Monte Carlo evaluation of trial wave functions for the fractional quantized Hall effect: Disk geometry

Abstract

Monte Carlo methods have been employed to evaluate the energy of two previously proposed trial wave functions for the quasiparticle at the v= 3 quantized Hall state of the two-dimensional electron system. The two wave functions have the same energy within our statistical accuracy, and are consistent with a value e+( 3 )=(0.073%0.008)et/el"where io is the insgnetic length, and e the background dielectric constant. Simulations of the quasihole state confirm previous estimates of e (T)=0.026e /elo. We have also studied the charge distributions of the quasiparticle and quasihole states, and we have evaluated the energies of a previously proposed microscopic trial wave function for the ground state at v= -, , 3, and 7.

A new method of calculation in the Fractional Quantum Hall Effect regime

“…The latter is determined classically without using the wave function of the electron system. The two others are quantum operators acting on wave functions and are in general determined via numerical calculations with either exact diagonalization [12][13][14][15][16][17] or Monte Carlo simulations [22][23][24] . In this work we propose an analytical method based on complex polar coordinates to calculate the electronelectron and electron-background interaction energies for systems with several electrons.…”

Finite-size Monte Carlo results for anisotropic quantum Hall liquids

“…In order to obtain a more meaningful comparison between the energies of isotropic (α = 0) and anisotropic BRS states (those with lowest energy for a value α 0 = 0), we performed a more detailed size-dependence of the data. To this effect, we followed the procedure of Morf and Halperin 22 and fitted the available energies in Ta Even though the convergence of the results (as a function of N ) is quite slow (typical for such systems), the N → ∞ extrapolation seems unambiguous suggesting that the negative energy difference (while being size-dependent), (ǫ α0 − ǫ 0 ) favours a BRS liquid crystalline state even in the complete bulk limit. In Fig.…”

Spin and Charge Ordering in the Quantum Hall Regime

“…This general phenomenon has been encountered in different manifestations in recent years, for example as magnetic monopoles in spin ice materials [71][72][73] or as deconfinement of an electron into holon, spinon and orbiton [74][75][76]. Further support for Laughlin's theory comes from exact diagonalization studies [77] and Monte Carlo simulations [78]. Here, it was shown that Laughlin's wavefunction yields the correct ground state for short range interactions.…”