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Number of zero-energy eigenstates in the PXP model
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abstract
The PXP model is paradigmatic in the field of quantum many-body scars. This model has a number of zero-energy eigenstates that is exponentially large in system size. Lower bounds on the number of zero-energy eigenstates are obtained for both open and periodic (zero and $\pi$-momentum sectors) boundary conditions. These bounds are found to be tight up to system sizes accessible by numerical exact diagonalization, and can be expected to be tight in general. In addition to previous results, separate lower bounds are obtained for the spatial inversion-symmetric and inversion-antisymmetric symmetry sectors. Furthermore, the derivations improve on previous ones as these are free of assumptions.
Forward citations
Cited by 2 Pith papers
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Krylov-Space Memory Cores
Anomalous initial states in otherwise thermalizing models leave compact, stationary low-depth Krylov-space cores—regions with persistent fluctuations, Gibbs mismatch, and current activity—while generic states do not.
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Complexity of PXP scars revisited
In the PXP model, the arch in the Lanczos coefficients is traced to a linear sl(3) part of the Hamiltonian, and the arch width is proposed as a signal distinguishing scarred from thermalizing states.
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