摘要
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.
Abstract
In this work,we investigate the influence of quasi-periodic modulation on the localization properties of one-dimensional non-Hermitian cross-stitch lattices with flat bands.The crystalline Hamiltonian for this non-Hermitian cross-stitch lattice is given by:(H)=∑n[t(a†nbn+b(†)nan)+Jeh(a(†)nbn+1+a(†)nan+1+Ab(†)nan+1+Ab(†)nbn+1)+Je-h(Aa(†)n+1bn+a(†)n+1an+b(†)n+1an+Ab(†)+1bn)]with A=±1.When A=1,the clean lattice supports two bands with dispersion relations E0=-t,E1=4cos(k-ih)+t.The compact localized states(CLSs)within the flat band E0 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±=±√t2+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-periodic modulations εβn=λβ cos(2παn+φβ)(β={a,b}),delocalization-localization transitions can be observed by numerically calculating the fractal dimension D2 and imaginary part of the energy spectrum ln|Im(E)|.Our findings indicate that the symmetry of quasi-periodic modulations plays an important role in determining the localization properties of the system.For the case of U=1,the symmetric quasi-periodic modulation leads to two independent spectra σf and σp.Theσf retains its compact properties,while the σp owns an extended-localized transition at λc1=4M with M=max{eh,e-h}.However,in the case of antisymmetric modulation,the system exhibits an exact mobility edge λc2=2√2|E-t|M.For the U=2 class,all the eigenstates remain localized under any symmetric quasi-periodic modulation.In the case of antisymmetric modulation,all states transition from multifractal to localized states as the modulation strength increases,with a critical point at λc3=4M.This work expands the understanding of localization properties in non-Hermitian flat-band systems and provides a new perspective on delocalization-localization transitions.
基金项目
国家自然科学基金(12375016)
山西省基础研究计划(20210302123442)
北京凝聚态物理国家实验室(2023BNLCMPKF001)
山西省"1331工程"重点学科建设计划(12375016)
Fund for Shanxi"1331 Project"Key Subjects,China()
维普
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