Excitation energies from ground-state DMRG on the fuzzy sphere

Résumé :

It has been observed that some eigenvalues of the effective local Hamiltonian built during a ground-state DMRG sweep of a one-dimensional critical chain stay nearly flat across iterations. Those flat levels correspond to true low-energy excitations, giving access to the excitation spectrum at no extra cost. We ask whether the same holds on the fuzzy sphere, a geometry used to study two-dimensional critical theories by mapping them onto a one-dimensional orbital chain. Getting excited states there directly is costly. We find numerical evidence that flat levels appear in the eigenvalues of the effective local Hamiltonian during our sweeps and match the expected low-energy spectrum. The symmetries of the fuzzy sphere and orthogonalization across symmetry sectors introduce additional structure into those eigenvalues, which helps in resolving and assigning the excitations.

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Contact : loic.herviou@lpmmc.cnrs.fr