{"title":"波动虚规场中的拓扑相变","authors":"B. Midya","doi":"10.1103/PhysRevA.109.L061502","DOIUrl":null,"url":null,"abstract":"We investigate the exact solvability and point-gap topological phase transitions in non-Hermitian lattice models. These models incorporate site-dependent nonreciprocal hoppings $J e^{\\pm g_n}$, facilitated by a spatially fluctuating imaginary gauge field $ig_n \\hat~x$ that disrupts translational symmetry. By employing suitable imaginary gauge transformations, it is revealed that a lattice characterized by any given $g_n$ is spectrally equivalent to a lattice devoid of fields, under open boundary conditions. Furthermore, a system with closed boundaries can be simplified to a spectrally equivalent lattice featuring a uniform mean field $i\\bar{g}\\hat~x$. This framework offers a comprehensive method for analytically predicting spectral topological invariance and associated boundary localization phenomena for bond-disordered nonperiodic lattices. These predictions are made by analyzing gauge-transformed isospectral periodic lattices. Notably, for a lattice with quasiperiodic $g_n= \\ln |\\lambda \\cos 2\\pi \\alpha n|$ and an irrational $\\alpha$, a previously unknown topological phase transition is unveiled. It is observed that the topological spectral index $W$ assumes values of $-N$ or $+N$, leading to all $N$ open-boundary eigenstates localizing either at the right or left edge, solely dependent on the strength of the gauge field, where $\\lambda<2$ or $\\lambda>2$. A phase transition is identified at the critical point $\\lambda\\approx2$, at which all eigenstates undergo delocalization. The theory has been shown to be relevant for long-range hopping models and for higher dimensions.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":"105 24","pages":""},"PeriodicalIF":4.6000,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Topological phase transition in fluctuating imaginary gauge fields\",\"authors\":\"B. Midya\",\"doi\":\"10.1103/PhysRevA.109.L061502\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the exact solvability and point-gap topological phase transitions in non-Hermitian lattice models. These models incorporate site-dependent nonreciprocal hoppings $J e^{\\\\pm g_n}$, facilitated by a spatially fluctuating imaginary gauge field $ig_n \\\\hat~x$ that disrupts translational symmetry. By employing suitable imaginary gauge transformations, it is revealed that a lattice characterized by any given $g_n$ is spectrally equivalent to a lattice devoid of fields, under open boundary conditions. Furthermore, a system with closed boundaries can be simplified to a spectrally equivalent lattice featuring a uniform mean field $i\\\\bar{g}\\\\hat~x$. This framework offers a comprehensive method for analytically predicting spectral topological invariance and associated boundary localization phenomena for bond-disordered nonperiodic lattices. These predictions are made by analyzing gauge-transformed isospectral periodic lattices. Notably, for a lattice with quasiperiodic $g_n= \\\\ln |\\\\lambda \\\\cos 2\\\\pi \\\\alpha n|$ and an irrational $\\\\alpha$, a previously unknown topological phase transition is unveiled. It is observed that the topological spectral index $W$ assumes values of $-N$ or $+N$, leading to all $N$ open-boundary eigenstates localizing either at the right or left edge, solely dependent on the strength of the gauge field, where $\\\\lambda<2$ or $\\\\lambda>2$. A phase transition is identified at the critical point $\\\\lambda\\\\approx2$, at which all eigenstates undergo delocalization. The theory has been shown to be relevant for long-range hopping models and for higher dimensions.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":\"105 24\",\"pages\":\"\"},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-06-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/PhysRevA.109.L061502\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevA.109.L061502","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Topological phase transition in fluctuating imaginary gauge fields
We investigate the exact solvability and point-gap topological phase transitions in non-Hermitian lattice models. These models incorporate site-dependent nonreciprocal hoppings $J e^{\pm g_n}$, facilitated by a spatially fluctuating imaginary gauge field $ig_n \hat~x$ that disrupts translational symmetry. By employing suitable imaginary gauge transformations, it is revealed that a lattice characterized by any given $g_n$ is spectrally equivalent to a lattice devoid of fields, under open boundary conditions. Furthermore, a system with closed boundaries can be simplified to a spectrally equivalent lattice featuring a uniform mean field $i\bar{g}\hat~x$. This framework offers a comprehensive method for analytically predicting spectral topological invariance and associated boundary localization phenomena for bond-disordered nonperiodic lattices. These predictions are made by analyzing gauge-transformed isospectral periodic lattices. Notably, for a lattice with quasiperiodic $g_n= \ln |\lambda \cos 2\pi \alpha n|$ and an irrational $\alpha$, a previously unknown topological phase transition is unveiled. It is observed that the topological spectral index $W$ assumes values of $-N$ or $+N$, leading to all $N$ open-boundary eigenstates localizing either at the right or left edge, solely dependent on the strength of the gauge field, where $\lambda<2$ or $\lambda>2$. A phase transition is identified at the critical point $\lambda\approx2$, at which all eigenstates undergo delocalization. The theory has been shown to be relevant for long-range hopping models and for higher dimensions.
期刊介绍:
ACS Applied Bio Materials is an interdisciplinary journal publishing original research covering all aspects of biomaterials and biointerfaces including and beyond the traditional biosensing, biomedical and therapeutic applications.
The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrates knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important bio applications. The journal is specifically interested in work that addresses the relationship between structure and function and assesses the stability and degradation of materials under relevant environmental and biological conditions.