39 research outputs found
Quantum Hall valley Ferromagnets as a platform for topologically protected quantum memory
Materials hosting topologically protected non-Abelian zero modes offer the
exciting possibility of storing and manipulating quantum information in a
manner that is protected from decoherence at the hardware level. In this work,
we study the possibility of realizing such excitations along line defects in
certain fractional quantum Hall states in multi-valley systems. Such line
defects have been recently observed experimentally between valley polarized
Hall states on the surface of Bi(111), and excitations near these defects
appear to be gapped (gapless) depending on the presence (absence) of
interaction-induced gapping perturbations constrained by momentum selection
rules, while the position of defects is determined by strain. In this work, we
use these selection rules to show that a hybrid structure involving a
superlattice imposed on such a multi-valley quantum Hall surface realizes
non-Abelian anyons which can then be braided by modulating strain locally to
move line defects. Specifically, we explore such defects in Abelian fractional
quantum Hall states of the form {\nu} = 2/m using a K-matrix approach, and
identify relevant gapping perturbations. Charged modes on these line defects
remain gapped, while charge netural valley pseudospin modes may be gapped with
the aid of two (mutually orthogonal) superlattices which pin non-commuting
fields. When these superlattices are alternated along the line defect,
non-Abelian zero modes result at points where the gapping perturbation changes.
Given that these pseudospin modes carry no net physical charge or spin, the
setup eschews utilizing superconducting and magnetic elements to engineer
gapping perturbations. We provide a scheme to braid these modes using strain
modulation, and confirm that the resulting unitaries satisfy a representation
of the braid group.Comment: 20 pages, 3 figures; comments welcom
Spatiotemporal Quenches in Long-Range Hamiltonians
Spatiotemporal quenches are efficient at preparing ground states of critical
Hamiltonians that have emergent low-energy descriptions with Lorentz
invariance. The critical transverse field Ising model with nearest neighbor
interactions, for instance, maps to free fermions with a relativistic low
energy dispersion. However, spin models realized in artificial quantum
simulators based on neutral Rydberg atoms, or trapped ions, generically exhibit
long range power-law decay of interactions with for a
wide range of . In this work, we study the fate of spatiotemporal
quenches in these models with a fixed velocity for the propagation of the
quench front, using the numerical time-dependent variational principle. For
, where the critical theory is suggested to have a dynamical
critical exponent , our simulations show that optimal cooling is
achieved when the front velocity approaches , the effective speed of
excitations in the critical model. The energy density is inhomogeneously
distributed in space, with prominent hot regions populated by excitations
co-propagating with the quench front, and cold regions populated by
counter-propagating excitations. Lowering largely blurs the boundaries
between these regions. For , we find that the Doppler cooling
effect disappears, as expected from renormalization group results for the
critical model which suggest a dispersion with .
Instead, we show that excitations are controlled by two relevant length scales
whose ratio is related to that of the front velocity to a threshold velocity
that ultimately determines the adiabaticity of the quench.Comment: 18 pages, 11 figures, 3 appendice
Localization and transport in a strongly driven Anderson insulator
We study localization and charge dynamics in a monochromatically driven
one-dimensional Anderson insulator focussing on the low-frequency,
strong-driving regime. We study this problem using a mapping of the Floquet
Hamiltonian to a hopping problem with correlated disorder in one higher
harmonic-space dimension. We show that (i) resonances in this model correspond
to \emph{adiabatic} Landau-Zener (LZ) transitions that occur due to level
crossings between lattice sites over the course of dynamics; (ii) the
proliferation of these resonances leads to dynamics that \emph{appear}
diffusive over a single drive cycle, but the system always remains localized;
(iii) actual charge transport occurs over many drive cycles due to slow
dephasing between these LZ orbits and is logarithmic-in-time, with a crucial
role being played by far-off Mott-like resonances; and (iv) applying a
spatially-varying random phase to the drive tends to decrease localization,
suggestive of weak-localization physics. We derive the conditions for the
strong driving regime, determining the parametric dependencies of the size of
Floquet eigenstates, and time-scales associated with the dynamics, and
corroborate the findings using both numerical scaling collapses and analytical
arguments.Comment: 7 pages + references, 6 figure
Fast preparation of critical ground states using superluminal fronts
We propose a spatio-temporal quench protocol that allows for the fast
preparation of ground states of gapless models with Lorentz invariance.
Assuming the system initially resides in the ground state of a corresponding
massive model, we show that a superluminally-moving `front' that
quenches the mass, leaves behind it (in space) a state
to the ground state of the gapless model.
Importantly, our protocol takes time to produce
the ground state of a system of size ( spatial dimensions), while
a fully adiabatic protocol requires time
to produce a state with exponential accuracy in . The physics of the
dynamical problem can be understood in terms of relativistic rarefaction of
excitations generated by the mass front. We provide proof-of-concept by solving
the proposed quench exactly for a system of free bosons in arbitrary
dimensions, and for free fermions in . We discuss the role of
interactions and UV effects on the free-theory idealization, before numerically
illustrating the usefulness of the approach via simulations on the quantum
Heisenberg spin-chain.Comment: 4.25 + 10 pages, 3 + 2 figure
Signatures of Majorana Zero-Modes in an isolated one-dimensional superconductor
We examine properties of the mean-field wave function of the one-dimensional
Kitaev model supporting Majorana Zero Modes (MZMs) \emph{when restricted} to a
fixed number of particles. Such wave functions can in fact be realized as exact
ground states of interacting number-conserving Hamiltonians and amount to a
more realistic description of the finite isolated superconductors. Akin to
their mean-field parent, the fixed-number wave functions encode a single
electron spectral function at zero energy that decays exponentially away from
the edges, with a localization length that agrees with the mean-field value.
Based purely on the structure of the number-projected ground states, we
construct the fixed particle number generalization of the MZM operators. They
can be used to compute the edge tunneling conductance; however, notably the
value of the zero-bias conductance remains the same as in the mean-field case,
quantized to . We also compute the topological entanglement entropy for
the number-projected wave functions and find that it contains a `robust'
component as well as a logarithmic correction to the mean field
result, which depends on the precise partitioning used to compute it. The
presence of the logarithmic term in the entanglement entropy indicates the
absence of a spectral gap above the ground state; as one introduces
fluctuations in the number of particles, the correction vanishes smoothly.Comment: 9+3 pages, 4+1 figure
Topology- and symmetry-protected domain wall conduction in quantum Hall nematics
We consider domain walls in nematic quantum Hall ferromagnets predicted to
form in multivalley semiconductors, recently probed by scanning tunnelling
microscopy experiments on Bi(111) surfaces. We show that the domain wall
properties depend sensitively on the filling factor of the underlying
(integer) quantum Hall states. For and in the absence of impurity
scattering we argue that the wall hosts a single-channel Luttinger liquid whose
gaplessness is a consequence of valley and charge conservation. For , it
supports a two-channel Luttinger liquid, which for sufficiently strong
interactions enters a symmetry-preserving thermal metal phase with a charge gap
coexisting with gapless neutral intervalley modes. The domain wall physics in
this state is identical to that of a bosonic topological insulator protected by
symmetry, and we provide a formal mapping between these
problems. We discuss other unusual properties and experimental signatures of
these `anomalous' one-dimensional systems.Comment: 11 pages, 3 figures, published versio