Semilocalization transition driven by a single asymmetrical tunneling

Abstract

A local impurity usually only strongly affects few single-particle energy levels, thus cannot induce a quantum phase transition (QPT), or any macroscopic quantum phenomena in a many-body system within the Hermitian regime. However, it may happen for a non-Hermitian impurity. We investigate the many-body ground state property of a one-dimensional tight-binding ring with an embedded single asymmetrical dimer based on exact solutions. We introduce the concept of semi-localization state to describe a new quantum phase, which is a crossover from extended to localized state. The peculiar feature is that the decay length is of the order of the system size, rather than fixed as a usual localized state. In addition, the spectral statistics is non-analytic as asymmetrical hopping strengths vary, resulting a sudden charge of the ground state. The distinguishing feature of such a QPT is that the density of ground state energy varies smoothly due to unbroken symmetry. However, there are other observables, such as the groundstate center of mass and average current, exhibit the behavior of second-order QPT. This behavior stems from time-reversal symmetry breaking of macroscopic number of single-particle eigen states.

Exceptional spectrum and dynamic magnetization

“…So that the manifestation of macroscopic effect is not surprising. In recent work, it has been shown that a continuous change of an asymmetric hopping strength can induce a sudden change of the single-particle spectral statistics, which results in nonanalytic behavior of some macroscopic quantities [68]. In addition [69], an EP with the order of the size of the system is created by a single impurity in an N-site quantum spin chain.…”

Accumulation of scale-free localized states induced by local non-Hermiticity

“…In this context, most previous studies focused on non-Hermitian systems with either global (i.e., the non-Hermitian terms have support on the whole lattice) nonreciprocal hoppings or gain/loss. A few exceptions include studies on the dynamical properties of quantum systems dissipatively coupled to baths at the boundary [30] or subject to local loss [31][32][33][34][35][36]. Two fundamental and interesting question naturally arise: (1) Is there any paradigmatic and universal phenomenon akin to the NHSE emerge from local non-Hermiticity?…”