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 $\nu = 1/3$, 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 $L = 0, 1$), whereas the nematic is favorable at the second excited LL ($L = 2$).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 $^4$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