arXiv subjects

Francisco Claro

Publications and source records attributed to Francisco Claro.

12 recordsLinked to original sources

arXiv2010

Effect of Laughlin correlations on crystalline mean field solutions of the 2DEG in FQHE regime

The energy per particle of many body wavefunctions that mix Laughlin liquid with crystalline correlations for periodic samples in the Haldane-Rezayi configuration is numerically evaluated for periodic samples. The Monte Carlo algorithm is employed and the wave functions are constructed in such a way that have the same zeroes as the periodic Laughlin states. Results with up to 16 particles show that these trial wavefunctions have lower energy than the periodic Laughlin states for finite samples even at $ν=1/3$. Preliminary results for 36 particles suggest that this tendency could reach the thermodynamic limit. These results get relevance in view of the very recent experimental measures that indicate the presence of periodic structures in the 2DEG for extremely small temperatures and clean samples, inclusive at main FQHE filling fractions $ν=1/3,2/3 $.

cond-mat.mes-hall↗

arXiv2009

Exact eigenfunctions of FQHE systems at fractional filling factors 1/q. I. Formal results

Eigenstates of the FQHE hamiltonian problem after to be projected on the LLL are determined for filling factors 1/q, with q an odd number. The solutions are found for an infinite class of finite samples in which the Coulomb potential is periodically extended. Therefore, a thermodynamic limit solution is also identified. The results suggest the presence of integrability properties in FQHE systems. The many particle states are simple Slater determinants constructed with special single particle states. These orbitals are defined as powers of order q of "composite fermion" like wavefunctions associated to a reduced magnetic field B/q. At the same time, those "composite fermion" states were obtained by factorizing and canceling fixed position (quasi-momentum independent) zeros in previously derived exact Hartree-Fock orbitals. A formula for the energy per particle of the FQHE states is given for finite samples as well as for the thermodynamic limit state. As a side result, the same "composite fermions" like orbitals are employed to construct variational wavefunctions of the system, showing zeros of order q as two electrons approach each other, as Laughlin states do. The long range spatial correlation associated to the starting HF solutions may further reduce the energy of these states.

cond-mat.mes-hall↗

arXiv2007

Crystal mean field based trial wavefunctions for the FQHE ground states

Employing the Haldane-Rezayi periodic representation, the crystalline determinantal Hall crystal mean field solutions derived in previous works are used to construct variational wavefunctions for the FQHE at $ν=1/q$. The proposed states optimize the short range correlations in a similar measure as the Laughlin ones, since the zero of the states when the coordinates of two particles join is of order $q$. However, the proposed wavefunctions also incorporate the crystalline correlations of the mean field problem, through a determinantal mean field function entering their construction. The above properties, lead to the expectation that the considered states can be competitive in energy per particle with the Laughlin ones. Their similar structure also could explain way the breaking of the translation invariance in the FQHE ground states can result to be a weak one, which after disregarded, produce the Laughlin states as good approximations. Calculation for checking these possibilities are under consideration.

cond-mat.mes-hall↗

arXiv2007

Mean field exact solutions showing charge density wave crossover at low fillings in the fractional quantum Hall regime

A general analytical framework for the determination of the mean field states at arbitrary rational filling factors for the 2DEG in FQHE regime is given. Its use allows to obtain analytic expressions for the solutions at filling factors of the form $ν=1/q$ for arbitrary odd $q$. The analysis can be performed for two general classes of states characterized by $γ=1$ or $γ={1/2}$ particles per unit cell. Instead of the periodic peaks of the Wigner solid solution, the new states show electron densities forming percolating ridges that may favor an energy decrease through correlated ring of exchange contributions. Therefore, we estimate that they can realize mean field versions of the so called Hall Crystal (HC) states. The obtained analytic HC solution shows the same crystalline symmetry that the corresponding WC state in its class $γ=1$, but a qualitatively different charge density distribution. The energy dependence of the corresponding HC and WC states on the filling factor is also evaluated here for the class $γ=1/2$. The results show a crossover between HC state and the Wigner crystal, close to filling 1/7. Therefore, transitions may occur from one to the other as the electron density is varied. This result is consistent with recent experimental findings.

cond-mat.mes-hall↗

arXiv2005

Phase diagram of two dimensional electron gas in a perpendicular magnetic field around Landau level filling factors ν=1 and ν=3

The measured melting curve $T_{m}(ν)$ between the crystal and liquid phases is analyzed using thermodynamics to extract the change of magnetization $ΔM$ as a function of the Landau level filling factor \ $ν,$ near $ν=1$. \ An explanation of $ΔM$($ν)$ is proposed \ in terms of Skyrmions. \ Near $ν=3$, a Wigner crystal is the most probable solid phase, experiments excluding Skyrmions.

cond-mat.mes-hall↗

arXiv2004

Stationary States of a Random Copying Mechanism over a Complex Networks

An analytical approach to network dynamics is used to show that when agents copy their state randomly the network arrives to a stationary status in which the distribution of states is independent of the agents degree. The effects of network topology on the process are characterized introducing a quantity called influence and studying its behavior for scale-free and random networks. We show that for this model degree averaged means are constant in time regardless of the number of states involved.

cond-mat.dis-nn↗

arXiv2004

A Proposal for a Modified Moller-Plesset Perturbation Theory

A modified version of the Moller-Plesset approach for obtaining the correlation energy associated to a Hartree-Fock ground state is proposed. The method is tested in a model of interacting fermions that allows for an exact solution. Using up to third order terms improved results are obtained, even more accurate in the limit of loosely bound particles. This result suggests the possible convenience of the scheme for the study of chemical bound problems.

cond-mat.mtrl-sci↗

arXiv2003

Melting curves and other phase transitions in a two dimensional electron assembly in a transverse magnetic field as a function of the Landau level filling factor

Besides Laughlin/composite Fermion liquid, and Wigner solid, there have been proposals for Hall crystals and condensed phases of skyrmions for inclusion in the QHE systems phase diagram. Some results on Hall crystals are reported, which suggest that at ν=1/3 such crystals can be the ground state of the 2DEG in a magnetic field. At ν=1 and 2, Chen et al. experimentally established that the Wigner solid is the ground state. An explanation is also given here for the coexistence in their experiments of an integral QHE plateau and the presence of the Wigner crystal phase near ν=1. Further, Mandal et al. showed that at ν=1/7, and most probably at ν=1/9, an incompressible liquid state should be the ground state. Thus, at least three non-entrant solid phases appear to exist: 0 < nu \leq 1/9, 1/9 < nu \leq 1/7 and,less certainly, 1/7 < ν\leq 1/5. In addition, points of solid nature are present at ν=1 and 2 (Wigner solid) and possibly at ν=1/3 (Hall crystal).

cond-mat↗

arXiv2003

Anlaytic mean-field Hall crystal solution at nu=1/3: composite fermion like sub-bands and correlation effects

An analytic solution of the Hartree-Fock problem for a 2DEG at filling 1/3 and half an electron per unit cell is presented. The Coulomb interaction dynamically breaks the first Landau level in three narrow sub-bands, one of which is fully occupied and the other empty, as in the composite fermion model. The localized orbitals associated to the Bloch like single electron wavefunctions are nearly static, resembling the angular momentum eigenstates within a Landau level for non-interacting fermions. Strong correlations are expected owing to the large charge density overlap between neighboring plaquettes. A numerical evaluation brings the cohesive energy close to that of the best present day models. It is also found that correlations are long range, requiring over 50 particles spread over a finite sample to approach convergence. Since presently allowed exact calculations are far from this number, the question of how relevant the considered wave-function is for the description of the ground state of the 2DEG system remains open.

cond-mat↗

arXiv2001

The Hartree-Fock state for the 2DEG at filling factor 1/2 revisited: analytic solution, dynamics and correlation energy

The CDW Hartree-Fock state at half filling and half electron per unit cell is examined. Firstly, an exact solution in terms of Bloch-like states is presented. Using this solution we discuss the dynamics near half filling and show the mass to diverge logarithmically as this filling is approached. We also show how a uniform density state may be constructed from a linear combination of two degenerate solutions. Finally we show the second order correction to the energy to be an order of magnitude larger than that for competing CDW solutions with one electron per unit cell.

cond-mat.mes-hall↗

arXiv1999

Magnetic field induced directional localization in a 2D rectangular lattice

We study the effect of a perpendicular uniform magnetic field on the dissipative conductivity of a rectangular lattice with anisotropic hopping, $t_x\neq t_y $. We show that the magnetic field may enhance dramatically the directional anisotropy in the conductivity. The effect is a measurable physical realization of Aubry's duality in Harper systems.

cond-mat↗

arXiv1997

Exact Random Walk Distributions using Noncommutative Geometry

Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $ N $ on a two-dimensional square lattice for large $ N $, taking into account finite size contributions.

alg-geom↗