Delocalization effects and charge reorganizations induced by repulsive interactions in strongly disordered chains

We study the delocalization effect of a short-range repulsive interaction on the ground state of a finite density of spinless fermions in strongly disordered one dimensional lattices. The density matrix renormalization group method is used to explore the charge density and the sensitivity of the ground state energy with respect to the boundary condition (the persistent current) for a wide range of parameters (carrier density, interaction and disorder). Analytical approaches are developed and allow to understand some mechanisms and limiting conditions. For weak interaction strength, one has a Fermi glass of Anderson localized states, while in the opposite limit of strong interaction, one has a correlated array of charges (Mott insulator). In the two cases, the system is strongly insulating and the ground state energy is essentially invariant under a twist of the boundary conditions. Reducing the interaction strength from large to intermediate values, the quantum melting of the solid array gives rise to a more homogeneous distribution of charges, and the ground state energy changes when the boundary conditions are twisted. In individual chains, this melting occurs by abrupt steps located at sample-dependent values of the interaction where an (avoided) level crossing between the ground state and the first excitation can be observed. Important charge reorganizations take place at the avoided crossings and the persistent currents are strongly enhanced around the corresponding interaction value. These large delocalization effects become smeared and reduced after ensemble averaging. They mainly characterize half filling and strong disorder, but they persist away of this optimal condition. Received 5 July 2000 and Received in final form 8 November 2000     

Melting of a Wigner crystal in an ionic dielectric

The melting of a Wigner Crystal of electrons placed into a host polar material is examined as a function of the density and the temperature. When the coupling to the longitudinal optical modes of the host medium is turned on, the WC is progressively transformed into a polaronic Wigner crystal. We estimate the critical density for crystal melting at zero temperature using the Lindeman criterion. We show that above a certain critical value of the Fr?hlich electron-phonon coupling, the melting towards a quantum liquid of polarons is not possible, and the insulator-to-metal transition is driven by the ionization of the polarons (polaron dissociation). The phase diagram at finite temperature is obtained by making use of the same Lindeman criterion. Results are also provided in the case of an anisotropic electron band mass, showing that the scenario of polaron dissociation can be relevant in anisotropic compounds such as the superconducting cuprates at rather moderate e-ph couplings. Received 13 August 1999     

Influence of atomic order on TA1[110] phonon softening [4] and displacive phase transition in Fe72Pt28 Invar alloys

The acoustic phonon dispersions of two Invar crystals , one ordered with the () structure, the other disordered fcc, have been investigated between 3.4 K and 470 K by inelastic and elastic neutron scattering. For the ordered crystal, pronounced softening of the whole phonon branch is observed on cooling below the Curie temperature. Particularly strong phonon softening at the M-point zone boundary of the structure leads to a displacive, antiferrodistortive phase transition at low temperatures. For the disordered crystal, much weaker softening of the phonons is observed and restricted to the region near the Brillouin zone center, where increasing elastic scattering with decreasing temperature indicates the growth of local tetragonal strain. This strain is considered as a typical precursor of the transformation to bct martensite. Specific heat measurements, performed at low temperatures on both crystals confirm the neutron scattering results and reveal considerable enhancement of the low energy phonon density of states in the ordered crystal. Received 18 January 1999     

Distribution of the delay time and the dwell time for wave reflection from a long random potential

We re-examine and correct an earlier derivation of the distribution of the Wigner phase delay time for wave reflection from a long one-dimensional disordered conductor treated in the continuum limit. We then numerically compare the distributions of the Wigner phase delay time and the dwell time, the latter being obtained by the use of an infinitesimal imaginary potential as a clock, and investigate the effects of strong disorder and a periodic (discrete) lattice background. We find that the two distributions coincide even for strong disorder, but only for energies well away from the band-edges. Received 11 June 2001 and Received in final form 30 July 2001     

Polarization catastrophe in the polaronic Wigner crystal

We consider a three dimensional Wigner crystal of electrons lying in a host ionic dielectric. Owing to their interaction with the lattice polarization, each localized electron forms a polaron. We study the collective excitations of such a polaronic Wigner crystal at zero temperature, taking into account the quantum fluctuations of the polarization within the Feynman harmonic approximation. We show that, contrary to the ordinary electron crystal, the system undergoes a polarization catastrophe when the density is increased. An optical signature of this instability is derived, whose trend agrees with the experiments carried out in Nd-based cuprates. Received 4 July 2002 Published online 17 September 2002     

Rate of equilibration of a one-dimensional Wigner crystal

We consider a system of one-dimensional spinless particles interacting via long-range repulsion. In the limit of strong interactions the system is a Wigner crystal, with excitations analogous to phonons in solids. In a harmonic crystal the phonons do not interact, and the system never reaches thermal equilibrium. We account for the anharmonism of the Wigner crystal and find the rate at which it approaches equilibrium. The full equilibration of the system requires umklapp scattering of phonons, resulting in exponential suppression of the equilibration rate at low temperatures.     

Phase diagram of two-component dipolar fermions in one-dimensional optical lattices

We theoretically map out the ground state phase diagram of interacting dipolar fermions in one-dimensional lattice. Using a bosonization theory in the weak coupling limit at half filing, we show that one can construct a rich phase diagram by changing the angle between the lattice orientation and the polarization direction of the dipoles. In the strong coupling limit, at a general filing factor, we employ a variational approach and find that the emergence of a Wigner crystal phases. The structure factor provides clear signatures of the particle ordering in the Wigner crystal phases.     

Low-temperature thermodynamic properties of a one-dimensional disordered electron lattice system

A new method of low-temperature thermodynamic calculation of a one-dimensional generalized Wigner crystal on a disordered host-lattice is proposed. This method is based on the system statistical sum presentation in terms of modified transfer-matrixes. A gapless structure of the elementary excitations spectrum of the system under consideration is found.     

Persistent currents in interacting lattice models

We present the results of an exact calculation of the averaged persistent current and its root mean square value in interacting disordered 1D rings. While the averaged persistent current exhibits a variety of interesting behaviors depending on the disorder and the strength of electron-electron interactions, the r.m.s. value depends very weakly on the strength of interaction. In general we observe that no dramatical increase of the averaged current or its r.m.s. value as a result of interactions is possible for these systems.     

Plaquette ground state in the two-dimensional SU(4) spin-orbital model

In order to understand the properties of Mott insulators with strong ground state orbital fluctuations, we study the zero temperature properties of the SU(4) spin-orbital model on a square lattice. Exact diagonalizations of finite clusters suggest that the ground state is disordered with a singlet-multiplet gap and possibly low-lying SU(4) singlets in the gap. An interpretation in terms of plaquette SU(4) singlets is proposed. The implications for LiNiO₂ are discussed. Received 6 July 2000     

Quantum theory of the magneto-optical effect induced by Ni ions in barium ferrites

To reveal the physical origin of the giant magneto-optical enhancement of Ni²⁺ ions in barium ferrite, quantitative calculations of the contributions of both the intra-ionic electric dipole transition between the 3d⁸ and 3d^{7 4p} configurations of the Ni²⁺ ions and the intra-ionic electric dipole transition induced by odd-parity crystal field terms are presented. It is deduced that the transition is important in the origin of the considered magneto-optical enhancement. The most important factor is the Ni-Fe superexchange interaction; since it is strong enough, the Faraday rotation produced by the Ni²⁺ ions is large though the energy difference between the 3d⁸ and 3 d7 4 p configurations is large. It is demonstrated that though the intra-ionic electric dipole transition does produce Faraday rotation peaks in the visible range, their magnitude is too small to explain the observed Faraday rotation. The effect of the spin-orbit interaction on the Faraday rotation is analysed. The spin-orbit interaction of the ground configuration plays a very important role in the occurrence of Faraday effects, but the Faraday rotation does not increase linearly with the strength of the spin-orbit coupling. On the contrary, the spin-orbit interaction of the excited configuration has almost no effect on the Faraday rotation. It is shown that the mixing of the different multiplets of the ground term induced by the crystal field has a great influence on the magneto-optical properties. Received 7 January 1998     

Thermopower evidence for Wigner crystallization in the insulating phase of two-dimensional GaAs bilayer hole systems

We report on low-temperature thermopower measurements of interacting GaAs bilayer hole systems in the limit of no interlayer tunneling. These systems exhibit a reentrant insulating phase near the many-body quantum Hall state (QHS) at total filling factor ν=1, when both layers have the same density. The diffusion thermopower is expected to diverge as T^-1 in the presence of an energy gap (Wigner crystal) or to vanish in the case of a disordered induced mobility gap. Our results show that, as the temperature is decreased, the diffusion thermopower exhibits a T^-1 dependence in the insulating phase around ν=1. This behavior clearly indicates the opening of an energy gap at low temperature, in agreement with the formation of a pinned Wigner solid. Finally, we report on the T-dependence of the thermopower at ν=1.     

Quantum spherical model in a random field: coherent state path integral approach

By introducing boson operators, a quantum spherical XY model in the presence of a random field has been studied by the coherent state path integral approach. The phase diagram is obtained, and the effects of the random-field fluctuations on the possibilities of the existence of a ferromagnetic phase are discussed. At the critical point, , the order parameter M describing the ordered ferromagnetic phase disappears as .Since the model is equivalent to a Bose system, we also show that the phase transition at zero temperature between the superfluid and the disordered Mott insulator phases occurs at the chemical potential , where J₀ is the strength of the exchange interaction. As the temperature T goes to zero, the asymptotic behavior of the entropy and the specific heat are and , respectively. Received: 20 May 1997 / Accepted: 20 October 1997     

On the role of electron correlation and disorder on persistent currents in isolated one-dimensional rings

To understand the role of electron correlation and disorder on persistent currents in isolated 1D rings threaded by magnetic flux ?, we study the behavior of persistent currents in aperiodic and ordered binary alloy rings. These systems may be regarded as disordered systems with well-defined long-range order so that we do not have to perform any configuration averaging of the physical quantities. We see that in the absence of interaction, disorder suppresses persistent currents by orders of magnitude and also removes its discontinuity as a function of ?. As we introduce electron correlation, we get enhancement of the currents in certain disordered rings. Quite interestingly we observe that in some cases, electron correlation produces kink-like structures in the persistent current as a function of ?. This may be considered as anomalous Aharonov-Bohm oscillations of the persistent current and recent experimental observations support such oscillations. We find that the persistent current converges with the size of the rings.     

Persistent current in metals with a large dephasing rate

In a weakly disordered metal electron interactions are responsible for both decoherence of the quasi-particles as well as for quantum corrections to thermodynamic properties. We consider electrons which are interacting with two-level-systems. We show that the two-level-systems enhance the average equilibrium (“persistent”) current in an ensemble of mesoscopic rings. The result supports the recent suggestion that two puzzles in mesoscopic physics may be related: The low temperature saturation of the dephasing time and the high persistent current in rings. Received 26 May 2000     

Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

For two particles in a disordered chain of length L with on-site interaction U, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics. Received: 22 May 1998 / Received in final form: 24 August 1998 / Accepted: 4 September 1998     

The statistical mechanics of turbo codes

The “turbo codes”, recently proposed by Berrou et al. [1] are written as a disordered spin Hamiltonian. It is shown that there exists a threshold such that for signal to noise ratios the error probability per bit vanishes in the thermodynamic limit, i.e. the limit of infinitely long sequences. The value of the threshold has been computed for two particular turbo codes. It is found that it depends on the code. These results are compared with numerical simulations. Received 14 March 2000 and Received in final form 17 July 2000     

Persistent currents in two dimensions: New regimes induced by the interplay between electronic correlations and disorder

Using the persistent current I induced by an Aharonov-Bohm flux in square lattices with random potentials, we study the interplay between electronic correlations and disorder upon the ground state (GS) of a few polarized electrons (spinless fermions) with Coulomb repulsion. being the total momentum, we show that in the continuum limit. We use this relation to distinguish between the continuum regimes, where the lattice GS behaves as in the continuum limit and I is independent of the interaction strength U when is conserved, and the lattice regimes where I decays as U increases. Changing the disorder strength W and U, we obtain many regimes which we study using the map of local currents carried by three spinless fermions. The decays of I characterizing three different lattice regimes are described by large U perturbative expansions. In one of them, I forms a stripe of current flowing along the axis of the diamagnetic Wigner molecule induced by large electronic correlations. This stripe of current persists in the continuum limit. The quantum melting of the diamagnetic molecule gives rise to an intermediate “supersolid” regime where a paramagnetic correlated pair co-exists with a third particle, before the total melting. The concepts of stripe and of supersolid which we use to describe certain regimes exhibited by three spinless fermions are reminiscent of the observations and conjectures done in other fields at the thermodynamic limit (stripe for high-Tc cuprates, supersolid for Helium quantum solids).