arXiv subjects

Qi Hu

Publications and source records attributed to Qi Hu.

41 records · Page 3Linked to original sources

arXiv2017

Non-local Geometry inside Lifshitz Horizon

Based on the quantum renormalization group, we derive the bulk geometry that emerges in the holographic dual of the fermionic U(N) vector model at a nonzero charge density. The obstruction that prohibits the metallic state from being smoothly deformable to the direct product state under the renormalization group flow gives rise to a horizon at a finite radial coordinate in the bulk. The region outside the horizon is described by the Lifshitz geometry with a higher-spin hair determined by microscopic details of the boundary theory. On the other hand, the interior of the horizon is not described by any Riemannian manifold, as it exhibits an algebraic non-locality. The non-local structure inside the horizon carries the information on the shape of the filled Fermi sea.

hep-th↗

arXiv2017

Spacetime symmetries and conformal data in the continuous multi-scale entanglement renormalization ansatz

The generalization of the multi-scale entanglement renormalization ansatz (MERA) to continuous systems, or cMERA [Haegeman et al., Phys. Rev. Lett, 110, 100402 (2013)], is expected to become a powerful variational ansatz for the ground state of strongly interacting quantum field theories. In this paper we investigate, in the simpler context of Gaussian cMERA for free theories, the extent to which the cMERA state $|Ψ^Λ\rangle$ with finite UV cut-off $Λ$ can capture the spacetime symmetries of the ground state $|Ψ\rangle$. For a free boson conformal field theory (CFT) in 1+1 dimensions as a concrete example, we build a quasi-local unitary transformation $V$ that maps $|Ψ\rangle$ into $|Ψ^Λ\rangle$ and show two main results. (i) Any spacetime symmetry of the ground state $|Ψ\rangle$ is also mapped by $V$ into a spacetime symmetry of the cMERA $|Ψ^Λ\rangle$. However, while in the CFT the stress-energy tensor $T_{μν}(x)$ (in terms of which all the spacetime symmetry generators are expressed) is local, the corresponding cMERA stress-energy tensor $T_{μν}^Λ(x) = V T_{μν}(x) V^{\dagger}$ is quasi-local. (ii) From the cMERA, we can extract quasi-local scaling operators $O^Λ_α(x)$ characterized by the exact same scaling dimensions $Δ_α$, conformal spins $s_α$, operator product expansion coefficients $C_{αβγ}$, and central charge $c$ as the original CFT. Finally, we argue that these results should also apply to interacting theories.

quant-ph↗

arXiv2014

Preconditioned Krylov solvers for kernel regression

A primary computational problem in kernel regression is solution of a dense linear system with the $N\times N$ kernel matrix. Because a direct solution has an O($N^3$) cost, iterative Krylov methods are often used with fast matrix-vector products. For poorly conditioned problems, convergence of the iteration is slow and preconditioning becomes necessary. We investigate preconditioning from the viewpoint of scalability and efficiency. The problems that conventional preconditioners face when applied to kernel methods are demonstrated. A \emph{novel flexible preconditioner }that not only improves convergence but also allows utilization of fast kernel matrix-vector products is introduced. The performance of this preconditioner is first illustrated on synthetic data, and subsequently on a suite of test problems in kernel regression and geostatistical kriging.

math.NA↗

arXiv2013

Parallel Algorithms for Constructing Data Structures for Fast Multipole Methods

We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With these algorithms it is possible to map the FMM efficiently on to the GPU or distributed heterogeneous CPU-GPU systems. Further, in dynamic problems, as the distribution of the particles change, the reduced cost of building the data structures improves performance. Using these algorithms, we demonstrate example high fidelity simulations with large problem sizes by using FMM on both single and multiple heterogeneous computing facilities equipped with multi-core CPU and many-core GPUs.

cs.MS↗

arXiv2007

The mass and luminosity functions and the formation rate of DA white dwarfs in the Sloan Digital Sky Survey

The SDSS Data Release 1 includes 1833 DA white dwarfs (WDs) and forms the largest homogeneous sample of WDs. This sample provides the best opportunity to study the statistical properties of WDs. We adopt a recently established theoretical model to calculate the mass and distance of each WD using the observational data. Then we adopt a bin-correction method to correct for selection effects and use the 1/V weight-factor method to calculate the luminosity function, the continuous mass function and the formation rate of these WDs. The SDSS DA WD sample is incomplete and suffers seriously from selection effects. After corrections for the selection effects, only 531 WDs remain. From this final sample we derive the most up-to-date luminosity function and mass function, in which we find a broad peak of WD masses centered around 0.58$M_{\odot}$. The DA WD space density is calculated as $8.81\times10^{-5}pc^{-3}$ and the formation rate is $2.579\times 10^{-13}pc^{-3}yr^{-1}$. The statistical properties of the SDSS DA WD sample are generally in good agreement with previous observational and theoretical studies, and provide us information on the formation and evolution of WDs. However, a larger and more complete all-sky WD sample is still needed to explain some subtle disagreements and unresolved issues.

astro-ph↗