Scott D. Geraedts

The half-filled Landau level:The case for Dirac composite fermions

All is well with particle-hole symmetry In an external magnetic field, the energy of an electron in a two-dimensional system takes discrete values, called Landau levels. At high enough fields, all electrons in a solid can fit in the lowest Landau level. If exactly half of that level is filled with electrons, standard theory predicts that a special fermion liquid phase will form that makes a distinction between the filled and empty states (particles and holes). A recent conjecture, in contrast, predicted a liquid consisting of massless Dirac particles that respects the symmetry between particles and holes. Geraedts et al. used sophisticated numerical methods to provide strong evidence for this conjecture. Science, this issue p. 197 Density matrix renormalization group calculations show that particle-hole symmetry is preserved in a half-filled Landau level. In a two-dimensional electron gas under a strong magnetic field, correlations generate emergent excitations distinct from electrons. It has been predicted that “composite fermions”—bound states of an electron with two magnetic flux quanta—can experience zero net magnetic field and form a Fermi sea. Using infinite-cylinder density matrix renormalization group numerical simulations, we verify the existence of this exotic Fermi sea, but find that the phase exhibits particle-hole symmetry. This is self-consistent only if composite fermions are massless Dirac particles, similar to the surface of a topological insulator. Exploiting this analogy, we observe the suppression of 2kF backscattering, a characteristic of Dirac particles. Thus, the phenomenology of Dirac fermions is also relevant to two-dimensional electron gases in the quantum Hall regime.

Emergent particle-hole symmetry in spinful bosonic quantum Hall systems

Recently, a reevaluation of particle-hole symmetry in fermionic quantum Hall systems has led to a wealth of new insights about quantum Hall phases and connections between quantum Hall physics and other topological phases as well as high-energy physics. Similar progress may be possible in the bosonic case if such a symmetry exists, unlike the fermionic case such a symmetry is not exact. Here, the authors provide the first evidence for the existence of an emergent bosonic particle-hole symmetry.

Competing Abelian and non-Abelian topological orders in ν=1/3+1/3 quantum Hall bilayers

Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two subbands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν=1/3+1/3. We first consider the Coulomb interaction at bilayer separation d, bilayer tunneling energy Δ_(SAS), and individual layer width w, where we find a phase diagram which includes three competing Abelian phases: a bilayer Laughlin phase (two nearly decoupled ν=1/3 layers), a bilayer spin-singlet phase, and a bilayer symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases has also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the “interlayer-Pfaffian” phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν=1/3+1/3 systems merit further experimental study.

Monte Carlo study of a U(1)×U(1) system with π-statistical interaction

We study a U(1)×U(1) system with two species of loops with mutual π statistics in (2 + 1) dimensions. We are able to reformulate the model in a way that can be studied by Monte Carlo and we determine the phase diagram. In addition to a phase with no loops, we find two phases with only one species of loop proliferated. The model has a self-dual line, a segment of which separates these two phases. Everywhere on the segment, we find the transition to be first-order, signifying that the two loop systems behave as immiscible fluids when they are both trying to condense. Moving further along the self-dual line, we find a phase where both loops proliferate, but they are only of even strength and, therefore, avoid the statistical interactions. We study another model, which does not have this phase, and also find first-order behavior on the self-dual segment.

Composite fermions in bands with N -fold rotational symmetry

We study the effect of band anisotropy with discrete rotational symmetry

Numerical study of anisotropy in a composite Fermi liquid

C_N

Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases

(where

Model of Fractionalization of Faraday Lines in Compact Electrodynamics

N\ge 2

Line of continuous phase transitions in a three-dimensional U(1) loop model with 1/r^2 current-current interactions

) in the quantum Hall regime of two-dimensional electron systems. We focus on the composite Fermi liquid (CFL) at half filling of the lowest Landau level. We find that the magnitude of anisotropy transferred to the composite fermions decreases very rapidly with

Absence of many-body localization in a single Landau level

N