Undecidability of the Spectral Gap in One Dimension
Johannes Bausch, Toby S. Cubitt, Angelo Lucia, David Perez-Garcia
Abstract
A new analysis proves that it is not possible for numerical algorithms to determine if a 1D quantum system has a spectral gap, showing that basic properties of even simple systems are, in some instances, impossible to predict.
Topics & Concepts
Dimension (graph theory)Simple (philosophy)Spectral gapQuantumQuantum systemMathematicsPhysicsSpectrum (functional analysis)Multidimensional systemsSpectral propertiesSpectral analysisStatistical physicsPure mathematicsTheoretical physicsQuantum mechanicsDecidabilityComputer scienceAlgebra over a fieldQuantum computerDiscrete mathematicsComplex systemQuantum many-body systemsQuasicrystal Structures and PropertiesQuantum Computing Algorithms and Architecture