- 必威体育下载

姓名
邮箱
手机号码
标题
留言内容
验证码

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.

关键词:

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: $\hat{H}=\displaystyle\sum\limits_{n}\left[t(a_n^{\dagger} b_n + b_n^{\dagger}a_n ) + J{\mathrm{e}}^{h}\left(a_n^{\dagger}b_{n + 1} + a_n^{\dagger} a_{n + 1} + Ab_n^{\dagger}a_{n + 1} + Ab_n^{\dagger}b_{n + 1}\right) + J{\mathrm{e}}^{ - h} \left(Aa_{n + 1}^{\dagger}b_n + a_{n + 1}^{\dagger}a_n + b_{n + 1}^{\dagger}a_n + Ab_{n + 1}^{\dagger}b_n\right)\right] $ with $A =\pm 1$ . When A= 1, the clean lattice supports two bands with dispersion relations $E_0=- t, $ $ E_1=4\cos (k - {\mathrm{i}}h) + t$ . The compact localized states (CLSs) within the flat band E ₀are 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: $E_{\pm}=\pm\sqrt{t^2 + 4}$ . 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 $\varepsilon_n^{\beta}=\lambda_{\beta}\cos(2\pi\alpha n + \phi_{\beta})$ ( $\beta=\{a,b\}$ ), delocalization-localization transitions can be observed by numerically calculating the fractal dimension D ₂and imaginary part of the energy spectrum $\ln{|{\rm{Im}}(E)|}$ . 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 $\sigma_f$ and $\sigma_p$ . The $\sigma_f$ retains its compact properties, while the $\sigma_p$ owns an extended-localized transition at $\lambda_{{\mathrm{c}}1}=4M$ with $M=\max\{{\mathrm{e}}^{h},\;{\mathrm{e}}^{ - h}\}$ . However, in the case of antisymmetric modulation, the system exhibits an exact mobility edge $\lambda_{{\mathrm{c}}2}=2\sqrt{2|E - t|M}$ . 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 $\lambda_{{\mathrm{c}}3}=4M$ . This work expands the understanding of localization properties in non-Hermitian flat-band systems and provides a new perspective on delocalization-localization transitions.

Keywords:

作者及机构信息

1.
2.

通信作者:徐志浩,xuzhihao@sxu.edu.cn

基金项目:国家自然科学基金(批准号: 12375016)、山西省基础研究计划(批准号: 20210302123442)、北京凝聚态物理国家实验室(批准号: 2023BNLCMPKF001)和山西省“1331工程”重点学科建设计划资助的课题.

Authors and contacts

1.
2.

Corresponding author:Xu Zhi-Hao,xuzhihao@sxu.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 12375016), the Fundamental Research Program of Shanxi Province, China (Grant No. 20210302123442), the Beijing National Laboratory for Condensed Matter Physics (Grant No. 2023BNLCMPKF001), and the Fund for Shanxi “1331 Project” Key Subjects, China.

文章全文: translate this paragraph

参考文献

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]

施引文献

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

下载: 全尺寸图片幻灯片

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]

[1]	冯曦曦, 陈文, 高先龙.量子信息中的度量空间方法在准周期系统中的应用. 必威体育下载 , 2024, 73(4): 040501.doi:10.7498/aps.73.20231605
[2]	刘敬鹄, 徐志浩.随机两体耗散诱导的非厄米多体局域化. 必威体育下载 , 2024, 73(7): 077202.doi:10.7498/aps.73.20231987
[3]	陆展鹏, 徐志浩.具有平带的一维十字型晶格中重返局域化现象. 必威体育下载 , 2024, 73(3): 037202.doi:10.7498/aps.73.20231393
[4]	李竞, 丁海涛, 张丹伟.非厄米哈密顿量中的量子Fisher信息与参数估计. 必威体育下载 , 2023, 72(20): 200601.doi:10.7498/aps.72.20230862
[5]	孙思彤, 丁应星, 刘伍明.基于线性与非线性干涉仪的量子精密测量研究进展. 必威体育下载 , 2022, 71(13): 130701.doi:10.7498/aps.71.20220425
[6]	刘佳琳, 庞婷方, 杨孝森, 王正岭.无序非厄米Su-Schrieffer-Heeger中的趋肤效应. 必威体育下载 , 2022, 71(22): 227402.doi:10.7498/aps.71.20221151
[7]	张禧征, 王鹏, 张坤亮, 杨学敏, 宋智.非厄米临界动力学及其在量子多体系统中的应用. 必威体育下载 , 2022, 71(17): 174501.doi:10.7498/aps.71.20220914
[8]	侯博, 曾琦波.非厄米镶嵌型二聚化晶格. 必威体育下载 , 2022, 71(13): 130302.doi:10.7498/aps.71.20220890
[9]	高雪儿, 李代莉, 刘志航, 郑超.非厄米系统的量子模拟新进展. 必威体育下载 , 2022, 71(24): 240303.doi:10.7498/aps.71.20221825
[10]	祝可嘉, 郭志伟, 陈鸿.实验观测非厄米系统奇异点的手性翻转现象. 必威体育下载 , 2022, 71(13): 131101.doi:10.7498/aps.71.20220842
[11]	吴瑾, 陆展鹏, 徐志浩, 郭利平.由超辐射引起的迁移率边和重返局域化. 必威体育下载 , 2022, 71(11): 113702.doi:10.7498/aps.71.20212246
[12]	傅聪, 叶梦浩, 赵晖, 陈宇光, 鄢永红.共轭聚合物链中光激发过程的无序效应. 必威体育下载 , 2021, 70(11): 117201.doi:10.7498/aps.70.20201801
[13]	侯碧辉, 刘凤艳, 岳明, 王克军.纳米金属镝的传导电子定域化. 必威体育下载 , 2011, 60(1): 017201.doi:10.7498/aps.60.017201
[14]	丁锐, 金亚秋, 小仓久直.二维随机介质中柱面波传播及其局域性的随机泛函分析. 必威体育下载 , 2010, 59(6): 3674-3685.doi:10.7498/aps.59.3674
[15]	李晓春, 高俊丽, 刘绍娥, 周科朝, 黄伯云.无序对二维声子晶体平板负折射成像的影响. 必威体育下载 , 2010, 59(1): 376-380.doi:10.7498/aps.59.376
[16]	曹永军, 杨旭, 姜自磊.弹性波通过一维复合材料系统的透射性质. 必威体育下载 , 2009, 58(11): 7735-7740.doi:10.7498/aps.58.7735
[17]	王慧琴, 刘正东, 王冰.二维随机介质中的能量分布和频谱特性. 必威体育下载 , 2008, 57(9): 5550-5557.doi:10.7498/aps.57.5550
[18]	王慧琴, 刘正东, 王冰.同材质颗粒不同填充密度的随机介质中光场的空间分布. 必威体育下载 , 2008, 57(4): 2186-2191.doi:10.7498/aps.57.2186
[19]	许兴胜, 陈弘达, 张道中.非晶光子晶体中的光子局域化. 必威体育下载 , 2006, 55(12): 6430-6434.doi:10.7498/aps.55.6430
[20]	刘小良, 徐慧, 马松山, 宋招权.一维无序二元固体中电子局域性质的研究. 必威体育下载 , 2006, 55(6): 2949-2954.doi:10.7498/aps.55.2949

计量

文章访问数:969
PDF下载量:34
被引次数:0

搜索

留言板