1,321 research outputs found
Hardy-Sobolev-Maz'ya inequalities for arbitrary domains
We prove a Hardy-Sobolev-Maz'ya inequality for arbitrary domains
\Omega\subset\R^N with a constant depending only on the dimension N\geq 3. In
particular, for convex domains this settles a conjecture by Filippas, Maz'ya
and Tertikas. As an application we derive Hardy-Lieb-Thirring inequalities for
eigenvalues of Schr\"odinger operators on domains.Comment: 19 page
Structure factor of interacting one-dimensional helical systems
We calculate the dynamical structure factor S(q, {\omega}) of a weakly
interacting helical edge state in the presence of a magnetic field B. The
latter opens a gap of width 2B in the single-particle spectrum, which becomes
strongly nonlinear near the Dirac point. For chemical potentials |{\mu}| > B,
the system then behaves as a nonlinear helical Luttinger liquid, and a
mobile-impurity analysis reveals interaction-dependent power-law singularities
in S(q,{\omega}). For |{\mu}| < B, the low-energy excitations are gapped, and
we determine S(q,{\omega}) by using an analogy to exciton physics.Comment: 5 pages, 3 figure
Long-Range Interaction of Spin-Qubits via Ferromagnets
We propose a mechanism of coherent coupling between distant spin qubits
interacting dipolarly with a ferromagnet. We derive an effective two-spin
interaction Hamiltonian and estimate the coupling strength. We discuss the
mechanisms of decoherence induced solely by the coupling to the ferromagnet and
show that there is a regime where it is negligible. Finally, we present a
sequence for the implementation of the entangling CNOT gate and estimate the
corresponding operation time to be a few tens of nanoseconds. A particularly
promising application of our proposal is to atomistic spin-qubits such as
silicon-based qubits and NV-centers in diamond to which existing coupling
schemes do not apply.Comment: 6 pages, 7 pages of appendi
Quantum memory coupled to cavity modes
Inspired by spin-electric couplings in molecular magnets, we introduce in the
Kitaev honeycomb model a linear modification of the Ising interactions due to
the presence of quantized cavity fields. This allows to control the properties
of the low-energy toric code Hamiltonian, which can serve as a quantum memory,
by tuning the physical parameters of the cavity modes, like frequencies, photon
occupations, and coupling strengths. We study the properties of the model
perturbatively by making use of the Schrieffer-Wolff transformation and show
that, depending on the specific setup, the cavity modes can be useful in
several ways. They allow to detect the presence of anyons through frequency
shifts and to prolong the lifetime of the memory by enhancing the anyon
excitation energy or mediating long-range anyon-anyon interactions with tunable
sign. We consider both resonant and largely detuned cavity modes.Comment: 16 pages, 6 figure
Physical solutions of the Kitaev honeycomb model
We investigate the exact solution of the honeycomb model proposed by Kitaev
and derive an explicit formula for the projector onto the physical subspace.
The physical states are simply characterized by the parity of the total
occupation of the fermionic eigenmodes. We consider a general lattice on a
torus and show that the physical fermion parity depends in a nontrivial way on
the vortex configuration and the choice of boundary conditions. In the
vortex-free case with a constant gauge field we are able to obtain an
analytical expression of the parity. For a general configuration of the gauge
field the parity can be easily evaluated numerically, which allows the exact
diagonalization of large spin models. We consider physically relevant
quantities, as in particular the vortex energies, and show that their true
value and associated states can be substantially different from the one
calculated in the unprojected space, even in the thermodynamic limit
The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space
It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on
the three dimensional upper half space is given by the Sobolev constant. This
is achieved by a duality argument relating the problem to a
Hardy-Littlewood-Sobolev type inequality whose sharp constant is determined as
well.Comment: 9 page
Ferromagnetic order of nuclear spins coupled to conduction electrons: a combined effect of the electron-electron and spin-orbit interactions
We analyze the ordered state of nuclear spins embedded in an interacting
two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction (SOI).
Stability of the ferromagnetic nuclear-spin phase is governed by nonanalytic
dependences of the electron spin susceptibility on the momentum
() and on the SOI coupling constant (). The uniform
(\tq=0) spin susceptibility is anisotropic (with the out-of-plane component,
, being larger than the in-plane one, , by a term
proportional to , where is the electron-electron
interaction). For \tq \leq 2m^*|\alpha|, corrections to the leading,
, term scale linearly with \tq for and are
absent for . This anisotropy has important consequences for the
ferromagnetic nuclear-spin phase: the ordered state--if achieved--is of
an Ising type and the spin-wave dispersion is gapped at \tq=0. To
second order in , the dispersion a decreasing function of \tq, and
anisotropy is not sufficient to stabilize long-range order. However,
renormalization in the Cooper channel for \tq\ll2m^*|\alpha| is capable of
reversing the sign of the \tq-dependence of and thus stabilizing
the ordered state. We also show that a combination of the electron-electron and
SO interactions leads to a new effect: long-wavelength Friedel oscillations in
the spin (but not charge) electron density induced by local magnetic moments.
The period of these oscillations is given by the SO length .Comment: 22 pages, 15 figure
Spin susceptibility of interacting two-dimensional electrons in the presence of spin-orbit coupling
A long-range interaction via virtual particle-hole pairs between Fermi-liquid
quasiparticles leads to a nonanalytic behavior of the spin susceptibility
as a function of the temperature (), magnetic field (),
and wavenumber. In this paper, we study the effect of the Rashba spin-orbit
interaction (SOI) on the nonanalytic behavior of for a two-dimensional
electron liquid. Although the SOI breaks the SU(2) symmetry, it does not
eliminate nonanalyticity but rather makes it anisotropic: while the linear
scaling of with and saturates at the energy
scale set by the SOI, that of () continues through this
energy scale, until renormalization of the electron-electron interaction in the
Cooper channel becomes important. We show that the Renormalization Group flow
in the Cooper channel has a non-trivial fixed point, and study the consequences
of this fixed point for the nonanalytic behavior of . An immediate
consequence of SOI-induced anisotropy in the nonanalytic behavior of is
a possible instability of a second-order ferromagnetic quantum phase transition
with respect to a first-order transition to an XY ferromagnetic state.Comment: 34 pages, 12 figure
Majorana states in inhomogeneous spin ladders
We propose an inhomogeneous open spin ladder, related to the Kitaev honeycomb
model, which can be tuned between topological and nontopological phases. In
extension of Lieb's theorem, we show numerically that the ground state of the
spin ladder is either vortex free or vortex full. We study the robustness of
Majorana end states (MES) which emerge at the boundary between sections in
different topological phases and show that while the MES in the homogeneous
ladder are destroyed by single-body perturbations, in the presence of
inhomogeneities at least two-body perturbations are required to destabilize
MES. Furthermore, we prove that x, y, or z inhomogeneous magnetic fields are
not able to destroy the topological degeneracy. Finally, we present a
trijunction setup where MES can be braided. A network of such spin ladders
provides thus a promising platform for realization and manipulation of MES
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