arXiv subjects

Luigi Amico

Publications and source records attributed to Luigi Amico.

116 records · Page 7Linked to original sources

arXiv2001

Integrable models for confined fermions: applications to metallic grains

We study integrable models for electrons in metals when the single particle spectrum is discrete. The electron-electron interactions are BCS-like pairing, Coulomb repulsion, and spin exchange coupling. These couplings are, in general, nonuniform in the sense that they depend on the levels occupied by the interacting electrons. By using the realization of spin 1/2-operators in terms of electrons the models describe spin 1/2 models with nonuniform long range interactions and external magnetic field. The integrability and the exact solution arise since the model Hamiltonians can be constructed in terms of Gaudin models. Uniform pairing and the resulting orthodox model correspond to an isotropic limit of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.

cond-mat.supr-con↗

arXiv2001

The BCS model and the off shell Bethe ansatz for vertex models

We study the connection between the BCS pairing model and the inhomogeneous vertex model. The two spectral problems coincide in the quasi-classical limit of the off-shell Bethe Ansatz of the disordered six vertex model. The latter problem is transformed into an auxiliary spectral problem which corresponds to the diagonalization of the integrals of motion of the BCS model. A generating functional whose quasi classical expansion leads to the constants of motion of the BCS model and in particular the Hamiltonian, is identified.

cond-mat.stat-mech↗

arXiv2001

Integrable model for interacting electrons in metallic grains

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 constants of motion of the model, contain the anisotropic Gaudin Hamiltonians. The exact solution is obtained diagonalizing them by means of Bethe Ansatz. Uniform pairing and Coulomb interaction are obtained as the ``isotropic limit'' of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.

cond-mat.supr-con↗

arXiv2000

Algebraic equivalence between certain models for superfluid--insulator transition

Algebraic contraction is proposed to realize mappings between models Hamiltonians. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic $XXZ$ Heisenberg model, the Quantum Phase Model, and the Bose Hubbard Model is established as the contractions of the algebra $u(2)$ underlying the dynamics of the $XXZ$ Heisenberg model.

cond-mat.stat-mech↗

arXiv2000

Fermionic long range correlations realized by particles obeying deformed statistics

Deformed exchange statistics is realized in terms of electronic operators. This is employed to rewrite Hubbard type lattice models for particles obeying deformed statistics (we refer to them as deformed models) as lattice models for electrons. The resulting models show up gauge--like modulations in the hopping processes, which induce long-range correlations in the lattice. The conditions for the Bethe ansatz solvability of the latter are interpreted as restrictions imposed on the statistics to be compatible with the Bethe ansatz solvability of the deformed models. It is found that solvable deformed models are not unitarily equivalent to fermionic models if the exchange of particles with the same spin-orientations is deformed. Statistics deformations, where the exchange relation of two particles is influenced by the presence of other particles, cannot be realized by fermionic operators.

cond-mat.str-el↗

arXiv2000

Time dependent mean field theory of the superfluid-insulator phase transition

We develop a time-dependent mean field approach, within the time-dependent variational principle, to describe the Superfluid-Insulator quantum phase transition. We construct the zero temperature phase diagram both of the Bose-Hubbard model (BHM), and of a spin-S Heisenberg model (SHM) with the XXZ anisotropy. The phase diagram of the BHM indicates a phase transition from a Mott insulator to a compressibile superfluid phase, and shows the expected lobe-like structure. The SHM phase diagram displays a quantum phase transition between a paramagnetic and a canted phases showing as well a lobe-like structure. We show how the BHM and Quantum Phase model (QPM) can be rigorously derived from the SHM. Based on such results, the phase boundaries of the SHM are mapped to the BHM ones, while the phase diagram of the QPM is related to that of the SHM. The QPM's phase diagram obtained through the application of our approach to the SHM, describes the known onset of the macroscopic phase coherence from the Coulomb blockade regime for increasing Josephson coupling constant. The BHM and the QPM phase diagrams are in good agreement with Quantum Monte Carlo results, and with the third order strong coupling perturbative expansion.

cond-mat.supr-con↗

arXiv1998

One-Dimensional XXZ Model for Particles Obeying Fractional Statistics

We define one-dimensional particles as non-abelian representations of the symmetric group $S_N$. The exact solution of an $XXZ$ type Hamiltonian built up with such particles is achieved using the coordinate Bethe Ansatz. The Bethe equations show that fractional statistics, effectively, accounts for coupling an external gauge field to an integer statistics' system.

cond-mat.str-el↗

arXiv1996

Supersolid phase in fully frustrated Josephson junction arrays

We study the phase diagram and the excitation spectra of an array of small Josephson junctions at $f=1/2$ and arbitrary charge frustration. We find that the supersolid region in the phase diagram is larger than the correspondent region at $f=0$ and it includes two different phases.In the chiral supersolid (SS) charges and vortices are arranged in a checkerboard pattern on a $2\:\times \:2$ supercell analogously to the unfrustrated case. We find a new phase, which we term {\em non-chiral supersolid} (NCSS), which has no corresponding phase at $f=0$. The excitation spectra in the supersolid regions show particle like dispersions which is related to the defectons. The defecton condensation leads to superfluidity in the presence of charge ordered background.

cond-mat↗