Low-complexity eigenstates of a <b> <i>ν</i> </b> = 1/3 fractional quantum Hall system
Bruno Nachtergaele, Simone Warzel, Amanda Young
Abstract
Abstract We identify the ground-state of a truncated version of Haldane’s pseudo-potential Hamiltonian in the thin cylinder geometry as being composed of exponentially many fragmented matrix product states. These states are constructed by lattice tilings and their properties are discussed. We also report on a proof of a spectral gap, which implies the incompressibility of the underlying fractional quantum Hall liquid at maximal filling ν = 1/3. Low-energy excitations and an extensive number of many-body scars at positive energy density, but nevertheless low complexity, are also identified using the concept of tilings.
Topics & Concepts
Hamiltonian (control theory)Quantum Hall effectPhysicsQuantumLattice (music)Eigenvalues and eigenvectorsQuantum mechanicsFractional quantum Hall effectProduct (mathematics)Quantum systemMatrix (chemical analysis)MathematicsMatrix multiplicationExcited stateSpectral propertiesQuantum spin Hall effectMathematical physicsDiagonalizable matrixCylinderQuantization (signal processing)Quantum numberNorm (philosophy)Quantum and electron transport phenomenaQuantum many-body systemsTopological Materials and Phenomena