arXiv subjects

S. Viefers

Publications and source records attributed to S. Viefers.

At least 19 recordsLinked to original sources

arXiv2015

Linear dependencies between Composite Fermion states

It has been observed that the composite fermion (CF) approach tends to overcount the number of linearly independent candidate states for fixed sets of quantum numbers [number of particles, total angular momentum, and (pseudo)spin if applicable]. That is, CF Slater determinants that are orthogonal before projection, may lead to wave functions that are identical, or possess linear dependencies, after projection. This has been pointed out both in the context of rotating bosons in the lowest Landau level, and for excited bands of the (fermionic) fractional quantum Hall effect. We present a systematic approach that enables us to reveal all linear dependencies between bosonic compact states in the lowest CF "cyclotron energy" sub-band, and almost all dependencies in higher sub-bands, at the level of the CF Slater determinants, i.e. before projection, which implies a major computational simplification. Our approach is introduced for so-called simple states of two-species rotating bosons, and then generalised to generic compact bosonic states, both one- and two-species. Some perspectives also apply to fermionic systems. The identities and linear dependencies we find, are analytically exact for "brute force" projection in the disk geometry.

cond-mat.quant-gas↗

arXiv2014

Rotational properties of two-component Bose gases in the lowest Landau level

We study the rotational (yrast) spectra of dilute two-component atomic Bose gases in the low angular momentum regime, assuming equal interspecies and intraspecies interaction. Our analysis employs the composite fermion (CF) approach including a pseudospin degree of freedom. While the CF approach is not {\it a priori} expected to work well in this angular momentum regime, we show that composite fermion diagonalization gives remarkably accurate approximations to low energy states in the spectra. For angular momenta $0 < L < M$ (where $N$ and $M$ denote the numbers of particles of the two species, and $M \geq N$), we find that the CF states span the full Hilbert space and provide a convenient set of basis states which, by construction, are eigenstates of the symmetries of the Hamiltonian. Within this CF basis, we identify a subset of the basis states with the lowest $Λ$-level kinetic energy. Diagonalization within this significally smaller subspace constitutes a major computational simplification and provides very close approximations to ground states and a number of low-lying states within each pseudospin and angular momentum channel.

cond-mat.quant-gas↗

arXiv2012

Quantum rings for beginners II: Bosons versus fermions

The purpose of this overview article, which can be viewed as a supplement to our previous review on quantum rings, [S. Viefers {\it et al}, Physica E {\bf 21} (2004), 1-35], is to highlight the differences of boson and fermion systems in one-dimensional (1D) and quasi-one-dimensional (Q1D) quantum rings. In particular this involves comparing their many-body spectra and other properties, in various regimes and models, including spinless and spinful particles, finite versus infinite interaction, and continuum versus lattice models. Our aim is to present the topic in a comprehensive way, focusing on small systems where the many-body problem can be solved exactly. Mapping out the similarities and differences between the bosonic and fermionic cases is of renewed interest due to the experimental developments in recent years, allowing for more controlled fabrication of both fermionic and bosonic quantum rings.

cond-mat.mes-hall↗

arXiv2010

A general approach to quantum Hall hierarchies

The abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states emanating from the ν = 5/2 Moore-Read state in the second Landau level. Extending a recently developed formalism for hierarchical quasihole condensation, we present a theory that allows for the explicit construction of the ground state wave function, as well as its quasiparticle excitations, for any state based on the abelian hierarchy. We relate our construction to structures in rational conformal field theory and stress the importance of using coherent state wave functions which allows us to formulate an extension of the bulk - edge correspondence that was conjectured by Moore and Read. Finally, we study the proposed ground state wave functions in the limiting geometry of a thin torus and argue that they coincide with the known exact results.

cond-mat.str-el↗

arXiv2010

Quasihole condensates in quantum Hall liquids

We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states, and to several classes of non-Abelian hierarchical states. Most previously proposed spin-polarized quantum Hall wave functions appear as special cases. In this paper we explain the physical motivations for the approach, and exemplify it by explicitly constructing the level-two quasihole condensate state at filling fraction 2/3, and the two level-three states at 5/13 and 5/7 which are built from combinations of quasielectron and quasihole condensates.

cond-mat.str-el↗

arXiv2009

Quantum Hall quasielectron operators in conformal field theory

In the conformal field theory (CFT) approach to the quantum Hall effect, the multi-electron wave functions are expressed as correlation functions in certain rational CFTs. While this approach has led to a well-understood description of the fractionally charged quasihole excitations, the quasielectrons have turned out to be much harder to handle. In particular, forming quasielectron states requires non-local operators, in sharp contrast to quasiholes that can be created by local chiral vertex operators. In both cases, the operators are strongly constrained by general requirements of symmetry, braiding and fusion. Here we construct a quasielectron operator satisfying these demands and show that it reproduces known good quasiparticle wave functions, as well as predicts new ones. In particular we propose explicit wave functions for quasielectron excitations of the Moore-Read Pfaffian state. Further, this operator allows us to explicitly express the composite fermion wave functions in the positive Jain series in hierarchical form, thus settling a longtime controversy. We also critically discuss the status of the fractional statistics of quasiparticles in the Abelian hierarchical quantum Hall states, and argue that our construction of localized quasielectron states sheds new light on their statistics. At the technical level we introduce a generalized normal ordering, that allows us to "fuse" an electron operator with the inverse of an hole operator, and also an alternative approach to the background charge needed to neutralize CFT correlators. As a result we get a fully holomorphic CFT representation of a large set of quantum Hall wave functions.

cond-mat.mes-hall↗

arXiv2009

Quantum Hall quasielectrons - Abelian and non-Abelian

The quasiparticles in Quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could in principle be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes both in Abelian and non-Abelian QH states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons, and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.

cond-mat.mes-hall↗

arXiv2007

Hierarchy wave functions--from conformal correlators to Tao-Thouless states

Laughlin's wave functions, describing the fractional quantum Hall effect at filling factors $ν=1/(2k+1)$, can be obtained as correlation functions in conformal field theory, and recently this construction was extended to Jain's composite fermion wave functions at filling factors $ν=n/(2kn+1)$. Here we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multi-hole states, make the connection to Wen's general classification of abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally we discuss to what extent our wave functions can be described in the language of composite fermions.

cond-mat.mes-hall↗

arXiv2006

Conformal Field Theory of Composite Fermions

We show that the quantum Hall wave functions for the ground states in the Jain series can be exactly expressed in terms of correlation functions of local vertex operators, V_n, corresponding to composite fermions in the n:th composite-fermion (CF) Landau level. This allows for the powerful mathematics of conformal field theory to be applied to the successful CF phenomenology. Quasiparticle and quasihole states are expressed as correlators of anyonic operators with fractional (local) charge, allowing a simple algebraic understanding of their topological properties that are not manifest in the CF wave functions.

cond-mat.mes-hall↗

arXiv2003

Effects of surface forces and phonon dissipation in a three-terminal nano relay

We have performed a theoretical analysis of the operational characteristics of a carbon-nanotube-based three-terminal nanorelay. We show that short range and van der Waals forces have a significant impact on the characteristics of the relay and introduce design constraints. We also investigate the effects of dissipation due to phonon excitation in the drain contact, which changes the switching time scales of the system, decreasing the longest time scale by two orders of magnitude. We show that the nanorelay can be used as a memory element and investigate the dynamics and properties of such a device.

cond-mat.mes-hall↗

arXiv2003

Energy spectrum, persistent current and electron localization in quantum rings

Energy spectra of quasi-one-dimensional quantum rings with a few electrons are studied using several different theoretical methods. Discrete Hubbard models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body system can be described with a rotation-vibration spectrum of a 'Wigner molecule' of 'localized' electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of magnetic flux through the ring shows periodic oscillations arising from the 'rigid rotation' of the electron ring. For polarized electrons the periodicity of the oscillations is always the flux quantum Phi_0. For nonpolarized electrons the periodicity depends on the strength of the effective Heisenberg coupling and changes from Φ_0 first to Phi_0/2 and eventually to Phi_0/N when the ring gets narrower.

cond-mat.mes-hall↗

arXiv2003

Quantum rings for beginners: Energy spectra and persistent currents

Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body states can be described by a rotation-vibration spectrum of a 'Wigner molecule' of 'localized' electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of the magnetic flux through the ring shows periodic oscillations arising from the 'rigid rotation' of the electron ring. For polarized electrons the periodicity of the oscillations is always the flux quantum Phi_0. For nonpolarized electrons the periodicity depends on the strength of the effective Heisenberg coupling and changes from Phi_0 first to Phi_0/2 and eventually to Phi_0/N when the ring gets narrower.

cond-mat.mes-hall↗

arXiv2003

Effective photon-photon interaction in a two-dimensional "photon fluid"

We formulate an effective theory for the atom-mediated photon-photon interactions in a two-dimensional ``photon fluid'' confined in a Fabry-Perot resonator. With the atoms modelled by a collection of anharmonic Lorentz oscillators, the effective interaction is evaluated to second order in the coupling constant (the anharmonicity parameter). The interaction has the form of a renormalized two-dimensional delta-function potential, with the renormalization scale determined by the physical parameters of the system, such as density of atoms and the detuning of the photons relative to the resonance frequency of the atoms. For realistic values of the parameters, the perturbation series has to be resummed, and the effective interaction becomes independent of the ``bare'' strength of the anharmonic term. The resulting expression for the non-linear Kerr susceptibility, is parametrically equal to the one found earlier for a dilute gas of two-level atoms. Using our result for the effective interaction parameter, we derive conditions for the formation of a photon fluid, both for Rydberg atoms in a microwave cavity and for alkali atoms in an optical cavity.

physics.atom-ph↗

arXiv2002

A Carbon Nanotube Based Nanorelay

We investigate the operational characteristics of a nanorelay based on a conducting carbon nanotube placed on a terrace in a silicon substrate. The nanorelay is a three terminal device that acts as a switch in the GHz regime. Potential applications include logic devices, memory elements, pulse generators, and current or voltage amplifiers.

cond-mat.mes-hall↗

arXiv2001

Many-body spectrum and particle localization in quantum dots and finite rotating Bose condensates

The yrast spectra (i.e. the lowest states for a given total angular momentum) of quantum dots in strong magnetic fields, are studied in terms of exact numerical diagonalization and analytic trial wave functions. We argue that certain features (cusps) in the many-body spectrum can be understood in terms of particle localization due to the strong field. A new class of trial wavefunctions supports the picture of the electrons being localized in Wigner molecule-like states consisting of consecutive rings of electrons, with low-lying excitations corresponding to rigid rotation of the outer ring of electrons. The geometry of the Wigner molecule is independent of interparticle interactions and the statistics of the particles.

cond-mat.mes-hall↗

arXiv2001

Exclusion Statistics in a two-dimensional trapped Bose gas

We briefly explain the notion of exclusion statistics and in particular discuss the concept of an ideal exclusion statistics gas. We then review a recent work where it is demonstrated that a {\em two-dimensional} Bose gas with repulsive delta function interactions obeys ideal exclusion statistics, with a fractional parameter related to the interaction strength.

cond-mat.stat-mech↗

arXiv2000

Exclusion Statistics in a trapped two-dimensional Bose gas

We study the statistical mechanics of a two-dimensional gas with a repulsive delta function interaction, using a mean field approximation. By a direct counting of states we establish that this model obeys exclusion statistics and is equivalent to an ideal exclusion statistics gas.

cond-mat.stat-mech↗

arXiv2000

Current-spin-density functional study of persistent currents in quantum rings

We present a numerical study of persistent currents in quantum rings using current spin density functional theory (CSDFT). This formalism allows for a systematic study of the joint effects of both spin, interactions and impurities for realistic systems. It is illustrated that CSDFT is suitable for describing the physical effects related to Aharonov-Bohm phases by comparing energy spectra of impurity-free rings to existing exact diagonalization and experimental results. Further, we examine the effects of a symmetry-breaking impurity potential on the density and current characteristics of the system and propose that narrowing the confining potential at fixed impurity potential will suppress the persistent current in a characteristic way.

cond-mat.mes-hall↗