Diffusive-Ballistic Crossover and the Persistent Spin Helix

Conventional transport theory focuses on either the diffusive or ballistic regimes and neglects the crossover region between the two. In the presence of spin-orbit coupling, the transport equations are known only in the diffusive regime, where the spin precession angle is small. In this paper, we develop a semiclassical theory of transport valid throughout the diffusive - ballistic crossover of a special SU(2) symmetric spin-orbit coupled system. The theory is also valid in the physically interesting regime where the spin precession angle is large. We obtain exact expressions for the density and spin structure factors in both 2 and 3 dimensional samples with spin-orbit coupling.Comment: 4 pages, 3 figure

Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions

Using the newly developed Matrix Product State (MPS) formalism for non-abelian Fractional Quantum Hall (FQH) states, we address the question of whether a FQH trial wave function written as a correlation function in a non-unitary Conformal Field Theory (CFT) can describe the bulk of a gapped FQH phase. We show that the non-unitary Gaffnian state exhibits clear signatures of a pathological behavior. As a benchmark we compute the correlation length of Moore-Read state and find it to be finite in the thermodynamic limit. By contrast, the Gaffnian state has infinite correlation length in (at least) the non-Abelian sector, and is therefore gapless. We also compute the topological entanglement entropy of several non-abelian states with and without quasiholes. For the first time in FQH the results are in excellent agreement in all topological sectors with the CFT prediction for unitary states. For the non-unitary Gaffnian state in finite size systems, the topological entanglement entropy seems to behave like that of the Composite Fermion Jain state at equal filling.Comment: 5 pages, 5 figures, and supplementary material. Published versio

Berry-phase description of Topological Crystalline Insulators

We study a class of translational-invariant insulators with discrete rotational symmetry. These insulators have no spin-orbit coupling, and in some cases have no time-reversal symmetry as well, i.e., the relevant symmetries are purely crystalline. Nevertheless, topological phases exist which are distinguished by their robust surface modes. Like many well-known topological phases, their band topology is unveiled by the crystalline analog of Berry phases, i.e., parallel transport across certain non-contractible loops in the Brillouin zone. We also identify certain topological phases without any robust surface modes -- they are uniquely distinguished by parallel transport along bent loops, whose shapes are determined by the symmetry group. Our findings have experimental implications in cold-atom systems, where the crystalline Berry phase has been directly measured.Comment: Latest version is accepted to PR

Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators

The energy and entanglement spectrum of fractionally filled interacting topological insulators exhibit a peculiar manifold of low energy states separated by a gap from a high energy set of spurious states. In the current manuscript, we show that in the case of fractionally filled Chern insulators, the topological information of the many-body state developing in the system resides in this low-energy manifold. We identify an emergent many-body translational symmetry which allows us to separate the states in quasi-degenerate center of mass momentum sectors. Within one center of mass sector, the states can be further classified as eigenstates of an emergent (in the thermodynamic limit) set of many-body relative translation operators. We analytically establish a mapping between the two-dimensional Brillouin zone for the Fractional Quantum Hall effect on the torus and the one for the fractional Chern insulator. We show that the counting of quasi-degenerate levels below the gap for the Fractional Chern Insulator should arise from a folding of the states in the Fractional Quantum Hall system at identical filling factor. We show how to count and separate the excitations of the Laughlin, Moore-Read and Read-Rezayi series in the Fractional Quantum Hall effect into two-dimensional Brillouin zone momentum sectors, and then how to map these into the momentum sectors of the Fractional Chern Insulator. We numerically check our results by showing the emergent symmetry at work for Laughlin, Moore-Read and Read-Rezayi states on the checkerboard model of a Chern insulator, thereby also showing, as a proof of principle, that non-Abelian Fractional Chern Insulators exist.Comment: 32 pages, 9 figure

D-Algebra Structure of Topological Insulators

In the quantum Hall effect, the density operators at different wave-vectors generally do not commute and give rise to the Girvin MacDonald Plazmann (GMP) algebra with important consequences such as ground-state center of mass degeneracy at fractional filling fraction, and W_{1 + \infty} symmetry of the filled Landau levels. We show that the natural generalization of the GMP algebra to higher dimensional topological insulators involves the concept of a D-algebra formed by using the fully anti-symmetric tensor in D-dimensions. For insulators in even dimensional space, the D-algebra is isotropic and closes for the case of constant non-Abelian F(k) ^ F(k) ... ^ F(k) connection (D-Berry curvature), and its structure factors are proportional to the D/2-Chern number. In odd dimensions, the algebra is not isotropic, contains the weak topological insulator index (layers of the topological insulator in one less dimension) and does not contain the Chern-Simons \theta form (F ^ A - 2/3 A ^ A ^ A in 3 dimensions). The Chern-Simons form appears in a certain combination of the parallel transport and simple translation operator which is not an algebra. The possible relation to D-dimensional volume preserving diffeomorphisms and parallel transport of extended objects is also discussed.Comment: 5 page

Holonomic Quantum Computing Based on the Stark Effect

We propose a spin manipulation technique based entirely on electric fields applied to acceptor states in $p$-type semiconductors with spin-orbit coupling. While interesting in its own right, the technique can also be used to implement fault-resilient holonomic quantum computing. We explicitly compute adiabatic transformation matrix (holonomy) of the degenerate states and comment on the feasibility of the scheme as an experimental technique.Comment: 5 page