Ground state energy calculations of the ν=1/2 and the ν=5/2 FQHE system

We reconsider energy calculations of the spin polarized ν = 1/2 Chern-Simons theory. We show that one has to be careful in the definition of the Chern-Simons path integral in order to avoid an IR divergent magnetic ground state energy in RPA as in [J. Dietel et al, Eur. Phys. J. B 5, 439 (1998)]. We correct the path integral and get a well behaved magnetic energy by considering the energy of the maximal divergent graphs as well as the Hartree-Fock graphs. Furthermore, we consider the ν = 1/2 and the ν = 5/2 system with spin degrees of freedom. In doing this we formulate a Chern-Simons theory of the ν = 5/2 system by transforming the interaction operator to the next lower Landau level. We calculate the Coulomb energy of the spin polarized as well as the spin unpolarized ν = 1/2 and the ν = 5/2 system as a function of the interaction strength in RPA. These energies are in good agreement with numerical simulations of interacting electrons in the first as well as in the second Landau level. Furthermore, we calculate the compressibility, the effective mass and the excitations of the spin polarized ν = 2 + 1/ systems where is an even number. Received 13 June 2000     

The asymptotic behaviour of the exact and approximative ν = 1/2 Chern-Simons Green's functions

We consider the asymptotic behaviour of the Chern-Simons Green's function of the ν = 1/ system for an infinite area in position-time representation. We calculate explicitly the asymptotic form of the Green's function of the interaction free Chern-Simons system for small times. The calculated Green's function vanishes exponentially with the logarithm of the area. Furthermore, we discuss the form of the divergence for all τ and also for the Coulomb interacting Chern-Simons system. We compare the asymptotics of the exact Chern-Simons Green's function with the asymptotics of the Green's function in the Hartree-Fock as well as the random-phase approximation (RPA). The asymptotics of the Hartree-Fock Green's function correspondence well with the exact Green's function. In the case of the RPA Green's function we do not get the correct asymptotics. At last, we calculate the self consistent Hartree-Fock Green's function. Received 5 July 2001 and Received in final form 30 November 2001     

The Fermi-sea-like limit of the composite fermion wave function

The experimentally observed filling factors of the fractional quantum Hall effect can be described in terms of the composite fermion wave function of the Jastrow-Slater form [0pt] fully projected into the lowest Landau level. The Slater determinant of the above composite fermion wave function represents the filled Landau levels of composite fermions evaluated at the corresponding reduced magnetic field. For a system of fermions studied in the thermodynamic limit, we prove that in the even-denominator-filled state limit (when the number of filled Landau levels of composite fermions becomes infinite), the above composite fermion wave function exactly transforms into the Rezayi-Read Fermi-sea-like wave function [0pt] constructed by attaching 2m flux quanta to the Slater determinant of two-dimensional free fermions at the density corresponding to that filling. We study the composite fermion wave function and its evolution into the Fermi-sea-like wave function for a range of filling factors very close to the even-denominator-filled state. Received 19 March 1999     

Charge localization in organic conductors (TM)X: The influence of anion ordering

An investigation of the different contributions leading to charge localization in a 1/2 or 1/4 filled band 1D conductor has been conducted through a study of transport properties in the solid solution [(TMTSF)_1-x (TMTTF) _x]₂ReO₄. The existence of an ordering transition of the anions allows to identify two contributions to the electronic potential with wave vector 4k_F. A dominant on-site 4k_F potential besides the bond contribution is revealed when Umklapp scattering is pertinent via the weakening of the localization arising at the (0, 1/2, 1/2) anion ordering which is stabilized under pressure in the compound [(TMTSF) _0.5 (TMTTF)_0.5]₂ReO₄ at variance with the enhancement of localization observed in the homomolecular (TMTTF)₂ReO ₄ material. Received: 13 May 1998 / Revised: 8 July 1998 / Accepted: 9 July 1998     

Energy gaps for fractional quantum Hall states described by a Chern-Simons composite fermion wavefunction

The Jain's composite fermion wavefunction has proven quite succesful to describe most of the fractional quantum Hall states. Its mathematical foundation lies in the Chern-Simons field theory for the electrons in the lowest Landau level, despite the fact that such wavefunction is different from a typical mean-field level Chern-Simons wavefunction. It is known that the energy excitation gaps for fractional Hall states described by Jain's composite fermion wavefunction cannot be calculated analytically. We note that analytic results for the energy excitation gaps of fractional Hall states described by a fermion Chern-Simons wavefunction are readily obtained by using a technique originating from nuclear matter studies. By adopting this technique to the fractional quantum Hall effect we obtained analytical results for the excitation energy gaps of all fractional Hall states described by a Chern-Simons wavefunction. Received 9 March 2001     

Damping of zero sound in Luttinger liquids

We calculate the damping γ_q of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k² / 2 m at zero temperature. Using standard many-body perturbation theory, we obtain γ_q from the expansion of the inverse irreducible polarization to first order in the effective screened (RPA) interaction. For wave-vectors | q| /k_F ≪F (where k_F = m v_F is the Fermi wave-vector) we find to leading order γ_q ∝| q |³ /(v_F m²). On the other hand, for F ≪| q| /k_F most of the spectral weight is carried by the particle-hole continuum, which is distributed over a frequency interval of the order of q²/m. We also show that zero sound damping leads to a finite maximum proportional to |k - k_F | ^{-2 + 2 η} of the charge peak in the single-particle spectral function, where η is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K_0.3MoO₃. We comment on other recent calculations of γ_q.     

Correlated transport and non-Fermi-liquid behavior in single-wall carbon nanotubes

We derive the effective low-energy theory for single-wall carbon nanotubes including the Coulomb interactions among electrons. The generic model found here consists of two spin-fermion chains which are coupled by the interaction. We analyze the theory using bosonization, renormalization-group techniques, and Majorana refermionization. Several experimentally relevant consequences of the breakdown of Fermi liquid theory observed here are discussed in detail, e.g., magnetic instabilities, anomalous conductance laws, and impurity screening profiles. Received: 12 December 1997 / Revised: 9 March 1998 / Accepted: 12 March 1998     

The smooth structural change in mesoscopic Peierls chains

We investigate the Peierls transition in finite chains by exact (Lanczos) diagonalization and within a seminumerical method based on the factorization of the electron-phonon wave function (Adiabatic Ansatz, AA). AA can be applied for mesoscopic chains up to micrometer sizes and its reliability can be checked self-consistently. Our study demonstrates the important role played for finite systems by the tunneling in the double well potential. The chains are dimerized only if their size N exceeds a critical value N_c which increases with increasing phonon frequency. Quantum phonon fluctuations yield a broad transition region. This smooth Peierls transition contrasts not only to the sharp mean field transition, but also with the sharp RPA soft mode instability, although RPA partially accounts for quantum phonon fluctuations. For weak coupling the dimerization disappears below micrometer sizes; therefore, this effect could be detected experimentally in mesoscopic systems. Received: 3 January 1998 / Revised: 13 March 1998 / Accepted: 3 April 1998     

Spectral densities of response functions for the O(3) symmetric Anderson and two channel Kondo models

The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln divergence found in the low frequency behaviour of the T=0 dynamic susceptibility. Received 29 January 1999     

Flow equations and extended Bogoliubov transformation for the Heisenberg antiferromagnet near the classical limit

The Heisenberg spin-S quantum antiferromagnet is studied near the large-spin limit, applying a new continuous unitary transformation which extends the usual Bogoliubov transformation to higher order in the 1/S-expansion of the Hamiltonian. This allows to diagonalize the bosonic Hamiltonian resulting from the Holstein-Primakoff representation beyond the conventional spin-wave approximation. The zero-temperature flow equations derived from the extension of the Bogoliubov transformation to order for the ground-state energy, the spin-wave velocity, and the staggered magnetization are solved exactly and yield results which are in agreement with those obtained by a perturbative treatment of the magnon interactions. Received: 19 March 1998 / Revised: 2 June 1998 / Accepted: 8 June 1998     

On the incommensurate phase in modulated Heisenberg chains

Using the density matrix renormalization group method (DMRG) we calculate the magnetization of frustrated S=1/2 Heisenberg chains for various modulation patterns of the nearest neighbour coupling: commensurate, incommensurate with sinusoidal modulation and incommensurate with solitonic modulation. We focus on the order of the phase transition from the commensurate dimerized phase (D) to the incommensurate phase (I). It is shown that the order of the phase transition depends sensitively on the model. For the solitonic model in particular, a k-dependent elastic energy modifies the order of the transition. Furthermore, we calculate gaps in the incommensurate phase in adiabatic approximation. Received: 9 March 1998 / Accepted: 17 April 1998     

Universal conductance in quantum wires in the presence of Umklapp scattering

The effects of Umklapp scattering on the zero-temperature conductance in one-dimensional quantum wires are reexamined by taking into account both the screening of external potential and the non-uniform chemical potential shift due to electron-electron interaction. It is shown that in the case away from half-filling the conductance is given by the universal value, 2e ² /h, even in the presence of Umklapp scattering, owing to these renormalization effects of external potential. The conclusion is in accordance with the recent claim obtained for the system with non-interacting leads being attached to a quantum wire. Received: 5 February 1998 / Received in final form: 16 March 1998 / Accepted: 17 April 1998     

Influence of excited Landau levels on a two-dimensional electron-hole system in a strong perpendicular magnetic field

The study of the quantum states of a two-dimensional electron-hole system in a strong perpendicular magnetic field is carried out with special attention to the influence of virtual quantum transitions of interacting particles between the Landau levels. These virtual quantum transitions from the lowest Landau levels to excited Landau levels with arbitrary quantum numbers n and m and their reversion to the lowest Landau levels in second order perturbation theory result in an indirect attraction between the particles. The influence of the indirect interaction on the magnetoexciton ground state, on the chemical potential of the Bose-Einstein condensed magnetoexcitons, and on the ground state energy of the metallic-type electron-hole liquid is investigated in the Hartree-Fock approximation. The coexistence of different phases is suggested.     

Determination of the chemical potential and the energy of the ν=1/2 FQHE system for low temperatures

We consider the energy density of a spin polarized ν = 1/2 system for low temperatures. We show that due to the elimination of the magnetic field and the field of the positive background charge in the calculation of the grand canonical potential of Chern-Simons systems through a mean field formalism one gets corrections to the well known equations which determine the chemical potential and the energy from the grand canonical potential. We use these corrected equations to calculate the chemical potential and the energy of the ν = 1/2 system at low temperatures in two different approximations. Received 14 March 2001     

Positions of the magnetoroton minima in the fractional quantum Hall effect

The multitude of excitations of the fractional quantum Hall state are very accurately understood, microscopically, as excitations of composite fermions across their Landau-like Λ levels. In particular, the dispersion of the composite fermion exciton, which is the lowest energy spin conserving neutral excitation, displays filling-factor-specific minima called “magnetoroton” minima. Simon and Halperin employed the Chern-Simons field theory of composite fermions [Phys. Rev. B 48, 17368 (1993)] to predict the magnetoroton minima positions. Recently, Golkar et al. [Phys. Rev. Lett. 117, 216403 (2016)] have modeled the neutral excitations as deformations of the composite fermion Fermi sea, which results in a prediction for the positions of the magnetoroton minima. Using methods of the microscopic composite fermion theory we calculate the positions of the roton minima for filling factors up to 5/11 along the sequence s/ (2s + 1) and find them to be in reasonably good agreement with both the Chern-Simons field theory of composite fermions and Golkar et al.’s theory. We also find that the positions of the roton minima are insensitive to the microscopic interaction in agreement with Golkar et al.’s theory. As a byproduct of our calculations, we obtain the charge and neutral gaps for the fully spin polarized states along the sequence s/ (2s ± 1) in the lowest Landau level and the n = 1 Landau level of graphene.     

A Discrete Density Matrix Theory for Atoms¶in Strong Magnetic Fields

This paper concerns the asymptotic ground state properties of heavy atoms in strong, homogeneous magnetic fields. In the limit when the nuclear charge Z tends to ∞ with the magnetic field B satisfying B>> Z ^4/3 all the electrons are confined to the lowest Landau band. We consider here an energy functional, whose variable is a sequence of one-dimensional density matrices corresponding to different angular momentum functions in the lowest Landau band. We study this functional in detail and derive various interesting properties, which are compared with the density matrix (DM) theory introduced by Lieb, Solovej and Yngvason. In contrast to the DM theory the variable perpendicular to the field is replaced by the discrete angular momentum quantum numbers. Hence we call the new functional a discrete density matrix (DDM) functional. We relate this DDM theory to the lowest Landau band quantum mechanics and show that it reproduces correctly the ground state energy apart from errors due to the indirect part of the Coulomb interaction energy. Received: 20 October 2000 / Accepted: 3 November 2000     

On the Uniqueness of the Solution to the Three-Body Problem with Zero-Range Interactions

We consider the uniqueness of the solution to a three-body problem with zero-range Skyrme interactions in configuration space. With the lowest, k⁰, two-body term alone the problem is known to have no unique solution as the system collapses – the variational estimate of the energy tends towards negative infinity, the size of the system towards zero. We argue that the next, k², two-body term removes the collapse and the three-body system acquires finite ground-state energy and size. The three-body interaction term is thus not necessary to provide a unique solution to the problem.     

Perturbation theory for isotropic velocity-dependent potentials: Bound-states case

Starting from the time-independent Schr?dinger equation we develop formulae for the changes in the bound-state energies in the presence of an isotropic, velocity-dependent perturbing potential. The corresponding changes in the wave functions are also obtained. Unlike the case of the standard perturbation theory, determination of the changes in the energy and the wave function of a state only requires knowledge of the unperturbed ground-state wave function in addition to the perturbing potential. Evaluations of the energy changes and the corresponding wave functions are given for two examples in the s-wave case.     

Competition of disorder and interchain hopping in a two-chain Hubbard model

We study the interplay of Anderson localization and interaction in a two chain Hubbard ladder allowing for arbitrary ratio of disorder strength to interchain coupling. We obtain three different types of spin gapped localized phases depending on the strength of disorder: a pinned 4k _F Charge Density Wave (CDW) for weak disorder, a pinned 2k _F CDW^π for intermediate disorder and two independently pinned single chain 2k _F CDW for strong disorder. Confinement of electrons can be obtained as a result of strong disorder or strong attraction. We give the full phase diagram as a function of disorder, interaction strength and interchain hopping. We also study the influence of interchain hopping on localization length and show that localization is enhanced by a small interchain hopping but suppressed by a large interchain hopping. Received 6 April 2001