Numerical methods for detecting symmetries and commutant algebras
Sanjay Moudgalya, Olexei I. Motrunich
Abstract
Utilizing the understanding of symmetries in the framework of commutant algebras, the authors introduce here general methods to numerically construct symmetry operators and quantum number sectors. One method uses simultaneous block diagonalization of two generic Hamiltonians to construct symmetry sectors, while another method uses the fact that symmetries in the commutant framework are frustration-free ground states of local superoperators, which leads to efficient algorithms. These methods are applied to conventional on-site symmetries, as well as unconventional symmetries such as Hilbert space fragmentation and quantum many-body scars.
Topics & Concepts
Centralizer and normalizerHomogeneous spaceHilbert spaceSymmetry (geometry)Construct (python library)Theoretical physicsQuantumPure mathematicsOperator (biology)MathematicsPhysicsAlgebra over a fieldQuantum mechanicsComputer scienceGeometryChemistryTranscription factorBiochemistryRepressorGeneProgramming languageQuantum many-body systemsAlgebraic structures and combinatorial modelsPhysics of Superconductivity and Magnetism