Exactly Solvable Models

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

Zewei Chen, Xiaohui Li, Tai Kai Ng

We introduce in this Letter an exact solvable BCS-Hubbard model in arbitrary dimensions. The model describes a p-wave BCS superconductor with equal spin pairing moving on a bipartite (cubic, square, etc.) lattice with on-site Hubbard interaction U. We show that the model becomes exactly solvable for arbitrary U when the BCS pairing amplitude Δ equals the hopping amplitude t. The nature of the solution is described in detail in this Letter. The construction of the exact solution is parallel to the exactly solvable Kitaev honeycomb model for S=1/2 quantum spins and can be viewed as a generalization of Kitaev's construction to S=1/2 interacting lattice fermions. The BCS-Hubbard model discussed in this Letter is just an example of a large class of exactly solvable lattice fermion models that can be constructed similarly.

Yves Brihaye, Ancilla Nininahazwe

The original Jaynes–Cummings model is described by a Hamiltonian which is Hermitian and exactly solvable. Here, we extend this model by several types of interactions leading to a non-Hermitian operator which does not satisfy the physical condition of spacetime reflection symmetry ( PT symmetry). The new Hamiltonians are either exactly solvable admitting an entirely real spectrum or quasi-exactly solvable with a real algebraic part of their spectrum.

Gerald Dennis Mahan

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.