相关论文: Ground-state energy of a Richardson-Gaudin integra…

Using the exact Bethe Ansatz solution, we investigate methods for calculating the ground-state energy for the $p + ip$-pairing Hamiltonian. We first consider the Hamiltonian isolated from its environment (closed model) through two forms of…

We present a variational method for approximating the ground state of spin models close to (Richardson-Gaudin) integrability. This is done by variationally optimizing eigenstates of integrable Richardson-Gaudin models, where the toolbox of…

We summarize previous works on the exact ground state and the elementary excitations of the exactly solvable BCS model in the canonical ensemble. The BCS model is solved by Richardson equations, and, in the large coupling limit, by Gaudin…

We introduce a Hamiltonian for two interacting $su(2)$ spins. We use a mean-field analysis and exact Bethe ansatz results to investigate the ground-state properties of the system in the classical limit, defined as the limit of infinite spin…

For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a…

We have studied the numerical solutions of Richardson equations of the BCS model in the limit of large number of energy levels at half-filling, and compare them with the analytic results derived by Gaudin and Richardson, which in turn leads…

Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an…

The Bethe roots describing the ground state energy of the integrable 1D model of interacting bosons with weakly repulsive two-body delta interactions are seen to satisfy the set of Richardson equations appearing in the strong coupling limit…

This Letter provides the solution to a yet unsolved basic problem of Solid State Physics: the ground state energy of an arbitrary number of Cooper pairs interacting via the Bardeen-Cooper-Schrieffer potential. We here break a 50 year old…

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant…

We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that…

We propose a new quantum computational way of obtaining a ground-state energy and expectation values of observables of interacting Hamiltonians. It is based on the combination of the adiabatic quantum evolution to project a ground state of…

We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number $N$ becomes large. In the dilute regime, when the interaction potentials have the length scale of order $O(N^{-1})$, we show…

The ground state energy and energy gap to the first excited state are calculated for the attractive Hubbard model in one dimension using both the Bethe Ansatz equations and the variational BCS wavefunction. Comparisons are provided as a…

We show that the thermodynamic limit of the ground state energy in the mixed p-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature.

We find an integrable generalization of the BCS model with non-uniform Coulomb and pairing interaction. The Hamiltonian is integrable by construction since it is a functional of commuting operators; these operators, which therefore are…

We introduce an integrable Hamiltonian which is an extended d+id-wave pairing model. The integrability is deduced from a duality relation with the Richardson-Gaudin (s-wave) pairing model, and associated to this there exists an exact Bethe…

The work presents a simple formalism which proposes an estimate of the ground state energy from a single reference function. It is based on a perturbative expansion but leads to non linear coupled equations. It can be viewed as well as a…

Several approximations are tested by calculating the ground-state energy and the energy of the first excited $0^{+}$ state using an exactly solvable model with two symmetric levels interacting via a pairing force. They are the BCS…

We extend previous studies of the BCS canonical approach for the attractive Hubbard model. A derivation of the BCS formulation is presented for both the Hubbard and a simpler reduced Hamiltonian. Using direct diagonalization, exact one and…