379 research outputs found
Effect of long-range hopping on Tc in a two-dimensional Hubbard-Holstein model of the cuprates
We study the effect of long-range hoppings on Tc for the two-dimensional (2D)
Hubbard model with and without Holstein phonons using parameters evaluated from
band-structure calculations for cuprates. Employing the dynamical cluster
approximation (DCA) with a quantum Monte Carlo (QMC) cluster solver for a
4-site cluster, we observe that without phonons, the long-range hoppings, t'
and t'', generally suppress Tc. We argue that this trend remains valid for
larger clusters. In the presence of the Holstein phonons, a finite t' enhances
Tc in the under-doped region for the hole-doped system, consistent with
local-density approximation (LDA) calculations and experiment. This is
interpreted through the suppression of antiferromagnetic (AF) correlations and
the interplay between polaronic effects and the antiferromagnetism.Comment: 5 pages, 4 figure
Short-Range Correlations and Cooling of Ultracold Fermions in the Honeycomb Lattice
We use determinantal quantum Monte Carlo simulations and numerical
linked-cluster expansions to study thermodynamic properties and short-range
spin correlations of fermions in the honeycomb lattice. We find that, at half
filling and finite temperatures, nearest-neighbor spin correlations can be
stronger in this lattice than in the square lattice, even in regimes where the
ground state in the former is a semimetal or a spin liquid. The honeycomb
lattice also exhibits a more pronounced anomalous region in the double
occupancy that leads to stronger adiabatic cooling than in the square lattice.
We discuss the implications of these findings for optical lattice experiments.Comment: 5 pages, 4 figure
Quantum Criticality and Incipient Phase Separation in the Thermodynamic Properties of the Hubbard Model
Transport measurements on the cuprates suggest the presence of a quantum
critical point hiding underneath the superconducting dome near optimal hole
doping. We provide numerical evidence in support of this scenario via a
dynamical cluster quantum Monte Carlo study of the extended two-dimensional
Hubbard model. Single particle quantities, such as the spectral function, the
quasiparticle weight and the entropy, display a crossover between two distinct
ground states: a Fermi liquid at low filling and a non-Fermi liquid with a
pseudogap at high filling. Both states are found to cross over to a marginal
Fermi-liquid state at higher temperatures. For finite next-nearest-neighbor
hopping t' we find a classical critical point at temperature T_c. This
classical critical point is found to be associated with a phase separation
transition between a compressible Mott gas and an incompressible Mott liquid
corresponding to the Fermi liquid and the pseudogap state, respectively. Since
the critical temperature T_c extrapolates to zero as t' vanishes, we conclude
that a quantum critical point connects the Fermi-liquid to the pseudogap
region, and that the marginal-Fermi-liquid behavior in its vicinity is the
analogous of the supercritical region in the liquid-gas transition.Comment: 18 pages, 9 figure
Thermodynamics of the Quantum Critical Point at Finite Doping in the 2D Hubbard Model: A Dynamical Cluster Approximation Study
We study the thermodynamics of the two-dimensional Hubbard model within the
dynamical cluster approximation. We use continuous time quantum Monte Carlo as
a cluster solver to avoid the systematic error which complicates the
calculation of the entropy and potential energy (double occupancy). We find
that at a critical filling, there is a pronounced peak in the entropy divided
by temperature, S/T, and in the normalized double occupancy as a function of
doping. At this filling, we find that specific heat divided by temperature,
C/T, increases strongly with decreasing temperature and kinetic and potential
energies vary like T^2 ln(T). These are all characteristics of quantum critical
behavior.Comment: 4 pages, 4 figures. Submitted to Phys. Rev. B Rapid Communications on
June 27, 200
A perspective on machine learning and data science for strongly correlated electron problems
Numerical approaches to the correlated electron problem have achieved
considerable success, yet are still constrained by several bottlenecks,
including high order polynomial or exponential scaling in system size, long
autocorrelation times, challenges in recognizing novel phases, and the Fermion
sign problem. Methods in machine learning (ML), artificial intelligence, and
data science promise to help address these limitations and open up a new
frontier in strongly correlated quantum system simulations. In this paper, we
review some of the progress in this area. We begin by examining these
approaches in the context of classical models, where their underpinnings and
application can be easily illustrated and benchmarked. We then discuss cases
where ML methods have enabled scientific discovery. Finally, we will examine
their applications in accelerating model solutions in state-of-the-art quantum
many-body methods like quantum Monte Carlo and discuss potential future
research directions
Magnetic Correlations and Pairing in the 1/5-Depleted Square Lattice Hubbard Model
We study the single-orbital Hubbard model on the 1/5-depleted square-lattice geometry, which arises in such diverse systems as the spin-gap magnetic insulator CaV4O9 and ordered-vacancy iron selenides, presenting new issues regarding the origin of both magnetic ordering and superconductivity in these materials. We find a rich phase diagram that includes a plaquette singlet phase, a dimer singlet phase, a NĂ©el and a block-spin antiferromagnetic phase, and stripe phases. Quantum Monte Carlo simulations show that the dominant pairing correlations at half filling change character from d wave in the plaquette phase to extended s wave upon transition to the NĂ©el phase. These findings have intriguing connections to iron-based superconductors, and suggest that some physics of multiorbital systems can be captured by a single-orbital model at different dopings
Application of the Adjusted Weak Axiom of Profit Maximization to New Zealand Dairy Farming
The weak axiom of profit maximization is a nonparametric, empirical approach that has been used in the United States to analyze dairy farmers’ production and profit behavior under input and output price changes to determine whether farmers effectively respond to these changes. The expectation is that profit calculated using the current year’s input and output combination will be greater than that calculated from the previous year’s combination with current prices more often than due to chance. This approach was replicated using New Zealand dairy farm data (1,785 pairs of records over five years). Current year’s profits were significantly greater in two of the years and less in two years and in total. New Zealand’s pasture-based systems mean that this approach has limitations in evaluating farmers’ input and output decisions in response to price changes. Factors such as climatic impacts on pasture availability (a volatile input not included in the data set), and hence purchased feed requirements, affected the results. Farmer responses to costs and prices were not readily differentiated from other factors that affected input decisions or output. Results were interpreted with respect to climate, production, and income and cost changes, both nationally and regionally, with some interesting observations on farmer responses to variability
Machine Learning in Electronic Quantum Matter Imaging Experiments
Essentials of the scientific discovery process have remained largely
unchanged for centuries: systematic human observation of natural phenomena is
used to form hypotheses that, when validated through experimentation, are
generalized into established scientific theory. Today, however, we face major
challenges because automated instrumentation and large-scale data acquisition
are generating data sets of such volume and complexity as to defy human
analysis. Radically different scientific approaches are needed, with machine
learning (ML) showing great promise, not least for materials science research.
Hence, given recent advances in ML analysis of synthetic data representing
electronic quantum matter (EQM), the next challenge is for ML to engage
equivalently with experimental data. For example, atomic-scale visualization of
EQM yields arrays of complex electronic structure images, that frequently elude
effective analyses. Here we report development and training of an array of
artificial neural networks (ANN) designed to recognize different types of
hypothesized order hidden in EQM image-arrays. These ANNs are used to analyze
an experimentally-derived EQM image archive from carrier-doped cuprate Mott
insulators. Throughout these noisy and complex data, the ANNs discover the
existence of a lattice-commensurate, four-unit-cell periodic,
translational-symmetry-breaking EQM state. Further, the ANNs find these
phenomena to be unidirectional, revealing a coincident nematic EQM state.
Strong-coupling theories of electronic liquid crystals are congruent with all
these observations.Comment: 44 pages, 15 figure
Case Notes
For decades, optical time-domain searches have been tuned to find ordinary supernovae, which rise and fall in brightness over a period of weeks. Recently, supernova searches have improved their cadences and a handful of fast-evolving luminous transients have been identified(1-5). These have peak luminosities comparable to type Ia supernovae, but rise to maximum in less than ten days and fade from view in less than one month. Here we present the most extreme example of this class of object thus far: KSN 2015K, with a rise time of only 2.2 days and a time above half-maximum of only 6.8 days. We show that, unlike type Ia supernovae, the light curve of KSN 2015K was not powered by the decay of radioactive elements. We further argue that it is unlikely that it was powered by continuing energy deposition from a central remnant (a magnetar or black hole). Using numerical radiation hydrodynamical models, we show that the light curve of KSN 2015K is well fitted by a model where the supernova runs into external material presumably expelled in a pre-supernova mass-loss episode. The rapid rise of KSN 2015K therefore probes the venting of photons when a hypersonic shock wave breaks out of a dense extended medium.NASA
NNH15ZDA001N
NNX17AI64G
Australian Research Council Centre of Excellence for All-sky Astrophysics
CE11000102
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