Abstract
The celebrated Dyson singularity signals the relative delocalization of single-particle wave functions at the zero-energy symmetry point of disordered systems with a chiral symmetry. Here we show that analogous zero modes in interacting quantum systems can fully localize at sufficiently large disorder, but do so less strongly than nonzero modes, as signifed by their real-space and Fock-space localization characteristics. We demonstrate this effect in a spin-1 Ising chain, which naturally provides a chiral symmetry in an odd-dimensional Hilbert space, thereby guaranteeing the existence of a many-body zero mode at all disorder strengths. In the localized phase, the bipartite entanglement entropy of the zero mode follows an area law, but is enhanced by a system-size-independent factor of order unity when compared to the nonzero modes. Analytically, this feature can be attributed to a specific zero-mode hybridization pattern on neighboring spins. The zero mode also displays a symmetry-induced even-odd and spin-orientation fragmentation of excitations, characterized by real-space spin correlation functions, which generalizes the sublattice polarization of topological zero modes in noninteracting systems, and holds at any disorder strength.
Highlights
Complex quantum systems owe their rich physical properties to the intricate interplay of symmetries, disorder, and interactions
Symmetry-reduced representations of quantum systems were established at the beginning of quantum mechanics [1], while the absence of unitary symmetries allows for complex wave dynamics even for low numbers of degrees of freedom [2]
In many-body systems zero modes protected by a chiral symmetry can localize, but do so with distinctively different characteristics than nonzero modes
Summary
Complex quantum systems owe their rich physical properties to the intricate interplay of symmetries, disorder, and interactions. Random-matrix theory describes wave functions ergodically spreading across the whole system, but this can be amended to provide statistical descriptions of Anderson-localized systems, in particular in onedimensional or quasi-one-dimensional geometries [9] These descriptions can be organized according to the universality classes of the tenfold way [10], and account for topological phenomena in nonperiodic, disordered settings. Within the classification framework described above, this relative delocalization phenomenon becomes tied to the existence of a topologically protected zero mode in a chirally symmetric system with an odd-dimensional Hilbert space [12], and occurs in higherdimensional systems, where the anomalously localized states can resemble those at a metal-insulator transition [13,14] Weaker analogs of such anomalous localization characteristics occur in absence of spectral symmetries [15,16]. VI we summarize and discuss the results and put them into further context
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