By means of the Lanczos method we analyze superconducting correlations in ultrasmall grains at fixed particle number. We compute the ground-state properties and the excitation gap of the pairing Hamiltonian as a function of the level spacing $\ensuremath{\delta}$. Both quantities turn out to be parity dependent and universal functions of the ratio $\ensuremath{\delta}/\ensuremath{\Delta}$ ( $\ensuremath{\Delta}$ is the BCS gap). We then characterize superconductivity in the canonical ensemble from the scaling behavior of correlation functions in energy space.By means of the Lanczos method we analyze superconducting correlations in ultrasmall grains at fixed particle number. We compute the ground-state properties and the excitation gap of the pairing Hamiltonian as a function of the level spacing $\ensuremath{\delta}$. Both quantities turn out to be parity dependent and universal functions of the ratio $\ensuremath{\delta}/\ensuremath{\Delta}$ ( $\ensuremath{\Delta}$ is the BCS gap). We then characterize superconductivity in the canonical ensemble from the scaling behavior of correlation functions in energy space.

arXiv:cond-mat/9801179Physical Review LettersMay 18, 1998137 citations

Parity and finite size effects in the thermodynamics of small superconductors

R. Rossignoli, Juan P. Zagorodny, N. Canosa

Physics Letters AJul 1, 199913 citations

Study of the superconducting order parameter in the two-dimensional negative- U Hubbard model by grand-canonical twist-averaged boundary conditions

Seher Karakuzu, Kazuhiro Seki, Sandro Sorella

By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the $s$ -wave superconducting order parameter and the pairing correlations for the negative- $U$ Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs are much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of $|U|/t$ and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behavior of the superconducting phase by means of a suitably chosen Jastrow factor including long-range density-density correlations.By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the $s$-wave superconducting order parameter and the pairing correlations for the negative-$U$ Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs are much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of $|U|/t$ and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behavior of the superconducting phase by means of a suitably chosen Jastrow factor including long-range density-density correlations.

arXiv:1806.06736Physical review. B./Physical review. BAug 29, 201812 citations

Superconductivity and superfluidity

WORLD SCIENTIFIC eBooksMay 30, 20161 citation

Superfluidity and superconductivity

C. Di Castro, Roberto Raimondi

Cambridge University Press eBooksAug 27, 20154 citations

Derivation and improvements of the quantum canonical ensemble from a regularized microcanonical ensemble

Jani Lukkarinen

We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by giving an explanation for the, at the first sight unreasonable, effectiveness of the canonical ensemble when applied to certain small, isolated, systems. This method also allows a direct identification between the parameters of the microcanonical and the canonical ensemble and it yields simple indicators and rigorous bounds for the effectiveness of the approximation. Finally, we derive an asymptotic expansion of the microcanonical corrections to the canonical ensemble for those systems, which are near, but not quite, at the thermodynamical limit and show how and why the canonical ensemble can be applied also for systems with an exponentially increasing density of states. The aim throughout the paper is to keep mathematical rigour intact while attempting to produce results which are both physically and practically interesting.We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by giving an explanation for the, at the first sight unreasonable, effectiveness of the canonical ensemble when applied to certain small, isolated, systems. This method also allows a direct identification between the parameters of the microcanonical and the canonical ensemble and it yields simple indicators and rigorous bounds for the effectiveness of the approximation. Finally, we derive an asymptotic expansion of the microcanonical corrections to the canonical ensemble for those systems, which are near, but not quite, at the thermodynamical limit and show how and why the canonical ensemble can be applied also for systems with an exponentially increasing density of states. The aim throughout the paper is to keep mathematical rigour intact while attempting to produce results which are both physically and practically interesting.

arXiv:cond-mat/9809102Journal of Physics A Mathematical and GeneralJan 1, 19998 citations

By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the

s

-wave superconducting order parameter and the pairing correlations for the negative-

U

Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs are much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of

|U|/t

and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behavior of the superconducting phase by means of a suitably chosen Jastrow factor including long-range density-density correlations.