Alexander Seidel

S = 1 2 chains and spin-Peierls transition in TiOCl

We study TiOCI as an example of an S= ½ layered Mott insulator. From our analysis of susceptibility data, combined with local-density-approximation (LDA) and LDA+ U band-structure calculations, we conclude that orbital ordering produces quasi-one-dimensional spin chains and that TiOCI is an example of Heisenberg chains that undergo a spin-Peierls transition. The energy scale is an order of magnitude larger than that of previously known examples. The effects of nonmagnetic Sc impurities are explained using a model of broken finite chains.

Incompressible Quantum Liquids and New Conservation Laws

In this Letter, we investigate a class of Hamiltonians which, in addition to the usual center-of-mass momentum conservation, also have center-of-mass position conservation. We find that, regardless of the particle statistics, the energy spectrum is at least q-fold degenerate when the filling factor is p/q, where and are coprime integers. Interestingly, the simplest Hamiltonian respecting this type of symmetry encapsulates two prominent examples of novel states of matter, namely, the fractional quantum Hall liquid and the quantum dimer liquid. We discuss the relevance of this class of Hamiltonian to the search for featureless Mott insulators.

Abelian and non-abelian hall liquids and charge-density wave : Quantum number fractionalization in one and two dimensions

Previously, we have demonstrated that, on a torus, the Abelian quantum Hall liquid is adiabatically connected to a charge-density wave as the smaller dimension of the torus is varied. In this work, we extend this result to the non-Abelian bosonic Hall state. The outcome of these works is the realization that the paradigms of quantum number fractionalization in one dimension (polyacetylene) and two dimensions (fractional quantum Hall effect) are, in fact, equivalent.

Pfaffian statistics through adiabatic transport in the 1D coherent state representation.

Recent work has shown that the low energy sector of certain quantum Hall states is adiabatically connected to simple charge-density-wave patterns that appear, e.g., when the system is deformed into a thin torus. Here it is shown that the patterns emerging in this limit already determine the non-Abelian statistics of the nu=1 Moore-Read state. Aside from the knowledge of these patterns, the method only relies on the principle of adiabatic continuity, the effectively noncommutative geometry in a strong magnetic field, and topological as well as locality arguments.

The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models

We investigate the possibility of exactly flat non-trivial Chern bands in tight binding models with local (strictly short-ranged) hopping parameters. We demonstrate that while any two of three criteria can be simultaneously realized (exactly flat band, non-zero Chern number, local hopping), it is not possible to simultaneously satisfy all three. Our theorem covers both the case of a single flat band, for which we give a rather elementary proof, as well as the case of multiple degenerate flat bands. In the latter case, our result is obtained as an application of

Gapless excitations in the Haldane-Rezayi state: The thin-torus limit

K

Abelian and Non-Abelian Statistics in the Coherent State Representation

-theory. We also introduce a class of models on the Lieb lattice with nearest and next-nearest neighbor hopping parameters, which have an isolated exactly flat band of zero Chern number but, in general, non-zero Berry curvature.

Spin glassiness and power law scaling in anisotropic triangular spin-1/2 antiferromagnets

We study the thin-torus limit of the Haldane-Rezayi state. Eight of the ten ground states are found to assume a simple product form in this limit, as is known to be the case for many other quantum Hall trial wave functions. The two remaining states have a somewhat unusual thin-torus limit, where a broken pair of defects forming a singlet is completely delocalized. We derive these limits from the wave functions on the cylinder, and deduce the dominant matrix elements of the thin-torus hollow-core Hamiltonian. We find that there are gapless excitations in the thin-torus limit. This is in agreement with the expectation that local Hamiltonians stabilizing wave functions associated with nonunitary conformal field theories are gapless. We also use the thin-torus analysis to obtain explicit counting formulas for the zero modes of the hollow-core Hamiltonian on the torus, as well as for the parent Hamiltonians of several other paired and related quantum Hall states.

Momentum-resolved tunneling into the Pfaffian and anti-Pfaffian edges

We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between quantum Hall states on the torus and simple product states—or patterns—in the thin torus limit, together with a suitable coherent state ansatz for localized quasiholes that respects the modular invariance of the torus. We give a refined and unified account of the application of this method to the Laughlin and Moore-Read states, which may serve as a pedagogical introduction to the nuts and bolts of this technique. Our main result is that the approach is also applicable—without further assumptions—to more complicated non-Abelian states. We demonstrate this in great detail for the level k ¼ 3 Read-Rezayi state at filling factor � ¼ 3=2. These results may serve as an independent check of other techniques, where the statistics are inferred from conformal block monodromies. Our approach has the benefit of giving rise to intuitive pictures representing the transformation of topological sectors during braiding, and allows for a self-consistent derivation of non-Abelian statistics without heavy mathematical machinery.

Effect of single impurity on free fermion entanglement entropy

We present data on the magnetic properties of two classes of layered spin S=1/2 antiferromagnetic quasi-triangular lattice materials: Cu2(1?x)Zn2x(OH)3NO3(0?x?0.65) and its long-organic-chain?intercalated derivatives Cu2(1?x)Zn2x(OH)3(C7H15COO)?mH2O(0?x?0.29), where non-magnetic Zn substitutes for Cu isostructurally. It is found that the intercalated compounds, even in a clean system in the absence of dilution, x=0, show spin glass behaviour, as evidenced by DC and AC susceptibility, and by time-dependent magnetization measurements. A striking feature is the observation of a sharp crossover between two successive power law regimes in the DC susceptibility above the freezing temperature. In constrast to standard theoretical expectations, these power laws are insensitive to doping. Specific heat data are consistent with a conventional phase transition in the unintercalated compounds, and glassy behaviour in the intercalated compounds.