Disordered Chern insulator with a two step Floquet drive

We explore the physics of a Chern insulator subjected to a two step Floquet drive. We analytically obtain the phase diagram and show that the system can exhibit different topological phases characterized by presence and chirality of edge-modes in the two bulk gaps of the Floquet quasienergy spectrum, around $0$ and $\pi$. We find that the phase of the system depends on the mean but not on the amplitude of the drive. The bulk topological invariants characterizing the phases can be extracted by mapping the unitary evolution within a time period to an energetically trivial but topologically non-trivial time evolution. An extensive numerical study of the bulk topological invariants in the presence of quenched disorder reveals new transitions induced by strong disorder (i) from the different topological to trivial insulator phases and (ii) from a trivial to a topological Anderson insulator phase at intermediate disorder strengths. Careful analysis of level statistics of the quasienergy spectrum indicates a `levitation-annihilation' mechanism near these transitions.Comment: 15 pages, 10 figures, version published in Phys. Rev.

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 $\Lambda$-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

Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons

The possibility of realizing bosonic fractional quantum Hall effect in ultra-cold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and thus inherit their non-trivial braiding properties. States with localized quasiholes at any desired locations can be obtained by annihilating the auxiliary bosons at those locations. We explore how this method can be used to generate non-Abelian quasiholes of the Moore-Read Pfaffian state for bosons at filling factor $\nu=1$. We show that a Hamiltonian with an appropriate three-body interaction can produce two-quasihole states in two distinct fusion channels of the topological "qubit." Characteristics of these states that are related to the non-Abelian nature can be probed and verified by a measurement of the effective relative angular momentum of the auxiliary bosons, which is directly related to their pair distribution function. Moore-Read states of more than two quasiholes can also be produced in a similar fashion. We investigate some issues related to the experimental feasibility of this approach, in particular, how large the systems should be for a realization of this physics and to what extent this physics carries over to systems with the more standard two-body contact interaction.Comment: 16 pages, 6 figure

Public International Law and the WTO: A Reckoning of Legal Positivism and Neoliberalism

This Article proceeds in five parts. In part one, I review the scholarly skepticism as to how far international law is law in the hard sense and show that this skepticism has always permeated the discipline. In part two, I go on to examine what has prompted contemporary scholarship to credit the WTO with helping international law grow out of the thin normativity often attributed to it. The analysis suggests that certain features of legal positivism customarily associated with law in its strict sense, which were alleged to be lacking in international law, are found in the institutional apparatus of the WTO. To test this hypothesis, in part three, I examine that apparatus in light of the tenets of three prominent positivists-Bentham, Austin, and Hart-and enquire whether they would have sanctioned international law had the WTO existed in their day. The conclusion drawn is that, even with the WTO, their views on international law would not have been different than what they were. This finding rectifies the myths that regard the WTO as a positivist enterprise. Part four of the article undertakes to demonstrate that neoliberalism is the driving force of not only the WTO but also the normative and structural global changes all around. To this end, the analysis conceptualizes neoliberalism and then demonstrates how the WTO serves the implementation of the neoliberal agenda. As a corollary, in part five, positivism and neoliberalism are critically juxtaposed and shown to stand in harmony with one another. The conclusion highlights the extent to which the findings can restructure the outlook of international lawyers towards the WTO