Localization of single-particle states in the continuum

Béla Gazdy

I. V. Gornyi, A. D. Mirlin, Markus Müller +1 more

We consider an extended electronic system with localized single‐particle states coupled by short‐range interactions, in the absence of coupling to an external bath. We show that many‐body localization, which exists in tight‐binding models, is unstable in a continuum. Irrespective of the dimensionality of the system, many‐body localization does not survive the unbounded growth of the single‐particle localization length with increasing energy that is characteristic of the continuum limit. The system remains delocalized down to arbitrarily small temperature T , although its dynamics slows down as T decreases. Remarkably, the conductivity vanishes with decreasing T faster than in the Arrhenius law. The system can be characterized by an effective T ‐dependent single‐particle mobility edge which diverges in the limit of . Delocalization is driven by interactions between hot electrons above the mobility edge and the “bath” of thermal electrons in the vicinity of the Fermi level. image

Ole Keller

Shoki Sugimoto, Yuto Ashida, Masahito Ueda

A bound state in the continuum (BIC) is a spatially localized energy eigenstate embedded in a continuous spectrum of extended eigenstates. While diverse types of single-particle BICs have been reported in the literature, understanding how such localization persists in interacting many-body systems remains a fundamental problem. Here, we present numerical evidence and a perturbative analysis supporting the existence of many-body BICs in a one-dimensional Bose-Hubbard chain with an attractive impurity potential, a system previously known to host a BIC in the two-particle sector. Furthermore, we demonstrate that the Bethe-type construction of the known two-particle BIC breaks down already for three particles even for arbitrary finite superpositions of Bethe waves. The resulting BICs violate the eigenstate thermalization hypothesis for several local one- and two-body observables, leading to nonthermal dynamics from experimentally accessible initial states.

Phil Attard

Na Sun, Weixuan Zhang, Hao Yuan +1 more

Abstract Bound states in the continuum (BICs), referring to spatially localized bound states with energies falling within the range of extended modes, have been extensively investigated in single-particle systems, leading to diverse applications in photonics, acoustics, and other classical-wave systems. Recently, there has been theoretical interest in exploring many-body BICs in interacting quantum systems, which necessitate the careful design of impurity potentials or spatial profiles of interaction. Here, we propose a type of many-body BICs localized at boundaries, which can be purely induced by the uniform onsite interaction without requiring any specific design of impurity potential or nonlocal interaction. We numerically show that three or more interacting bosons can concentrate on the boundary of a homogeneous one-dimensional lattice, which is absent at single- and two-particle counterparts. Moreover, the eigenenergy of multi-boson bound states can embed within the continuous energy spectra of extended scattering states, thereby giving rise to interaction-induced boundary many-body BICs. Furthermore, by mapping Fock states of three and four bosons to nonlinear circuit networks, we experimentally simulate boundary many-body BICs. Our findings enrich the comprehension of correlated BICs beyond the single-particle level, and have the potential to inspire future investigations on exploring many-body BICs.