21,995 research outputs found
Exact holographic mapping and emergent space-time geometry
In this paper, we propose an {\it exact holographic mapping} which is a
unitary mapping from the Hilbert space of a lattice system in flat space
(boundary) to that of another lattice system in one higher dimension (bulk). By
defining the distance in the bulk system from two-point correlation functions,
we obtain an emergent bulk space-time geometry that is determined by the
boundary state and the mapping. As a specific example, we study the exact
holographic mapping for -dimensional lattice Dirac fermions and explore
the emergent bulk geometry corresponding to different boundary states including
massless and massive states at zero temperature, and the massless system at
finite temperature. We also study two entangled one-dimensional chains and show
that the corresponding bulk geometry consists of two asymptotic regions
connected by a worm-hole. The quantum quench of the coupled chains is mapped to
dynamics of the worm-hole. In the end we discuss the general procedure of
applying this approach to interacting systems, and other open questions.Comment: 15 pages, 7 figure
Topological Quantum Computation Based on Chiral Majorana Fermions
Chiral Majorana fermion is a massless self-conjugate fermion which can arise
as the edge state of certain two-dimensonal topological matters. It has been
theoretically predicted and experimentally observed in a hybrid device of
quantum anomalous Hall insulator and a conventional superconductor. Its closely
related cousin, Majorana zero mode in the bulk of the corresponding topological
matter, is known to be applicable in topological quantum computations. Here we
show that the propagation of chiral Majorana fermions lead to the same unitary
transformation as that in the braiding of Majorana zero modes, and propose a
new platform to perform quantum computation with chiral Majorana fermions. A
Corbino ring junction of the hybrid device can utilize quantum coherent chiral
Majorana fermions to implement the Hadamard gate and the phase gate, and the
junction conductance yields a natural readout for the qubit state.Comment: Accepted for publication at PNA
Space-time random tensor networks and holographic duality
In this paper we propose a space-time random tensor network approach for
understanding holographic duality. Using tensor networks with random link
projections, we define boundary theories with interesting holographic
properties, such as the Renyi entropies satisfying the covariant
Hubeny-Rangamani-Takayanagi formula, and operator correspondence with local
reconstruction properties. We also investigate the unitarity of boundary theory
in spacetime geometries with Lorenzian signature. Compared with the spatial
random tensor networks, the space-time generalization does not require a
particular time slicing, and provides a more covariant family of microscopic
models that may help us to understand holographic duality.Comment: 31 pages, 9 figure
Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK
In many-body chaotic systems, the size of an operator generically grows in
Heisenberg evolution, which can be measured by certain out-of-time-ordered
four-point functions. However, these only provide a coarse probe of the full
underlying operator growth structure. In this article we develop a methodology
to derive the full growth structure of fermionic systems, that also naturally
introduces the effect of finite temperature. We then apply our methodology to
the SYK model, which features all-to-all -body interactions. We derive the
full operator growth structure in the large limit at all temperatures. We
see that its temperature dependence has a remarkably simple form consistent
with the slowing down of scrambling as temperature is decreased. Furthermore,
our finite-temperature scrambling results can be modeled by a modified epidemic
model, where the thermal state serves as a vaccinated population, thereby
slowing the overall rate of infection.Comment: 31 pages, 10 figure
Eternal traversable wormhole
We construct a nearly- solution describing an eternal traversable
wormhole. The solution contains negative null energy generated by quantum
fields under the influence of an external coupling between the two boundaries.
In parallel, we discuss two SYK systems coupled by a relevant interaction. The
physics of the two cases is very similar. They both share a "gravitational"
subsector which is identical. The solution within this subsector sets the stage
for dynamics which is almost conformal invariant. We study this system in
detail, both in gravity and in the SYK model. The coupled SYK models have an
interesting phase diagram at finite temperature, displaying the usual
Hawking-Page transition between the thermal AdS phase at low temperature and
the black hole phase at high temperature. Interestingly, these two phases are
continuously connected in the microcannonical ensemble.Comment: 50 +21 pages. 23 figures. V2: Slightly expanded discussion of the
thermal phases. References added. V3 Latex issue fixe
Tunable circular dichroism due to the chiral anomaly in Weyl semimetals
Weyl semimetals are a three dimensional gapless topological phase in which
bands intersect at arbitrary points -- the Weyl nodes -- in the Brillouin zone.
These points carry a topological quantum number known as the \emph{chirality}
and always appear in pairs of opposite chiralities. The notion of chirality
leads to anomalous non-conservation of chiral charge, known as the \emph{chiral
anomaly}, according to which charge can be pumped between Weyl nodes of
opposite chiralities by an electromagnetic field with non-zero
. Here, we propose probing the chiral
anomaly by measuring the optical activity of Weyl semimetals via circular
dichroism. In particular, we observe that applying such an electromagnetic
field on this state gives it a non-zero gyrotropic coefficient or a Hall-like
conductivity, which may be detectable by routine circular dichroism
experiments. This method also serves as a diagnostic tool to discriminate
between Weyl and Dirac semimetals; the latter will give a null result. More
generally, any experiment that probes a bulk correlation function that has the
same symmetries as the gyrotropic coefficient can detect the chiral anomaly as
well as differentiate between Dirac and Weyl semimetals.Comment: Replaced Kubo calculation of dielectric tensor by a more intuitive
semiclassical calculation. Fixed error in assumptions about various time
scales, which changed the prediction from a Faraday effect to circular
dichrois
Characterizing eigenstate thermalization via measures in the Fock space of operators
The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap
between quantum mechanical and statistical mechanical descriptions of isolated
quantum systems. Here, we define unbiased measures for how well the ETH works
in various regimes, by mapping general interacting quantum systems on regular
lattices onto a single particle living on a high-dimensional graph. By
numerically analyzing deviations from ETH behavior in the non-integrable Ising
model, we propose a quantity that we call the - to democratically
characterize the average deviations for all operators residing on a given
number of sites, irrespective of their spatial structure. It appears to have a
simple scaling form, that we conjecture to hold true for all non-integrable
systems. A closely related quantity, that we term the -,
tells us how well two states can be distinguished if only -site operators
are measured. Along the way, we discover that complicated operators on average
are worse than simple ones at distinguishing between neighboring eigenstates,
contrary to the naive intuition created by the usual statements of the ETH that
few-body (many-body) operators acquire the same (different) expectation values
in nearby eigenstates at finite energy density. Finally, we sketch heuristic
arguments that the ETH originates from the limited ability of simple operators
to distinguish between quantum states of a system, especially when the states
are subject to constraints such as roughly fixed energy with respect to a local
Hamiltonian.Comment: 9 pages, 5 figures; Typos fixed, references adde
Fractional Statistics and the Butterfly Effect
Fractional statistics and quantum chaos are both phenomena associated with
the non-local storage of quantum information. In this article, we point out a
connection between the butterfly effect in (1+1)-dimensional rational conformal
field theories and fractional statistics in (2+1)-dimensional topologically
ordered states. This connection comes from the characterization of the
butterfly effect by the out-of-time-order-correlator proposed recently. We show
that the late-time behavior of such correlators is determined by universal
properties of the rational conformal field theory such as the modular S-matrix
and conformal spins. Using the bulk-boundary correspondence between rational
conformal field theories and (2+1)-dimensional topologically ordered states, we
show that the late time behavior of out-of-time-order-correlators is
intrinsically connected with fractional statistics in the topological order. We
also propose a quantitative measure of chaos in a rational conformal field
theory, which turns out to be determined by the topological entanglement
entropy of the corresponding topological order.Comment: Published version, 1+25 pages, 10 figure
An integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind
In the paper, the authors discover an integral representation, some
inequalities, and complete monotonicity of Bernoulli numbers of the second
kind.Comment: 10 page
Quantum Oscillations in Weyl and Dirac Semimetal Ultra-Thin Films
We show that a thin film of Weyl or Dirac semimetal with a strong in-plane
magnetic field becomes a novel two-dimensional Fermi liquid with interesting
properties. The Fermi surface in this system is strongly anisotropic, which
originates from a combination of chiral bulk channels and the Fermi arcs. The
area enclosed by the Fermi surface depends strongly on the in-plane magnetic
field component parallel to the Weyl/Dirac node splitting, which leads to
unusual behavior in quantum oscillations when the magnetic field is tilted out
of the plane. We estimate the oscillation frequencies and the regimes where
such effects could be seen in CdAs, NaBi, and TaAs.Comment: 4.5 pages, 4 figures and 2 pages of appendix with 2 figure
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