Low-complexity eigenstates of a $\nu =1/3$ fractional quantum Hall system

Abstract

We identify the the ground-state of a truncated version of Haldane's pseudo-potential Hamiltonian in a 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 $\nu =1/3$. 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.

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Cited by in corpus (11)

• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Quantum Many-Body Scars: A Quasiparticle Perspective
• Quantum scars from zero modes in an Abelian lattice gauge theory on ladders
• Minimal model for Hilbert space fragmentation with local constraints
• Spectral Gaps and Incompressibility in a $\nu =1/3$ Fractional Quantum Hall System
• The spectral gap of a fractional quantum Hall system on a thin torus
• Quantum statistics transmutation via magnetic flux attachment
• Emergent Fracton Hydrodynamics of Ultracold Atoms in Partially Filled Landau Levels
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• On a bulk gap strategy for quantum lattice models
• Stabilization of Granovskii-Zhedanov scars of the XYZ quantum spin chain via non-Hermitian spin relaxation