Dynamics of edge Majorana fermions in ν=52\nu=\frac{5}2 fractional quantum Hall effects

Commencing with the composite fermion description of the $\nu=5/2$ fractional quantum Hall effect, we study the dynamics of the edge neutral Majorana fermions. We confirm that these neutral modes are chiral and show that a conventional p-wave pairing interaction between CFs does not contribute to the dynamics of the edge neutral fermions. We find an important bilinear coupling between the charged and neutral modes. We show that owing to this coupling, the dispersion of the neutral modes is linear and their velocities are proportional to the wave vector of the charged mode. This dynamic origin of the motion of the edge Majorana fermions was never expected before.Comment: 5 pages, published versio

Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

We construct an exactly soluble spin-$\frac{1}2$ model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free states. Basically, there are two phases, A phase and B phase. The behaviors of both A and B phases may be studied by mapping the ground state sector into a general p-wave paired states of spinless fermions with tunable pairing parameters on a square lattice. In this p-wave paired state theory, the A phase is shown to be the strong paired phase, an insulating phase. The B phase may be either gapped or gapless determined by the generalized inversion symmetry is broken or not. The gapped B is the weak pairing phase described by either the Moore-Read Pfaffian state of the spinless fermions or anti-Pfaffian state of holes depending on the sign of the next nearest neighbor hopping amplitude. A phase transition between Pfaffian and anti-Pfaffian states are found in the gapped B phase. Furthermore, we show that there is a hidden SU(2) gauge symmetry in our model. In the gapped B phase, the ground state has a non-trivial topological number, the spectral first Chern number or the chiral central charge, which reflects the chiral anomaly of the edge state. We proved that the topological number is identified to the reduced eta-invariant and this anomaly may be cancelled by a bulk Wess-Zumino term of SO(3) group through an index theorem in 2+1 dimensions.Comment: longer version, 12 pages, to be published in Nucl. Phys.

A Microscopic Model of Edge States of Fractional Quantum Hall Liquid: From Composite Fermions to Calogero-Sutherland Model

Based on the composite fermion approach, we derive a microscopic theory describing the low-lying edge excitations in the fractional quantum Hall liquid with $\nu=\frac{\nu^*}{\tilde\phi\nu^*+1}$. For $\nu^*>0$, it is found that the composite fermion model reduces to an SU$(\nu^*)$ Calogero-Sutherland model in the one-dimensional limit, whereas it is not exact soluble for $\nu^*<0$. However, the ground states in both cases can be found and the low-lying excitations can be shown the chiral Luttinger liquid behaviors since a gap exists between the right- and left-moving sectors in each branch of the azimuthal excitations.Comment: minor revised with references adde

Gossamer supercoductivity and the mean field approximation of a new effective Hubbard model

We construct a new effective two-dimensional Hubbard model by taking the different electron occupancy on site into account. The mean field state of the new Hamiltonian gives rise to the gossamer superconducting state proposed by Laughlin recently(cond-mat/0209269).Comment: 4 pages, 2 figures,some typo errors are correcte

Short-range coherence of a lattice Bose atom gas in the Mott insulating phase

We study the short-range coherence of ultracold lattice Bose gases in the Mott insulating phase. We calculate the visibility of the interference pattern and the results agree quantitatively with the recent experimental measurement [Phys. Rev. Lett. 95, 050404 (2005)]. The visibility deviation from the inversely linear dependence on the bare on-site interaction U_0 is explained both in smaller and larger U_0. For a smaller U_0, it comes from a second order correction. For a larger U_0, except the breakdown of adiabaticity as analyzed by Gerbier et al, there might be another source to cause this deviation, which is the diversity between $U_0$ determined by the single atom Wannier function and the effective on site interaction U_eff for a multi-occupation per site.Comment: 4 pages, 2 figures; published in PR

Comments on `Rashba precession in quantum wire with interaction'

In a recent Rapid Communication (Phys. Rev. B {\bf 63}, 121210(R) (2001)), Ha\"usler showed that the interaction between electrons in quantum wires may enhance the persistent spin current arising from Rashba spin-orbital coupling. In this Comments, we would like to point out that this 'enhancement' comes from a misunderstanding to the boosting persistent current in the Luttinger liquid theory. A correct calculation will not give such an enhancement of the persistent spin current. Meanwhile, we provide a Luttinger liquid theory with Rashba spin-orbital interaction by bosonization, which may show how the Rashba precession is in a Luttinger liquid.Comment: 2 page

Seiberg-Witten monopoles: Weyl metal coupled to chiral magnets

We study a Weyl (semi)metal which couples to local magnets. In the continuum limit, the Hamiltonian of the system matches the Chern-Simons-Maxwell-Dirac functional and then the ground state is governed by generalized Seiberg-Witten (SW) or Freund equations in terms of the sign of Dzyaloshinskii-Moriya coupling. The ground states determined by the Freund equations may either be monopolar Weyl semimetal accompanied by the ferromagnetic magnets (MWFM) or SW monopoles which consist of spheric Weyl fermions coupled to chiral magnets, depending on the strength of the Kondo coupling. In the latter phase, the topological ground state is characterized by SW invariants and with a Weyl surface on which the Weyl metal is of an exotic dispersion $\propto \sqrt k$. There are also the metastable SW monopole solutions carrying an opposite SW invariant for the SW equations while the ground state in this case is the MWFM state.Comment: 5+2 pages 3 figure

A Novel Meron-induced Pseudospin Wave in Bilayer Quantum Hall Coherent State and the Residual Zero-bias Peak in Tunneling Conductance

In the bilayer quantum Hall coherent state for $\nu_T$ deviating slightly from one, we show that, instead of the global order parameter, the spontaneous breaking of the pseudospin U(1) rotational symmetry is reflected by the periodic domain structure accompanying with the charged meron pairs. The motion of meron pairs induces a novel pseudospin wave. The long range order of the periodic domains in a low bias voltage range leads to the residual zero-bias peak in the tunneling conductance even when the pseudopsin Goldstone feature in a high bias voltage range can be distinct from it.Comment: 4 pages, 1 figur

Time-evolution stability of order parameters and phase diagrams of bosons on optical lattice

Stemming from the Heisenberg equations of motion, we study the time-evolution stability of the order parameters for the cold atoms on optical lattices. The requirement of this stability of the order parameters endows the phase diagram with a fruitful structure in the superfluid phase. For the one-component Bose-Hubbard model, we see that this stability of order parameter leads to a physically receivable phase diagram. For two-component bosons, we show that the molecules are preformed in the atomic superfluid and then condenses into a molecular superfluid phase at a critical repulsive inter-species interaction, which resembles the pre-pairing mechanism in high $T_c$ superconductor of Cu-O cuprates.Comment: 4 pages, 2 figure

Incompressible excitonic superfluid of ultracold Bose atoms in an optical lattice: a new superfluid phase in the one-component Bose-Hubbard model

We predict that a new superfluid phase, the incompressible excitonic superfluid (IESF), in the phase diagram of ultracold Bose atoms in $d>1$ dimensional optical lattices, which is caused by the spontaneous breaking of the symmetry of translation of the lattice. Within mean field theory, the critical temperature of the phase transition from this IESF to the normal fluid (NF) is calculated and the triple-critical point of the three phases is determined. We also investigate both configuration and gauge field fluctuations and show the IESF state is stable against these fluctuations. We expect this IESF phase can be experimentally observed by loading cold Bose atoms into a two-dimensional lattice where the atom filling fraction deviates slightly from exact commensurations. The signatures distinguishing this IESF from the common atom superfluid (ASF) are that (i) the critical temperature of the IEST/NF transition is independent of interaction, unlike the ASF/NF transition; (ii) the IESF is incompressible while the ASF is compressible.Comment: 4 pages, 2 figure