一维非厄米十字晶格中的退局域-局域转变

Delocalization-localization transitions in 1D non-Hermitian cross-stitch lattices

本文研究了在具有平带的一维非厄米十字晶格中引入准周期调制所诱导的退局域-局域的转变.通过解析推导和数值分析分形维度和能谱的实复转变,发现在非厄米单平带十字晶格中引入对称的准周期调制会引起扩展相到局域相的转变,而反对称准周期调制能够诱导出精确的迁移率边.在非厄米全平带十字晶格中,对称的准周期调制情况下,系统一直处于局域相,当引入反对称的准周期调制时,系统具有从多重分形相到局域相的转变.该研究结果为非厄米平带的局域化性质研究提供了参考.

In this work,we investigate the influence of quasi-periodic modulation on the localization properties of onedimensional non-Hermitian cross-stitch lattices with flat bands.The crystalline Hamiltonian for this nonHermitian cross-stitch lattice is given by:H∑n[t(a_(n)+b(n)+a(n)+Je^(h)(a_(n)+b_(n+1)+a_(n)a_(n+1)+Ab_(n)+b_(n+1))+Je(^(-h))(Aa_(n+1)+b_(n)+a(n+1)+an+b_(n+1)a_(n)+Ab^(+)_(n+1)b_(n))]with A=±1.When A=1,the clean lattice supports two bands with dispersion relations E_0=-t,E_1=4cos(k-ih)+t.The compact localized states(CLSs)within the flat band E_0 are localized in one unit cell,indicating that the system is characterized by the U=1 class.Conversely,for A=-1,there are two flat bands in the system:E±√t(+)+4.The CLSs within the flat bands are localized in two unit cells,indicating that the system is marked by the U=2 class.After introducing quasi-per iodic modulationsε_n~β=λ_βcos(2παn+φβ)(β={a,b}),delocalization-localization transitions can be observed by numerically calculating the fractal dimension D_2 and imaginary part of the energy spectrum ln|Im(E)|.Our findings indicate that the symmetry of quasi-per iodic modulations plays an important role in determining the localization properties of the system.For the case of U=1,the symmetric quasi-per iodic modulation leads to two independent spectraσ_f andσ_p.Theσ_f retains its compact properties,while theσ_p owns an extended-localized transition atλ_(c1)=4M with M=max{e~h,e~(-h)}.However,in the case of antisymmetric modulation,the system exhibits an exact mobility edgeλ_(c2)=2√2|E-t|M.For the U=2 class,all the eigenstates remain localized under any symmetric quasiper iodic modulation.In the case of antisymmetric modulation,all states transition from multifractal to localized states as the modulation strength increases,with a critical point atλ_(c3)=4M.This work expands the understanding of localization properties in non-Hermitian flat-band systems and provides a new perspective on delocaliz ation-localization transitions.