Abstract
Inspired by the localization phenomenon in condensed matter systems, we explore constructions in the theory space of multiple scalar fields, in which exponentially suppressed couplings could originate from random parameters. In particular, we find a new class of non-local theory space models, in which scalar fields at non-adjacent sites interact with each other but with strengths decaying exponentially with the site separation. Such a model could have very different localization properties, compared to the local theory space scenarios with only nearest-site interactions, based on the original Anderson localization model. More specifically, we find that a particular non-local interaction pattern leads to bi-localization of the two lightest eigenstates. Exponential localization (and thus exponentially suppressed couplings) then emerges only and immediately when randomness is introduced, no matter how tiny it is. We discuss variants of the model and possible UV completions as well.
Highlights
In his seminal paper in 1958 [1], Anderson showed that electron energy eigenstates localize in a single-particle system with short range hopping between adjacent sites, even in the presence of disorder
II, we review the basics of localization phenomena in single-particle systems and random matrix theory, the main tool to study the localization property
We argue that the mechanism by which Lþ localizes is different from all the other examples that have been previously introduced in the literature
Summary
In his seminal paper in 1958 [1], Anderson showed that electron energy eigenstates localize in a single-particle system with short range hopping between adjacent sites, even in the presence of disorder. We consider two toy models of N real scalars in the theory space with exponentially decaying nonlocal interactions (i.e., interactions between scalars at nonadjacent sites, not to be confused with interactions that traverse the real space), that could be generated at loop levels through tree-level interactions between adjacent scalars. One type of construction and its variants could strengthen localization of the lightest mass eigenstates by making them more peaked at one site in the theory space, in the limit of small random diagonal perturbations This example addresses one of the major motivations of our study: to explore and identify novel classes of theory space models based on random matrices with different localization properties, especially those that could improve localization. In the nonlocal theory space model with the improved localization, localization at a single site originates from bilocalization due to the model structure without any randomness and emerges immediately when one turns on even a tiny random perturbation
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