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 ∆ 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.

Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

“…Here, the fermion at site i is composed of Majorana fermions η i and γ i . According to Kitaev [15,43], and in agreement with subsequent numerical verification [39] for the ground state in the thermodynamic limit, the product of the two η Majorana fermions reduces to a site-independent gauge field due to local conservations [43,45]. Consequently, as long as we are interested in ground states of the model, the z-component coupling terms can be treated as if they are only quadratic (in terms of γ Majorana fermions) and the quadratic in the η fermions can be replaced by the constant gauge field value.…”

“…Because of the generality of the exact solution procedures for the Kitaev-inspired models, the methods presented here can be readily applied to other Kitaev-inspired models. These include, for example, the generalizations of the original Kitaev honeycomb model to different lattices [16-19, 27, 34], different dimensions [20,23,24,[38][39][40], and higher spins [26,29]. In the Appendix D, one additional example of applying our approach to the 1D BCS-Hubbard model is provided.…”

“…1 would change according to different definitions of JW strings for the different models, the methodology to construct circuit will be the same. For example, in Appendix D we show that the circuit construction method can be applied to the 1D BCS-Hubbard model [39], which is another example of a Kitaev-inspired model.…”

“…According to Lieb's theorem and direct numerical verifications [15,39],D i = D should be uniform to minimize the energy of the system. To further diagonalize the Hamiltonian, we Perform Fourier transformation for the two sublattice as follows:…”

Unfrustrating the t-J Model: Exact d-wave BCS Superconductivity in the t'-J_z-V Model

“…To make progress, many works have considered a large variety of modifications to the t-J model in order to improve analytical tractability. Such modifications include explicit symmetry breaking [12,13], large spatial dimension [14], large N [15], nonlocality [16,17], SYK-like nonlocality with large N [18], and replacing the Heisenberg interaction J with an Ising interaction J z [19][20][21][22][23][24]. In this work, our goal will be to study the simplest modification to the t-J model (that does not enlarge the Hilbert space) such that a superconducting phases exists and can be well-understood with analytical control.…”