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.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.

arXiv:1709.08411Physical Review LettersJan 25, 201828 citations

Thermodynamics of the model of equal spin-spin interactions

Airat A. Khamzin, Raoul Rashidovich Nigmatullin

Theoretical and Mathematical PhysicsOct 1, 20104 citations

Classical Spin Models: An Introduction

Andreas Wipf

Lecture notes in physicsOct 26, 20121 citation

Fractional revivals, multiple-Schrödinger-cat states, and quantum carpets in the interaction of a qubit with N qubits

Shane Dooley, Timothy P. Spiller

We study the dynamics of a system comprised of a single qubit interacting equally with $N$ qubits (a ``spin star'' system). Although this model can be solved exactly, the exact solution does not give much intuition for the dynamics of the model. Here, we find an approximation that gives some insight into the dynamics for a particular class of initial spin-coherent states of the $N$ qubits. We find an effective Hamiltonian for the system that is a finite Kerr (one-axis twisting) Hamiltonian for the $N+1$ qubits. The initial spin-coherent state evolves to spin-squeezed states on short time scales, and to ``multiple-Schr\"odinger-cat'' states (superpositions of many spin-coherent states) on longer time scales, a manifestation of the phenomenon of fractional revivals of the initial state. The evolution of the system is visualized with phase-space plots ( $Q$ functions) that, when plotted against time, reveal a ``quantum carpet'' pattern. Of particular interest is the fact that our approximation captures the qualitative features of the model even for small values of $N$ . This suggests the possibility of observing the phenomenon of fractional revival in this model for systems of few qubits.We study the dynamics of a system comprised of a single qubit interacting equally with $N$ qubits (a ``spin star'' system). Although this model can be solved exactly, the exact solution does not give much intuition for the dynamics of the model. Here, we find an approximation that gives some insight into the dynamics for a particular class of initial spin-coherent states of the $N$ qubits. We find an effective Hamiltonian for the system that is a finite Kerr (one-axis twisting) Hamiltonian for the $N+1$ qubits. The initial spin-coherent state evolves to spin-squeezed states on short time scales, and to ``multiple-Schr\"odinger-cat'' states (superpositions of many spin-coherent states) on longer time scales, a manifestation of the phenomenon of fractional revivals of the initial state. The evolution of the system is visualized with phase-space plots ($Q$ functions) that, when plotted against time, reveal a ``quantum carpet'' pattern. Of particular interest is the fact that our approximation captures the qualitative features of the model even for small values of $N$. This suggests the possibility of observing the phenomenon of fractional revival in this model for systems of few qubits.

arXiv:1404.4296Physical Review AJul 14, 201413 citations

Exact solution of the infinite- U Hubbard problem and other models in one dimension

Brijesh Kumar

An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite $U$ (local interaction). Exact solution of its complete energy eigenspectrum is accomplished by introducing a unitary transformation which maps the original problem to a tight-binding model of the fermions only. Physically, the exact solution implies the absence of Nagaoka ferromagnetism in the ground state for arbitrary electron densities. The present method solves a class of very general models exactly. Few more problems are discussed as an application of this unitary transform method.An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite $U$ (local interaction). Exact solution of its complete energy eigenspectrum is accomplished by introducing a unitary transformation which maps the original problem to a tight-binding model of the fermions only. Physically, the exact solution implies the absence of Nagaoka ferromagnetism in the ground state for arbitrary electron densities. The present method solves a class of very general models exactly. Few more problems are discussed as an application of this unitary transform method.

arXiv:0812.2977Physical Review BApr 27, 200926 citations

Exact solution of a multicomponent coupled spin model

Fu‐Cho Pu, Yu‐Kui Zhou

Physics Letters ANov 1, 19870 citations

We study the dynamics of a system comprised of a single qubit interacting equally with

N

qubits (a ``spin star'' system). Although this model can be solved exactly, the exact solution does not give much intuition for the dynamics of the model. Here, we find an approximation that gives some insight into the dynamics for a particular class of initial spin-coherent states of the

N

qubits. We find an effective Hamiltonian for the system that is a finite Kerr (one-axis twisting) Hamiltonian for the

N+1

qubits. The initial spin-coherent state evolves to spin-squeezed states on short time scales, and to ``multiple-Schr\"odinger-cat'' states (superpositions of many spin-coherent states) on longer time scales, a manifestation of the phenomenon of fractional revivals of the initial state. The evolution of the system is visualized with phase-space plots (

Q

functions) that, when plotted against time, reveal a ``quantum carpet'' pattern. Of particular interest is the fact that our approximation captures the qualitative features of the model even for small values of

N

. This suggests the possibility of observing the phenomenon of fractional revival in this model for systems of few qubits.

An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite

U

(local interaction). Exact solution of its complete energy eigenspectrum is accomplished by introducing a unitary transformation which maps the original problem to a tight-binding model of the fermions only. Physically, the exact solution implies the absence of Nagaoka ferromagnetism in the ground state for arbitrary electron densities. The present method solves a class of very general models exactly. Few more problems are discussed as an application of this unitary transform method.