Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice. I

In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid phase taking place at zero temperature between the quantum liquid and the solid. In this and a succeeding paper, we re-visit this issue for a few polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. This paper is restricted to the magic number of particles N = 4 for which a square Wigner molecule is formed when U increases and to the size L = 6 suitable for exact numerical diagonalizations. When the Coulomb energy to kinetic energy ratio r _s = UL/(2t ) reaches a value r _s ^F ≈ 10, there is a level crossing between ground states of different momenta. Above r _s ^F, the mesoscopic crystallization proceeds through an intermediate regime ( r _s ^F < r _s < r _s ^W ≈ 28) where unpaired fermions with a reduced Fermi energy co-exist with a strongly paired, nearly solid assembly. We suggest that this is the mesoscopic trace of the supersolid proposed by Andreev and Lifshitz. When a random substrate is included, the level crossing at r _s ^F is avoided and gives rise to a lower threshold r _s ^F(W) < r _s ^F where two usual approximations break down: the Wigner surmise for the distribution of the first energy excitation and the Hartree-Fock approximation for the ground state. Received 21 June 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: jpichard@cea.fr     

BONDED TABLEAU AND UNITARY GROUP APPROACH FOR MANY-ELECTRON PROBLEMS

A unitary group approach based on the so-called bonded tableaux (VB) states is described. Several different realizations of the bonded tableaux are discussed and their relations are pointed out. From a viewpoint of the symmetric group we reveal a simple structure of the matrix elements of unitary group generators and generator products. This structure makes an efficient approach to the matrix element evaluation.     

Ground-state energy of a classical artificial molecule

We study the ground-state energy of a classical artificial molecule formed by two-dimensional clusters (artificial atoms) of N/2 charged particles separated by a distance d. For the small molecules of N = 2 and 4, we obtain analytical expressions for this energy. For the larger ones, we calculate the ground-state energy using molecular dynamics simulation for N up to 128. From our numerical results, we are able to find out a function to approximate the ground-state energy of the molecules covering the range from atoms to molecules for any inter-atom distance d and for particle number from N = 8 to 128 within a difference less than one percent from the MD data.     

Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice

The frequency-moment expansion method is developed to analyze the validity of the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the generalized Hubbard model at half filling and large U. For the particular case of the Hubbard model with nearest-neighbor hopping on a triangular lattice lacking the particle-hole symmetry results reveal substantial violation of the sum rule.     

Parity law of the singlet-triplet gap in graphitic ribbons

This work explores the possibility to transfer the parity law of the singlet-triplet gap established for square ladders (gapped for even number of legs, gapless for odd number of legs) to fused polyacenic 1-D systems, i.e., graphite ribbons. Qualitative arguments are presented in favor of a gapped character when the number n_ω of benzene rings along the ribbon width is odd. A series of numerical calculations (quantitative mapping on spin 1/2 chains, renormalized excitonic treatments and Quantum Monte Carlo) confirms the parity law and the gapless character of the ribbon for even n_ω.     

A theoretical analysis of the magnetic properties of La<Subscript>2</Subscript>CuO<Subscript>4</Subscript>

The magnetic properties of the La₂CuO₄ are analyzed by means of the paramagnetic solution of the Hubbard model within the composite operator method. The experimental findings of the inelastic neutron magnetic scattering [R. Coldea et al., Phys. Rev. Lett. 86, 5377 (2001)] for the spin spectrum, the spin-wave intensity and the behavior of the dispersion at the zone boundary are well described by our results although the difference in phase. The Hubbard model emerges has a minimal model capable to describe the anomalous magnetic behavior of such a strongly correlated material. Received 29 July 2002 / Received in final form 2 January 2003 Published online 14 March 2003     

Extended Hubbard model in the presence of a magnetic field

Within the Green’s function and equations of motion formalism it is possible to exactly solve a large class of models useful for the study of strongly correlated systems. Here, we present the exact solution of the one-dimensional extended Hubbard model with on-site U and first nearest neighbor repulsive V interactions in the presence of an external magnetic field h, in the narrow band limit. At zero temperature our results establish the existence of four phases in the three-dimensional space (U, n, h) – n is the filling – with relative phase transitions, as well as different types of charge ordering. The magnetic field may dramatically affect the behavior of thermodynamic quantities, inducing, for instance, magnetization plateaus in the magnetization curves, and a change from a single to a double-peak tructure in the specific heat. According to the value of the particle density, we find one or two critical fields, marking the beginning of full or partial polarization. A detailed study of several thermodynamic quantities is also presented at finite temperature.     

LOCV calculation for the uniform electron fluid at finite temperature

The free energy of the homogeneous electron fluid at finite temperature is obtained using the lowest order constrained variational (LOCV) method. In order to test the convergence of cluster expansion series the three-body cluster terms are calculated with the LOCV correlation functions. The results agree reasonably with those of Monte Carlo, coupled-cluster, perturbational expansion etc, techniques at zero temperature. The flashing and critical temperatures as well as the critical exponent are found to be about 0.6, 1.3 eV and 0.384 respectively. A similar liquid-gas phase transition to that of nuclear matter and liquid He³ is observed. Received 15 April 2002 / Received in final form 19 October 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: modarres@khayam.ut.ac.ir