Dirac equation as a quantum walk over the honeycomb and triangular lattices

6533b82ffe1ef96bd1295d2f

RESEARCH PRODUCT

Dirac equation as a quantum walk over the honeycomb and triangular lattices

Di Molfetta Giuseppe Pablo Arrighi Giuseppe Di Molfetta Iván Márquez-martín Armando Pérez

subject

FOS: Computer and information sciences [ INFO ] Computer Science [cs]Differential equation FOS: Physical sciences triangulation 01 natural sciences 010305 fluids & plasmas symbols.namesake High Energy Physics - Lattice [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]Lattice (order)Mesoscale and Nanoscale Physics (cond-mat.mes-hall)0103 physical sciences [ PHYS.PHYS.PHYS-GEN-PH ] Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]unitarity surface [INFO]Computer Science [cs]Quantum walk Hexagonal lattice Dirac equation continuum limit 010306 general physics Quantum ComputingMilieux_MISCELLANEOUS lattice Mathematical physics Physics Quantum Physics Partial differential equation Condensed Matter - Mesoscale and Nanoscale Physics Unitarity [PHYS.HLAT]Physics [physics]/High Energy Physics - Lattice [hep-lat]High Energy Physics - Lattice (hep-lat)[ PHYS.HLAT ] Physics [physics]/High Energy Physics - Lattice [hep-lat]differential equations [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]Computer Science - Distributed Parallel and Cluster Computing Dirac equation symbols Distributed Parallel and Cluster Computing (cs.DC)Quantum Physics (quant-ph)

description

A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in $(2+1)$--dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice. The former is of interest in the study of graphene-like materials. The latter, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces.

year	journal	country	edition	language
2018-01-01	Physical Review A

https://doi.org/10.1103/physreva.97.062111

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