arXiv subjects

Gunnar Moller

Publications and source records attributed to Gunnar Moller.

18 recordsLinked to original sources

arXiv2012

Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States

We show how the phases of interacting particles in topological flat bands, known as fractional Chern insulators, can be adiabatically connected to incompressible fractional quantum Hall liquids in the lowest Landau-level of an externally applied magnetic field. Unlike previous evidence suggesting the similarity of these systems, our approach enables a formal proof of the equality of their topological orders, and furthermore this proof robustly extends to the thermodynamic limit. We achieve this result using the hybrid Wannier orbital basis proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] in order to construct interpolation Hamiltonians that provide continuous deformations between the two models. We illustrate the validity of our approach for the groundstate of bosons in the half filled Chern band of the Haldane model, showing that it is adiabatically connected to the $ν=1/2$ Laughlin state of bosons in the continuum fractional quantum Hall problem.

cond-mat.mes-hall↗

arXiv2012

Fractional Quantum Hall Effect of Lattice Bosons Near Commensurate Flux

We study interacting bosons on a lattice in a magnetic field. When the number of flux quanta per plaquette is close to a rational fraction, the low energy physics is mapped to a multi-species continuum model: bosons in the lowest Landau level where each boson is given an internal degree of freedom, or pseudospin. We find that the interaction potential between the bosons involves terms that do not conserve pseudospin, corresponding to umklapp processes, which in some cases can also be seen as BCS-type pairing terms. We argue that in experimentally realistic regimes for bosonic atoms in optical lattices with synthetic magnetic fields, these terms are crucial for determining the nature of allowed ground states. In particular, we show numerically that certain paired wavefunctions related to the Moore-Read Pfaffian state are stabilized by these terms, whereas certain other wavefunctions can be destabilized when umklapp processes become strong.

cond-mat.mes-hall↗

arXiv2012

Correlated phases of bosons in the flat lowest band of the dice lattice

We study correlated phases occurring in the flat lowest band of the dice lattice model at flux density one half. We discuss how to realize the dice lattice model, also referred to as the T_3 lattice, in cold atomic gases. We construct the projection of the model to the lowest dice band, which yields a Hubbard-Hamiltonian with interaction-assisted hopping processes. We solve this model for bosons in two limits. In the limit of large density, we use Gross-Pitaevskii mean-field theory to reveal time-reversal symmetry breaking vortex lattice phases. At low density, we use exact diagonalization to identify three stable phases at fractional filling factors νof the lowest band, including a classical crystal at ν=1/3, a supersolid state at ν=1/2 and a Mott insulator at ν=1.

cond-mat.mes-hall↗

arXiv2012

Competing Topological Orders in the nu=12/5 Quantum Hall State

We provide numerical evidence that a p_{x}-i p_{y} paired Bonderson--Slingerland (BS) non-Abelian hierarchy state is a strong candidate for the observed nu=12/5 quantum Hall plateau. We confirm the existence of a gapped incompressible nu = 12/5 quantum Hall state with shift S=2 on the sphere, matching that of the BS state. The exact ground state of the Coulomb interaction at S=2 is shown to have large overlap with the BS trial wave function. Larger overlaps are obtained with BS-type wave functions that are hierarchical descendants of general p_{x}-i p_{y} weakly-paired states at nu=5/2. We perform a finite size scaling analysis of the ground state energies for nu=12/5 states at shifts corresponding to the BS (S=2) and 3-clustered Read-Rezayi (S=-2) universality classes. This analysis reveals very tight competition between these two non-Abelian topological orders.

cond-mat.mes-hall↗

arXiv2011

Neutral Fermion Excitations in the Moore-Read state at ν=5/2

We present evidence supporting the weakly paired Moore-Read phase in the half-filled second Landau level, focusing on some of the qualitative features of its excitations. Based on numerical studies, we show that systems with odd particle number at the flux $N_ϕ=2N-3$ can be interpreted as a neutral fermion mode of one unpaired fermion, which is gapped. The mode is found to have two distinct minima, providing a signature that could be observed by photoluminescence. In the presence of two quasiparticles the same neutral fermion excitation is shown to be gapless, confirming expectations for non-Abelian statistics of the Ising model with degenerate fusion channels 1 and $ψ$.

cond-mat.mes-hall↗

arXiv2010

Condensed Groundstates of Frustrated Bose-Hubbard Models

We study theoretically the groundstates of two-dimensional Bose-Hubbard models which are frustrated by gauge fields. Motivated by recent proposals for the implementation of optically induced gauge potentials, we focus on the situation in which the imposed gauge fields give rise to a pattern of staggered fluxes, of magnitude $α$ and alternating in sign along one of the principal axes. For $α=1/2$ this model is equivalent to the case of uniform flux per plaquette $n_ϕ=1/2$, which, in the hard-core limit, realizes the "fully frustrated" spin-1/2 XY model. We show that the mean-field groundstates of this frustrated Bose-Hubbard model typically break translational symmetry. We introduce a general numerical technique to detect broken symmetry condensates in exact diagonalization studies. Using this technique we show that, for all cases studied, the groundstate of the Bose-Hubbard model with staggered flux $α$ is condensed, and we obtain quantitative determinations of the condensate fraction. We discuss the experimental consequences of our results. In particular, we explain the meaning of gauge-invariance in ultracold atom systems subject to optically induced gauge potentials, and show how the ability to imprint phase patterns prior to expansion can allow very useful additional information to be extracted from expansion images.

cond-mat.quant-gas↗

arXiv2010

Trial wavefunctions for the Goldstone mode in ν=1/2+1/2 quantum Hall bilayers

Based on the known physics of the excitonic superfluid or 111 state of the quantum Hall ν=1/2+1/2 bilayer, we create a simple trial wavefunction ansatz for constructing a low energy branch of (Goldstone) excitations by taking the overall ground state and boosting one layer with respect to the other. This ansatz works extremely well for any interlayer spacing. For small d this is simply the physics of the Goldstone mode, whereas for large d this is a reflection of composite fermion physics. We find hints that certain aspects of composite fermion physics persist to low d whereas certain aspects of Goldstone mode physics persist to high d. Using these results we show nonmonotonic behavior of the Goldstone mode velocity as a function of d.

cond-mat.mes-hall↗

arXiv2010

Magnetic multipole analysis of kagome and artificial ice dipolar arrays

We analyse an array of linearly extended monodomain dipoles forming square and kagome lattices. We find that its phase diagram contains two (distinct) finite-entropy kagome ice regimes - one disordered, one algebraic - as well as a low-temperature ordered phase. In the limit of the islands almost touching, we find a staircase of corresponding entropy plateaux, which is analytically captured by a theory based on magnetic charges. For the case of a modified square ice array, we show that the charges ('monopoles') are excitations experiencing two distinct Coulomb interactions: a magnetic 'three-dimensional' one as well as a logarithmic `two dimensional' one of entropic origin.

cond-mat.stat-mech↗

arXiv2010

Composite fermion dynamics in half-filled Landau levels of graphene

We report on exact-diagonalization studies of correlated many-electron states in the half-filled Landau levels of graphene, including pseudospin (valley) degeneracy. We demonstrate that the polarized Fermi sea of non-interacting composite fermions remains stable against a pairing transition in the lowest two Landau levels. However, it undergoes spontaneous depolarization, which is unprotected owing to the lack of single-particle pseudospin splitting. These results suggest the absence of the Pfaffian phase in graphene.

cond-mat.str-el↗

arXiv2009

Skyrmions in the Moore-Read state at nu=5/2

We study charged excitations of the non-abelian Moore-Read liquid at filling factor nu=5/2, allowing for spin depolarization. Using a combination of numerical studies, and taking account of non-zero well widths, we find that at sufficiently low Zeeman energy it is energetically favourable for charge e/4 quasiholes to bind into "skyrmions" of charge e/2. We show that skyrmion formation is further promoted by disorder, and argue that this can lead to a depolarized nu=5/2 ground state in realistic experimental situations. We comment on the consequences for the activated transport.

cond-mat.str-el↗

arXiv2009

Composite Fermion Theory for Bosonic Atoms in Optical Lattices

We study the groundstates of cold atomic gases on rotating optical lattices, as described by the Bose-Hubbard model in a uniform effective magnetic field. Mapping the bosons to composite fermions leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial wavefunctions for these phases, and perform numerical tests of the predictions of the composite fermion model. Our results establish the existence of strongly correlated phases beyond those in the continuum limit, and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau-level.

cond-mat.mes-hall↗

arXiv2009

Trial Wavefunctions for ν= 1/2 + 1/2 Quantum Hall Bilayers

Quantum Hall bilayer systems at filling fractions near ν= 1/2 + 1/2 undergo a transition from a compressible phase with strong intralayer correlation to an incompressible phase with strong interlayer correlations as the layer separation d is reduced below some critical value. Deep in the intralayer phase (large separation) the system can be interpreted as a fluid of composite fermions (CFs), whereas deep in the interlayer phase (small separation) the system can be interpreted as a fluid of composite bosons (CBs). The focus of this paper is to understand the states that occur for intermediate layer separation by using trial variational wavefunctions. We consider two main classes of wavefunctions. In the first class, previously introduced by Moller et al. [PRL {\bf 101}, 176803 (2008)], we consider interlayer BCS pairing of two independent CF liquids. We find that these wavefunctions are exceedingly good for d >~ \ell_0 with \ell_0 the magnetic length. The second class of wavefunctions naturally follows the reasoning of Simon et al. [PRL {\bf 91}, 046803 (2003)] and generalizes the idea of pairing wavefunctions by allowing the CFs also to be replaced continuously by CBs. This generalization allows us to construct exceedingly good wavefunctions for interlayer spacings of d <~ \ell_0, as well. The accuracy of the wavefunctions discussed in this work, compared with exact diagonalization, approaches that of the celebrated Laughlin wavefunction.

cond-mat.mes-hall↗

arXiv2008

Paired composite fermion phase of quantum Hall bilayers at ν= 1/2 + 1/2

We provide numerical evidence for composite fermion pairing in quantum Hall bilayer systems at filling $ν=1/2 + 1/2$ for intermediate spacing between the layers. We identify the phase as $p_x + i p_y$ pairing, and construct high accuracy trial wavefunctions to describe the groundstate on the sphere. For large distances between the layers, and for finite systems, a competing "Hund's rule" state, or composite fermion liquid, prevails for certain system sizes. We argue that for larger systems, the pairing phase will persist to larger layer spacing.

cond-mat.mes-hall↗

arXiv2007

Paired composite fermion wavefunctions

We construct a family of BCS paired composite fermion wavefunctions that generalize, but remain in the same topological phase as, the Moore-Read Pfaffian state for the half-filled Landau level. It is shown that for a wide range of experimentally relevant inter-electron interactions the groundstate can be very accurately represented in this form.

cond-mat.mes-hall↗

arXiv2007

Density waves and supersolidity in rapidly rotating atomic Fermi gases

We study theoretically the low-temperature phases of a two-component atomic Fermi gas with attractive s-wave interactions under conditions of rapid rotation. We find that, in the extreme quantum limit, when all particles occupy the lowest Landau level, the normal state is unstable to the formation of "charge" density wave (CDW) order. At lower rotation rates, when many Landau levels are occupied, we show that the low-temperature phases can be supersolids, involving both CDW and superconducting order.

cond-mat.mes-hall↗

arXiv2006

Artificial square ice and related dipolar nanoarrays

We study a frustrated dipolar array recently manufactured lithographically by Wang {\em et al.} [Nature {\bf 439}, 303 (2006)] in order to realize the square ice model in an artificial structure. We discuss models for thermodynamics and dynamics of this system. We show that an ice regime can be stabilized by small changes in the array geometry; a different magnetic state, kagome ice, can similarly be constructed. At low temperatures, the square ice regime is terminated by a thermodynamic ordering transition, which can be chosen to be ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate experimentally, and identify a likely dynamical bottleneck.

cond-mat.stat-mech↗

arXiv2005

Dimensional reduction on a sphere

The question of the dimensional reduction of two-dimensional (2d) quantum models on a sphere to one-dimensional (1d) models on a circle is adressed. A possible application is to look at a relation between the 2d anyon model and the 1d Calogero-Sutherland model, which would allow for a better understanding of the connection between 2d anyon exchange statistics and Haldane exclusion statistics. The latter is realized microscopically in the 2d LLL anyon model and in the 1d Calogero model. In a harmonic well of strength ωor on a circle of radius R - both parameters ωand R have to be viewed as long distance regulators - the Calogero spectrum is discrete. It is well known that by confining the anyon model in a 2d harmonic well and projecting it on a particular basis of the harmonic well eigenstates, one obtains the Calogero-Moser model. It is then natural to consider the anyon model on a sphere of radius R and look for a possible dimensional reduction to the Calogero-Sutherland model on a circle of the same radius. First, the free one-body case is considered, where a mapping from the 2d sphere to the 1d chiral circle is established by projection on a special class of spherical harmonics. Second, the N-body interacting anyon model is considered : it happens that the standard anyon model on the sphere is not adequate for dimensional reduction. One is thus lead to define a new spherical anyon-like model deduced from the Aharonov-Bohm problem on the sphere where each flux line pierces the sphere at one point and exits it at its antipode.

cond-mat.mes-hall↗

arXiv2005

Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study

The method of Jain and Kamilla [PRB {\bf 55}, R4895 (1997)] allows numerical generation of composite fermion trial wavefunctions for large numbers of electrons in high magnetic fields at filling fractions of the form nu=p/(2mp+1) with m and p positive integers. In the current paper we generalize this method to the case where the composite fermions are in an effective (mean) field with opposite sign from the actual physical field, i.e. when p is negative. We examine both the ground state energies and the low energy neutral excitation spectra of these states. Using particle-hole symmetry we can confirm the correctness of our method by comparing results for the series m=1 with p>0 (previously calculated by others) to our results for the conjugate series m=1 with p <0. Finally, we present similar results for ground state energies and low energy neutral excitations for the states with m=2 and p <0 which were not previously addressable, comparing our results to the m=1 case and the p > 0, m=2 cases.

cond-mat.mes-hall↗