451 research outputs found

### Occupation of a resonant level coupled to a chiral Luttinger liquid

We consider a resonant level coupled to a chiral Luttinger liquid which can
be realized, e.g., at a fractional quantum Hall edge. We study the dependence
of the occupation probability n of the level on its energy \epsilon for various
values of the Luttinger-liquid parameter g. At g<1/2 a weakly coupled level
shows a sharp jump in n(\epsilon) at the Fermi level. As the coupling is
increased, the magnitude of the jump decreases until \sqrt{2g}, and then the
discontinuity in n(\epsilon) disappears. We show that n(\epsilon) can be
expressed in terms of the magnetization of a Kondo impurity as a function of
magnetic field.Comment: 5 pages including 1 figur

### Generalized two-leg Hubbard ladder at half-filling: Phase diagram and quantum criticalities

The ground-state phase diagram of the half-filled two-leg Hubbard ladder with
inter-site Coulomb repulsions and exchange coupling is studied by using the
strong-coupling perturbation theory and the weak-coupling bosonization method.
Considered here as possible ground states of the ladder model are four types of
density-wave states with different angular momentum (s-density-wave state,
p-density-wave state, d-density-wave state, and f-density-wave state) and four
types of quantum disordered states, i.e., Mott insulating states (S-Mott,
D-Mott, S'-Mott, and D'-Mott states, where S and D stand for s- and d-wave
symmetry). The s-density-wave state, the d-density-wave state, and the D-Mott
state are also known as the charge-density-wave (CDW) state, the staggered-flux
(SF) state, and the rung-singlet state, respectively. Strong-coupling approach
naturally leads to the Ising model in a transverse field as an effective theory
for the quantum phase transitions between the SF state and the D-Mott state and
between the CDW state and the S-Mott state, where the Ising ordered states
correspond to doubly degenerate ground states in the staggered-flux or the
charge-density-wave state. From the weak-coupling bosonization approach it is
shown that there are three cases in the quantum phase transitions between a
density-wave state and a Mott state: the Ising (Z_2) criticality, the SU(2)_2
criticality, and a first-order transition. The quantum phase transitions
between Mott states and between density-wave states are found to be the U(1)
Gaussian criticality. The ground-state phase diagram is determined by
integrating perturbative renormalization-group equations. It is shown that the
S-Mott state and the SF state exist in the region sandwiched by the CDW phase
and the D-Mott phase.Comment: 21 pages, 10 figure

### Resonant tunnelling in interacting 1D systems with an AC modulated gate

We present an analysis of transport properties of a system consisting of two
half-infinite interacting one-dimensional wires connected to a single fermionic
site, the energy of which is subject to a periodic time modulation. Using the
properties of the exactly solvable Toulouse point we derive an integral
equation for the localised level Keldysh Green's function which governs the
behaviour of the linear conductance. We investigate this equation numerically
and analytically in various limits. The period-averaged conductance G displays
a surprisingly rich behaviour depending on the parameters of the system. The
most prominent feature is the emergence of an intermediate temperature regime
at low frequencies, where G is proportional to the line width of the respective
static conductance saturating at a non-universal frequency dependent value at
lower temperatures.Comment: 12 pages, 3 figures (eps files

### Conductance of a helical edge liquid coupled to a magnetic impurity

Transport in an ideal two-dimensional quantum spin Hall device is dominated
by the counterpropagating edge states of electrons with opposite spins, giving
the universal value of the conductance, $2e^2/h$. We study the effect on the
conductance of a magnetic impurity, which can backscatter an electron from one
edge state to the other. In the case of isotropic Kondo exchange we find that
the correction to the electrical conductance caused by such an impurity
vanishes in the dc limit, while the thermal conductance does acquire a finite
correction due to the spin-flip backscattering.Comment: 5 pages, 2 figure

### Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

A time-reversal invariant Kitaev-type model is introduced in which spins
(Dirac matrices) on the square lattice interact via anisotropic
nearest-neighbor and next-nearest-neighbor exchange interactions. The model is
exactly solved by mapping it onto a tight-binding model of free Majorana
fermions coupled with static Z_2 gauge fields. The Majorana fermion model can
be viewed as a model of time-reversal invariant superconductor and is
classified as a member of symmetry class DIII in the Altland-Zirnbauer
classification. The ground-state phase diagram has two topologically distinct
gapped phases which are distinguished by a Z_2 topological invariant. The
topologically nontrivial phase supports both a Kramers' pair of gapless
Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana
states bound to a 0-flux vortex in the \pi-flux background. Power-law decaying
correlation functions of spins along the edge are obtained by taking the
gapless Majorana edge modes into account. The model is also defined on the
one-dimension ladder, in which case again the ground-state phase diagram has
Z_2 trivial and non-trivial phases.Comment: 17 pages, 9 figure

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