arXiv subjects

V. Melik-Alaverdian

Publications and source records attributed to V. Melik-Alaverdian.

6 recordsLinked to original sources

arXiv2000

Quantum Projector Method on Curved Manifolds

A generalized stochastic method for projecting out the ground state of the quantum many-body Schrödinger equation on curved manifolds is introduced. This random-walk method is of wide applicability to any second order differential equation (first order in time), in any spatial dimension. The technique reduces to determining the proper ``quantum corrections'' for the Euclidean short-time propagator that is used to build up their path-integral Monte Carlo solutions. For particles with Fermi statistics the ``Fixed-Phase'' constraint (which amounts to fixing the phase of the many-body state) allows one to obtain stable, albeit approximate, solutions with a variational property. We illustrate the method by applying it to the problem of an electron moving on the surface of a sphere in the presence of a Dirac magnetic monopole.

cond-mat.stat-mech↗

arXiv1999

Skyrmion Physics Beyond the Lowest Landau Level Approximation

The effects of Landau level mixing and finite thickness of the two-dimensional electron gas on the relative stability of skyrmion and single spin-flip excitations at Landau level filling factor $ν=1$ have been investigated. Landau level mixing is studied by fixed-phase diffusion Monte Carlo and finite thickness is included by modifying the effective Coulomb interaction. Both Landau level mixing and finite thickness lower skyrmion excitation energies and favor skyrmions with fewer spin flips. However, the two effects do not work `coherently'. When finite thickness is included the effect of Landau level mixing is strongly suppressed.

cond-mat.mes-hall↗

arXiv1998

Monte Carlo Comparison of Quasielectron Wave Functions

Variational Monte Carlo calculations of the quasielectron and quasihole excitation energies in the fractional quantum Hall effect have been carried out at filling fractions $ν=1/3$, 1/5, and 1/7. For the quasielectron both the trial wave function originally proposed by Laughlin and the composite fermion wave function proposed by Jain have been used. We find that for long-range Coulomb interactions the results obtained using these two wave functions are essentially the same, though the energy gap obtained using the composite fermion quasielectron is slightly smaller, and closer to extrapolated exact-diagonalization results.

cond-mat.mes-hall↗

arXiv1998

Possibility of p-wave pairing of composite fermions at $ν=1/2$

We find that for the pure Coulomb repulsion the composite Fermi sea at $ν=1/2$ is on the verge of an instability to triplet pairing of composite fermions. It is argued that a transition into the paired state, described by a Pfaffian wave function, may be induced if the short-range part of the interaction is softened by increasing the thickness of the two-dimensional electron system.

cond-mat.mes-hall↗

arXiv1997

Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study

A generalized diffusion Monte Carlo method for solving the many-body Schrödinger equation on curved manifolds is introduced and used to perform a `fixed-phase' simulation of the fractional quantum Hall effect on the Haldane sphere. This new method is used to study the effect of Landau level mixing on the $ν=1/3$ energy gap and the relative stability of spin-polarized and spin-reversed quasielectron excitations.

cond-mat.mes-hall↗

arXiv1995

Composite Fermions and Landau Level Mixing in the Fractional Quantum Hall Effect

The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter $λ= (e^2/εl_0)/\hbarω_c$, has been calculated by variational Monte Carlo for the fractional quantum Hall effect at filling fractions $ν=1/3$ and 1/5 using a modified version of Jain's composite fermion wave functions. These wave functions exploit the Landau level mixing already present in composite fermion wave functions by introducing a partial Landau level projection operator. Results for the energy gaps are consistent with experimental observations in $n$-type GaAs, but we conclude that Landau level mixing alone cannot account for the significantly smaller energy gaps observed in $p$-type systems.

cond-mat↗