scholarly journals Precise programmable quantum simulations with optical lattices

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Xingze Qiu ◽  
Jie Zou ◽  
Xiaodong Qi ◽  
Xiaopeng Li
Keyword(s):  
Large Scale ◽  
Optical Potential ◽  
Optical Lattices ◽  
High Efficiency ◽  
Tight Binding ◽  
Binding Model ◽  
Wannier Functions ◽  
Quantum Simulations ◽  
Binding Models ◽  
High Band

Abstract We present an efficient approach to precisely simulate tight binding models with optical lattices, based on programmable digital-micromirror-device (DMD) techniques. Our approach consists of a subroutine of Wegner-flow enabled precise extraction of a tight-binding model for a given optical potential, and a reverse engineering step of adjusting the potential for a targeting model, for both of which we develop classical algorithms to achieve high precision and high efficiency. With renormalization of Wannier functions and high band effects systematically calibrated in our protocol, we show the tight-binding models with programmable onsite energies and tunnelings can be precisely simulated with optical lattices integrated with the DMD techniques. With numerical simulation, we demonstrate that our approach would facilitate quantum simulation of localization physics with adequate programmability and atom-based boson sampling for illustration of quantum computational advantage. We expect this approach would pave a way towards large-scale and precise programmable quantum simulations based on optical lattices.

scholarly journals Enabling Large-Scale Simulations of Quantum Transport with Manycore Computing

Electronics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 253
Author(s):  
Yosang Jeong ◽  
Hoon Ryu
Keyword(s):  
Quantum Transport ◽  
Large Scale ◽  
Performance Enhancement ◽  
Silicon Nanowire ◽  
Matrix Multiplication ◽  
Tight Binding ◽  
Optimization Techniques ◽  
Wide Energy Range ◽  
Processing Unit ◽  
Binding Model

The non-equilibrium Green’s function (NEGF) is being utilized in the field of nanoscience to predict transport behaviors of electronic devices. This work explores how much performance improvement can be driven for quantum transport simulations with the aid of manycore computing, where the core numerical operation involves a recursive process of matrix multiplication. Major techniques adopted for performance enhancement are data restructuring, matrix tiling, thread scheduling, and offload computing, and we present technical details on how they are applied to optimize the performance of simulations in computing hardware, including Intel Xeon Phi Knights Landing (KNL) systems and NVIDIA general purpose graphic processing unit (GPU) devices. With a target structure of a silicon nanowire that consists of 100,000 atoms and is described with an atomistic tight-binding model, the effects of optimization techniques on the performance of simulations are rigorously tested in a KNL node equipped with two Quadro GV100 GPU devices, and we observe that computation is accelerated by a factor of up to ∼20 against the unoptimized case. The feasibility of handling large-scale workloads in a huge computing environment is also examined with nanowire simulations in a wide energy range, where good scalability is procured up to 2048 KNL nodes.

scholarly journals Tight-binding models for ultracold atoms in honeycomb optical lattices

2013 ◽  
Vol 87 (1) ◽  
Author(s):  
Julen Ibañez-Azpiroz ◽  
Asier Eiguren ◽  
Aitor Bergara ◽  
Giulio Pettini ◽  
Michele Modugno
Keyword(s):  
Ultracold Atoms ◽  
Optical Lattices ◽  
Tight Binding ◽  
Binding Models

scholarly journals Elastic Deformations and Wigner–Weyl Formalism in Graphene

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 317 ◽  
Author(s):  
I.V. Fialkovsky ◽  
M.A. Zubkov
Keyword(s):  
Magnetic Field ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Tight Binding ◽  
Tight Binding Model ◽  
Solid State Physics ◽  
Binding Model ◽  
Elastic Deformations ◽  
Binding Models ◽  
External Electromagnetic Fields

We discuss the tight-binding models of solid state physics with the Z 2 sublattice symmetry in the presence of elastic deformations in an important particular case—the tight binding model of graphene. In order to describe the dynamics of electronic quasiparticles, the Wigner–Weyl formalism is explored. It allows the calculation of the two-point Green’s function in the presence of two slowly varying external electromagnetic fields and the inhomogeneous modification of the hopping parameters that result from elastic deformations. The developed formalism allows us to consider the influence of elastic deformations and the variations of magnetic field on the quantum Hall effect.

scholarly journals Engineering spectral properties of non-interacting lattice Hamiltonians

2021 ◽  
Vol 11 (6) ◽  
Author(s):  
Ali Moghaddam ◽  
Dmitry Chernyavsky ◽  
Corentin Morice ◽  
Jasper van Wezel ◽  
Jeroen van den Brink
Keyword(s):  
Spectral Properties ◽  
Tight Binding ◽  
Integral Form ◽  
Higher Dimensions ◽  
Exact Diagonalization ◽  
Wannier Functions ◽  
One Dimensional ◽  
Binding Models ◽  
Bounded Functions ◽  
Position Dependence

We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of the position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites, which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next, we provide an exact solution for the inverse problem of constructing the position-dependence of hopping in a lattice model yielding a given DOS. We confirm analytic results by comparing them to numerics obtained by exact diagonalization for various incarnations of position-dependent hoppings and on-site potentials. Finally, we generalize the DOS integral form to multi-orbital tight-binding models with longer-range hoppings and in higher dimensions.

Large Scale Quantum Simulations Using Tight-Binding Hamiltonians and Linear Scaling Methods

1997 ◽  
Vol 491 ◽  
Author(s):  
Giulia Galli ◽  
Jeongnim Kim ◽  
Andrew Canning ◽  
Rainer Raerle
Keyword(s):  
Large Scale ◽  
Tight Binding ◽  
Electronic Structure Calculations ◽  
Linear Scaling ◽  
Quantum Molecular Dynamics ◽  
Open Problems ◽  
Quantum Simulations ◽  
Scaling Methods ◽  
Dynamics Simulations ◽  
Structure Calculations

ABSTRACTWe describe linear scaling methods for electronic structure calculations and quantum molecular dynamics simulations, which are based on an orbital formulation of the electronic problem. In particular, we discuss some open problems which need to be addressed to improve the performances of these methods, and briefly review some applications to carbon and silicon systems, within a Tight-Binding framework.

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