1,540 research outputs found
Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry
We show that a large class of bosonic spin-singlet Fractional Quantum Hall
model wave-functions and their quasi-hole excitations can be written in terms
of Jack polynomials with a prescribed symmetry. Our approach describes new
spin-singlet quantum Hall states at filling fraction nu = 2k/(2r-1) and
generalizes the (k,r) spin-polarized Jack polynomial states. The NASS and
Halperin spin singlet states emerge as specific cases of our construction. The
polynomials express many-body states which contain configurations obtained from
a root partition through a generalized squeezing procedure involving spin and
orbital degrees of freedom. The corresponding generalized Pauli principle for
root partitions is obtained, allowing for counting of the quasihole states. We
also extract the central charge and quasihole scaling dimension, and propose a
conjecture for the underlying CFT of the (k, r) spin-singlet Jack states.Comment: 17 pages, 1 figur
Theory of Four-dimensional Fractional Quantum Hall States
We propose a pseudo-potential Hamiltonian for the Zhang-Hu's generalized
fractional quantum Hall states to be the exact and unique ground states.
Analogously to Laughlin's quasi-hole (quasi-particle), the excitations in the
generalized fractional quantum Hall states are extended objects. They are
vortex-like excitations with fractional charges in the total
configuration space CP. The density correlation function of the Zhang-Hu
states indicates that they are incompressible liquid.Comment: 4 page
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
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
Holonomic Quantum Computing Based on the Stark Effect
We propose a spin manipulation technique based entirely on electric fields
applied to acceptor states in -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
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