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Abstract:

Eigenstates of fully many-body localized (FMBL) systems are described by quasilocal operators τzi (l-bits), which are conserved exactly under Hamiltonian time evolution. The algebra of the operators τzi and τxi associated with l-bits (τi) completely defines the eigenstates and the matrix elements of local operators between eigenstates at all energies. We develop a non-perturbative construction of the full set of l-bit algebras in the many-body localized phase for the canonical model of MBL. Our algorithm to construct the Pauli-algebra of l-bits combines exact diagonalization and a tensor network algorithm developed for efficient diagonalization of large FMBL Hamiltonians. The distribution of localization lengths of the l-bits is evaluated in the MBL phase and used to characterize the MBL-to-thermal transition.

Abstract:

We consider the behavior of quantum Hall edges away from the Luttinger liquid fixed point that occurs in the low-energy, large-system limit. Using the close links between quantum Hall wave functions and conformal field theories, we construct effective Hamiltonians from general principles and then constrain their forms by considering the effect of bulk symmetries on the properties of the edge. In examining the effect of bulk interactions on this edge, we find remarkable simplifications to these effective theories which allow for a very accurate description of the low-energy physics of quantum Hall edges relatively far away from the Luttinger liquid fixed point, and which apply to small systems and higher energies.

Abstract:

Feldman argues that simply having a large velocity mismatch and long wavelength disorder is not likely to result in sufficient non-equilibration of Majorana edge modes at ν=5/2 to explain recent thermal transport experiments. I agree that this picture alone is probably too simple, although small modifications of the mechanism could still be viable.