An exactly solvable BCS-Hubbard Model in arbitrary dimensions

Abstract

We introduce in this paper 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 $\Delta$ equals the hopping amplitude $t$. The nature of the solution is described in detail in this paper. 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 paper is just an example of a large class of exactly solvable lattice fermion models that can be constructed similarly.

5 pages, 3 figures

References in corpus (23)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Unpaired Majorana fermions in quantum wires
• Feshbach Resonances in Ultracold Gases
• Quantum orders in an exact soluble model
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Exact results for spin dynamics and fractionization in the Kitaev Model
• An exact chiral spin liquid with non-Abelian anyons
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Algebraic spin liquid in an exactly solvable spin model
• Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
• Weyl spin liquids
• Mosaic spin models with topological order
• A $\Gamma$-matrix generalization of the Kitaev model
• Exact Chiral Spin Liquid with Stable Spin Fermi Surface on the Kagome Lattice
• Thermodynamic properties of a small superconducting grain
• Conformal Field Theory and the Exact Solution of the BCS Hamiltonian
• Kaleidoscope of topological phases with multiple Majorana species
• Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
• Three-dimensional topological phases in a layered honeycomb spin-orbital model
• Exactly Solvable Models in Arbitrary Dimensions
• Entanglement of a 3D generalization of the Kitaev model on the diamond lattice

Cited by in corpus (13)

• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
• Solvable Periodic Anderson Model with Infinite-Range Hatsugai-Kohmoto Interaction: Ground-states and beyond
• Exactly Solvable Kondo Lattice Model in Anisotropic Limit
• Exact solutions in two-dimensional topological superconductors: Hubbard interaction induced spontaneous symmetry breaking
• Quantum oscillations in a doped Mott insulator beyond Onsager's relation
• Probing Majorana zero modes by measuring transport through an interacting magnetic impurity
• Solitonic in-gap modes in a superconductor-quantum antiferromagnet interface
• Exact Solution to Haldane-BCS-Hubbard Model Along the Symmetric Lines: Interaction Induced Topological Phase Transition
• Solvable BCS-Hubbard Liouvillians in arbitrary dimensions
• Generalized Falicov-Kimball Models
• Localization of Electronic States in Hybrid Nano-Ribbons in the Non-Perturbative Regime
• Confinement-induced Majorana modes in a nodal topological superconductor
• Unfrustrating the t-J Model: d-wave BCS Superconductivity in the $t^{\prime }$-$J_z$-$V$ Model