355 research outputs found
Monte Carlo study of Bose Laughlin wave function for filling factors 1/2, 1/4 and 1/6
Strongly correlated two-dimensional electronic systems subject to a
perpendicular magnetic field at lowest Landau level (LLL) filling factors: 1/2,
1/4 and 1/6 are believed to be composite fermion (CF) Fermi liquid phases. Even
though a Bose Laughlin wave function cannot describe these filling factors we
investigate whether such a wave function provides a lower energy bound to the
true CF Fermi liquid energies. By using Monte Carlo simulations in disk
geometry we compute the Bose Laughlin energies and compare them to
corresponding results for the spin-polarized LLL CF Fermi liquid state and
avalable data from literature.We find the unexpected result that, for filling
factors 1/4 and 1/6, the Bose Laughlin ground state energy is practically
identical to the true CF liquid energy while this is not the case at 1/2 where
the Bose Laughlin ground state energy is sizeably lower than the energy of the
CF Fermi liquid state.Comment: 7 pages, 2 figures, 2 table
Liquid crystalline states for two-dimensional electrons in strong magnetic fields
Based on the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory of
two-dimensional melting and the analogy between Laughlin states and the
two-dimensional one-component plasma (2DOCP), we investigate the possibility of
liquid crystalline states in a single Landau level (LL). We introduce many-body
trial wavefunctions that are translationally invariant but posess 2-fold (i.e.
{\em nematic}), 4-fold ({\em tetratic}) or 6-fold ({\em hexatic}) broken
rotational symmetry at respective filling factors , 1/5 and 1/7 of
the valence LL. We find that the above liquid crystalline states exhibit a soft
charge density wave (CDW) which underlies the translationally invariant state
but which is destroyed by quantum fluctuations. By means of Monte Carlo (MC)
simulations, we determine that, for a considerable variety of interaction
potentials, the anisotropic states are energetically unfavorable for the lowest
and first excited LL's (with index ), whereas the nematic is
favorable at the second excited LL ().Comment: 7 figures, submitted to PRB, high-quality figures available upon
reques
Monte Carlo simulation method for Laughlin-like states in a disk geometry
We discuss an alternative accurate Monte Carlo method to calculate the
ground-state energy and related quantities for Laughlin states of the
fractional quantum Hall effect in a disk geometry. This alternative approach
allows us to obtain accurate bulk regime (thermodynamic limit) values for
various quantities from Monte Carlo simulations with a small number of
particles (much smaller than that needed with standard Monte Carlo approaches).Comment: 13 pages, 6 figures, 2 table
Fermi hypernetted-chain study of half-filled Landau levels with broken rotational symmetry
DOI: 10.1103/PhysRevB.65.205307
http://link.aps.org/doi/10.1103/PhysRevB.65.205307We investigate broken rotational symmetry (BRS) states at half-filling of the valence Landau level (LL). We generalize Rezayi and Read's (RR) trial wave function, a special case of Jain's composite fermion (CF) wave functions, to include anisotropic coupling of the flux quanta to electrons, thus generating a nematic order in the underlying CF liquid. Using the Fermi hypernetted-chain method, which readily gives results in the thermodynamic limit, we determine the properties of these states in detail. By using the anisotropic pair distribution and static structure functions we determine the correlation energy and find that, as expected, RR's state is stable in the lowest LL, whereas BRS states may occur at half- filling of higher LL's, with a possible connection to the recently discovered quantum Hall liquid crystals
Spin dynamics of an ultra-small nanoscale molecular magnet
We present mathematical transformations which allow us to calculate the spin dynamics of an ultra-small nanoscale molecular magnet consisting of a dimer system of classical (high) Heisenberg spins. We derive exact analytic expressions (in integral form) for the time-dependent spin autocorrelation function and several other quantities. The properties of the time-dependent spin autocorrelation function in terms of various coupling parameters and temperature are discussed in detail
Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations
A variety of recent experiments probing the low-temperature transport
properties of quantum Hall systems have suggested an interpretation in terms of
liquid crystalline mesophases dubbed {\em quantum Hall liquid crystals}. The
single mode approximation (SMA) has been a useful tool for the determination of
the excitation spectra of various systems such as phonons in He and in the
fractional quantum Hall effect. In this paper we calculate (via the SMA) the
spectrum of collective excitations in a quantum Hall liquid crystal by
considering {\em nematic}, {\em tetratic}, and {\em hexatic} generalizations of
Laughlin's trial wave function having two-, four- and six-fold broken
rotational symmetry, respectively. In the limit of zero wavevector \qq the
dispersion of these modes is singular, with a gap that is dependent on the
direction along which \qq=0 is approached for {\em nematic} and {\em
tetratic} liquid crystalline states, but remains regular in the {\em hexatic}
state, as permitted by the fourth order wavevector dependence of the
(projected) oscillator strength and static structure factor.Comment: 6 pages, 5 eps figures include
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