6 research outputs found
Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases
We consider free fermions living on lattices in arbitrary dimensions, where hopping amplitudes follow a power-law decay with respect to the distance. We focus on the regime where this power is larger than the spatial dimension (i.e., where the single particle energies are guaranteed to be bounded) for which we provide a comprehensive series of fundamental constraints on their equilibrium and nonequilibrium properties. First, we derive a Lieb-Robinson bound which is optimal in the spatial tail. This bound then implies a clustering property with essentially the same power law for the Green’s function, whenever its variable lies outside the energy spectrum. The widely believed (but yet unproven in this regime) clustering property for the ground-state correlation function follows as a corollary among other implications. Finally, we discuss the impact of these results on topological phases in long-range free-fermion systems: they justify the equivalence between Hamiltonian and state-based definitions and the extension of the short-range phase classification to systems with decay power larger than the spatial dimension. Additionally, we argue that all the short-range topological phases are unified whenever this power is allowed to be smaller
Learning fermionic correlations by evolving with random translationally invariant Hamiltonians
Schemes of classical shadows have been developed to facilitate the read-out
of digital quantum devices, but similar tools for analog quantum simulators are
scarce and experimentally impractical. In this work, we provide a measurement
scheme for fermionic quantum devices that estimates second and fourth order
correlation functions by means of free fermionic, translationally invariant
evolutions - or quenches - and measurements in the mode occupation number
basis. We precisely characterize what correlation functions can be recovered
and equip the estimates with rigorous bounds on sample complexities, a
particularly important feature in light of the difficulty of getting good
statistics in reasonable experimental platforms, with measurements being slow.
Finally, we demonstrate how our procedure can be approximately implemented with
just nearest-neighbour, translationally invariant hopping quenches, a very
plausible procedure under current experimental requirements, and requiring only
random time-evolution with respect to a single native Hamiltonian. On a
conceptual level, this work brings the idea of classical shadows to the realm
of large scale analog quantum simulators.Comment: 27 pages, 10 figure
Geometry of variational methods: dynamics of closed quantum systems
We present a systematic geometric framework to study closed quantum systems
based on suitably chosen variational families. For the purpose of (A) real time
evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary
time evolution, we show how the geometric approach highlights the necessity to
distinguish between two classes of manifolds: K\"ahler and non-K\"ahler.
Traditional variational methods typically require the variational family to be
a K\"ahler manifold, where multiplication by the imaginary unit preserves the
tangent spaces. This covers the vast majority of cases studied in the
literature. However, recently proposed classes of generalized Gaussian states
make it necessary to also include the non-K\"ahler case, which has already been
encountered occasionally. We illustrate our approach in detail with a range of
concrete examples where the geometric structures of the considered manifolds
are particularly relevant. These go from Gaussian states and group theoretic
coherent states to generalized Gaussian states.Comment: Submission to SciPost, 47+10 pages, 8 figure
Inferences on the Timeline of Reionization at z~8 From the KMOS Lens-Amplified Spectroscopic Survey
Detections and non-detections of Lyman alpha (Ly) emission from
galaxies ( Gyr after the Big Bang) can be used to measure the timeline of
cosmic reionization. Of key interest to measuring reionization's mid-stages,
but also increasing observational challenge, are observations at z > 7, where
Ly redshifts to near infra-red wavelengths. Here we present a search
for z > 7.2 Ly emission in 53 intrinsically faint Lyman Break Galaxy
candidates, gravitationally lensed by massive galaxy clusters, in the KMOS
Lens-Amplified Spectroscopic Survey (KLASS). With integration times of ~7-10
hours, we detect no Ly emission with S/N>5 in our sample. We determine
our observations to be 80% complete for 5 spatially and spectrally
unresolved emission lines with integrated line flux erg
s cm. We define a photometrically selected sub-sample of 29
targets at , with a median 5 Ly EW limit of 58A.
We perform a Bayesian inference of the average intergalactic medium (IGM)
neutral hydrogen fraction using their spectra. Our inference accounts for the
wavelength sensitivity and incomplete redshift coverage of our observations,
and the photometric redshift probability distribution of each target. These
observations, combined with samples from the literature, enable us to place a
lower limit on the average IGM neutral hydrogen fraction of at z ~ 8, providing further evidence of rapid reionization
at z~6-8. We show that this is consistent with reionization history models
extending the galaxy luminosity function to , with
low ionizing photon escape fractions, .Comment: Accepted for publication in MNRA
Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model
We present an Ansatz for the ground states of the quantum Sherrington-Kirkpatrick model, a paradigmatic model for quantum spin glasses. Our Ansatz, based on the concept of generalized coherent states, very well captures the fundamental aspects of the model, including the ground state energy and the position of the spin glass phase transition. It further enables us to study some previously unexplored features, such as the nonvanishing longitudinal field regime and the entanglement structure of the ground states. We find that the ground state entanglement can be captured by a simple ensemble of weighted graph states with normally distributed phase gates, leading to a volume law entanglement, contrasting with predictions based on entanglement monogamy.ISSN:0031-9007ISSN:1079-711