani

D. Ya. Petrina

Daniel Ben-Zion, Diptarka Das, John McGreevy

We develop a scheme to make exactly solvable gauge theories whose electric flux lines host (1+1)-dimensional topological phases. We use this exact ``decorated-string-net'' framework to construct several classes of interesting models. In particular, we construct an exactly solvable model of a quantum spin liquid whose (gapped) elementary excitations form doublets under an internal symmetry, and hence may be regarded as spin-carrying spinons. The model may be formulated, and is solvable, in any number of dimensions on any bipartite graph. Another example, in any dimension, has ${\mathbb{Z}}_{2}$ topological order and anyons which are Kramers' doublets of time-reversal symmetry. Further, we make exactly solvable models of three-dimensional topological paramagnets.

E. de Prunelé

A solvable model for non relativistic quantum scattering in three-dimensional space of a particle off several interactions centred at n arbitrary points is given. The interaction at one centre can be very different from the interaction at another. Each interaction centred at a given point can be effective on any partial wave with respect to this point. Each centred interaction is a sum of projectors on a finite number of partial waves relative to the centre. Elementary applications are given.