Pub Date : 2020-09-13DOI: 10.1103/PHYSREVB.103.014201
Xiaoming Cai
We study a non-Hermitian Aubry-Andr'e-Harper model with both nonreciprocal hoppings and complex quasiperiodical potentials, which is a typical non-Hermitian quasicrystal. We introduce boundary-dependent self-dualities in this model and obtain analytical results to describe its Asymmetrical Anderson localization and topological phase transitions. We find that the Anderson localization is not necessarily in accordance with the topological phase transitions, which are characteristics of localization of states and topology of energy spectrum respectively. Furthermore, in the localized phase, single-particle states are asymmetrically localized due to non-Hermitian skin effect and have energy-independent localization lengths. We also discuss possible experimental detections of our results in electric circuits.
{"title":"Boundary-dependent self-dualities, winding numbers, and asymmetrical localization in non-Hermitian aperiodic one-dimensional models","authors":"Xiaoming Cai","doi":"10.1103/PHYSREVB.103.014201","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.014201","url":null,"abstract":"We study a non-Hermitian Aubry-Andr'e-Harper model with both nonreciprocal hoppings and complex quasiperiodical potentials, which is a typical non-Hermitian quasicrystal. We introduce boundary-dependent self-dualities in this model and obtain analytical results to describe its Asymmetrical Anderson localization and topological phase transitions. We find that the Anderson localization is not necessarily in accordance with the topological phase transitions, which are characteristics of localization of states and topology of energy spectrum respectively. Furthermore, in the localized phase, single-particle states are asymmetrically localized due to non-Hermitian skin effect and have energy-independent localization lengths. We also discuss possible experimental detections of our results in electric circuits.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87334256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Tikhodeev, E. Muljarov, W. Langbein, N. Gippius, H. Giessen, T. Weiss
Using the resonant-state expansion for leaky optical modes of a planar Bragg microcavity, we investigate the influence of disorder on its fundamental cavity mode. We model the disorder by randomly varying the thickness of the Bragg-pair slabs (composing the mirrors) and the cavity, and calculate the resonant energy and linewidth of each disordered microcavity exactly, comparing the results with the resonant-state expansion for a large basis set and within its 1st and 2nd orders of perturbation theory. We show that random shifts of interfaces cause a growth of the inhomogeneous broadening of the fundamental mode that is proportional to the magnitude of disorder. Simultaneously, the quality factor of the microcavity decreases inversely proportional to the square of the magnitude of disorder. We also find that 1st order perturbation theory works very accurately up to a reasonably large disorder magnitude, especially for calculating the resonance energy, which allows us to derive qualitatively the scaling of the microcavity properties with disorder strength.
{"title":"Influence of disorder on a Bragg microcavity","authors":"S. Tikhodeev, E. Muljarov, W. Langbein, N. Gippius, H. Giessen, T. Weiss","doi":"10.1364/josab.402986","DOIUrl":"https://doi.org/10.1364/josab.402986","url":null,"abstract":"Using the resonant-state expansion for leaky optical modes of a planar Bragg microcavity, we investigate the influence of disorder on its fundamental cavity mode. We model the disorder by randomly varying the thickness of the Bragg-pair slabs (composing the mirrors) and the cavity, and calculate the resonant energy and linewidth of each disordered microcavity exactly, comparing the results with the resonant-state expansion for a large basis set and within its 1st and 2nd orders of perturbation theory. We show that random shifts of interfaces cause a growth of the inhomogeneous broadening of the fundamental mode that is proportional to the magnitude of disorder. Simultaneously, the quality factor of the microcavity decreases inversely proportional to the square of the magnitude of disorder. We also find that 1st order perturbation theory works very accurately up to a reasonably large disorder magnitude, especially for calculating the resonance energy, which allows us to derive qualitatively the scaling of the microcavity properties with disorder strength.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85711930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Machine learning has recently been applied to many problems in condensed matter physics. A common point of many proposals is to save computational cost by training the machine with data from a simple example and then using the machine to make predictions for a more complicated example. Convolutional neural networks (CNN), which are one of the tools of machine learning, have proved to work well for assessing eigenfunctions in disordered systems. Here we apply a CNN to assess Kohn-Sham eigenfunctions obtained in density functional theory (DFT) simulations of the metal-insulator transition of a doped semiconductor. We demonstrate that a CNN that has been trained using eigenfunctions from a simulation of a doped semiconductor that neglects electron spin successfully predicts the critical concentration when presented with eigenfunctions from simulations that include spin.
{"title":"Analysis of Kohn-Sham Eigenfunctions Using a Convolutional Neural Network in Simulations of the Metal-insulator Transition in Doped Semiconductors.","authors":"Y. Harashima, T. Mano, K. Slevin, T. Ohtsuki","doi":"10.7566/JPSJ.90.094001","DOIUrl":"https://doi.org/10.7566/JPSJ.90.094001","url":null,"abstract":"Machine learning has recently been applied to many problems in condensed matter physics. A common point of many proposals is to save computational cost by training the machine with data from a simple example and then using the machine to make predictions for a more complicated example. Convolutional neural networks (CNN), which are one of the tools of machine learning, have proved to work well for assessing eigenfunctions in disordered systems. Here we apply a CNN to assess Kohn-Sham eigenfunctions obtained in density functional theory (DFT) simulations of the metal-insulator transition of a doped semiconductor. We demonstrate that a CNN that has been trained using eigenfunctions from a simulation of a doped semiconductor that neglects electron spin successfully predicts the critical concentration when presented with eigenfunctions from simulations that include spin.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85074545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-04DOI: 10.1103/physrevresearch.4.023067
I. Lovas, A. Kiss, C. Moca, G. Zar'and
We study the Coulomb glass emerging from the interplay of strong interactions and disorder in a model of spinless fermions on the Bethe lattice. In the infinite coordination number limit, strong interactions induce a metallic Coulomb glass phase with a pseudogap structure at the Fermi energy. Quantum and thermal fluctuations both melt this glass and induce a disordered quantum liquid phase. We combine self-consistent diagrammatic perturbation theory with continuous time quantum Monte-Carlo simulations to obtain the complete phase diagram of the electron glass, and to characterize its dynamical properties in the quantum liquid, as well as in the replica symmetry broken glassy phase. Tunneling spectra display an Efros-Shklovskii pseudogap upon decreasing temperatures, but the density of states remains finite at the Fermi energy due to residual quantum fluctuations. Our results bear relevance to the metallic glass phase observed in Si inversion layers.
{"title":"Quantum Coulomb glass on the Bethe lattice","authors":"I. Lovas, A. Kiss, C. Moca, G. Zar'and","doi":"10.1103/physrevresearch.4.023067","DOIUrl":"https://doi.org/10.1103/physrevresearch.4.023067","url":null,"abstract":"We study the Coulomb glass emerging from the interplay of strong interactions and disorder in a model of spinless fermions on the Bethe lattice. In the infinite coordination number limit, strong interactions induce a metallic Coulomb glass phase with a pseudogap structure at the Fermi energy. Quantum and thermal fluctuations both melt this glass and induce a disordered quantum liquid phase. We combine self-consistent diagrammatic perturbation theory with continuous time quantum Monte-Carlo simulations to obtain the complete phase diagram of the electron glass, and to characterize its dynamical properties in the quantum liquid, as well as in the replica symmetry broken glassy phase. Tunneling spectra display an Efros-Shklovskii pseudogap upon decreasing temperatures, but the density of states remains finite at the Fermi energy due to residual quantum fluctuations. Our results bear relevance to the metallic glass phase observed in Si inversion layers.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77139930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-21DOI: 10.1016/j.physleta.2020.127094
M. Molina
{"title":"Magnetic metamaterials with correlated disorder","authors":"M. Molina","doi":"10.1016/j.physleta.2020.127094","DOIUrl":"https://doi.org/10.1016/j.physleta.2020.127094","url":null,"abstract":"","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81896893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-17DOI: 10.1103/PHYSREVRESEARCH.3.L012019
A. Prakash, J. Pixley, M. Kulkarni
We theoretically study universal correlations present in the spectrum of many-body-localized systems. We obtain an exact analytical expression for the spectral form factor of Poisson spectra and show that it agrees well with numerical results on two models exhibiting a many-body-localization: a disordered quantum spin chain and a phenomenological l-bit model based on the existence of local integrals of motion. We find that the functional form of the Poisson spectral form factor is distinct from but complementary to the universal expectation of quantum chaotic systems obtained from random matrix theory.
{"title":"Universal spectral form factor for many-body localization","authors":"A. Prakash, J. Pixley, M. Kulkarni","doi":"10.1103/PHYSREVRESEARCH.3.L012019","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.3.L012019","url":null,"abstract":"We theoretically study universal correlations present in the spectrum of many-body-localized systems. We obtain an exact analytical expression for the spectral form factor of Poisson spectra and show that it agrees well with numerical results on two models exhibiting a many-body-localization: a disordered quantum spin chain and a phenomenological l-bit model based on the existence of local integrals of motion. We find that the functional form of the Poisson spectral form factor is distinct from but complementary to the universal expectation of quantum chaotic systems obtained from random matrix theory.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73227111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-23DOI: 10.1103/PHYSREVB.103.104204
D. A. Conyuh, Y. Beltukov
We show that the correlated Wishart ensemble can be used to study general vibrational properties of stable amorphous solids with translational invariance. Using the random matrix theory, we found the vibrational density of states and the dynamical structure factor. We demonstrate the presence of the Ioffe-Regel crossover between low-frequency propagating phonons and diffusons at higher frequencies. The reduced vibrational density of states shows the boson peak, which frequency is close to the Ioffe-Regel crossover.
{"title":"Random matrix approach to the boson peak and Ioffe-Regel criterion in amorphous solids","authors":"D. A. Conyuh, Y. Beltukov","doi":"10.1103/PHYSREVB.103.104204","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.104204","url":null,"abstract":"We show that the correlated Wishart ensemble can be used to study general vibrational properties of stable amorphous solids with translational invariance. Using the random matrix theory, we found the vibrational density of states and the dynamical structure factor. We demonstrate the presence of the Ioffe-Regel crossover between low-frequency propagating phonons and diffusons at higher frequencies. The reduced vibrational density of states shows the boson peak, which frequency is close to the Ioffe-Regel crossover.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73689595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-22DOI: 10.1103/physrevresearch.2.043291
Samaneh Esfandiary, A. Safari, Jakob Renner, P. Moretti, M. A. Muñoz
Network models of neural connectivity and function often invoke the ability of the brain to localize activity in distinct modules simultaneously. The propensity of a network to do the opposite instead, that is to transmit and diffuse information homogeneously, is measured by its spectral dimension, a quantity that is easily accessible through analyses of random walks, or equivalently diffusion processes. Here we show that diffusive dynamics in hierarchical modular network models, representing brain connectivity patterns, exhibit a strongly anomalous features, pointing to a global asymptotic slowdown at large times and to the emergence of localization phenomena. Using theoretical modeling and very-large-scale computer simulations, we demonstrate that the spectral dimension is not defined in such systems and that the observed anomalous dynamical features stem from the existence of Lifshitz tails in the lower spectral edge of the Laplacian matrix. We are able to derive the correct scaling laws relating the spectral density of states and anomalous dynamics, emphasizing the fundamental role played by the Lifshitz dimension. Our work contributes to establishing a theoretical framework for anomalous dynamical features, such as activity localization and frustrated synchronization in hierarchical and hierarchical-modular networks and helps contextualize previous observations of sub-diffusive behavior and rare-region effects in brain networks. More in general, our results, help shedding light on the relation between structure and function in biological information-processing complex networks.
{"title":"Anomalous Lifshitz dimension in hierarchical networks of brain connectivity","authors":"Samaneh Esfandiary, A. Safari, Jakob Renner, P. Moretti, M. A. Muñoz","doi":"10.1103/physrevresearch.2.043291","DOIUrl":"https://doi.org/10.1103/physrevresearch.2.043291","url":null,"abstract":"Network models of neural connectivity and function often invoke the ability of the brain to localize activity in distinct modules simultaneously. The propensity of a network to do the opposite instead, that is to transmit and diffuse information homogeneously, is measured by its spectral dimension, a quantity that is easily accessible through analyses of random walks, or equivalently diffusion processes. Here we show that diffusive dynamics in hierarchical modular network models, representing brain connectivity patterns, exhibit a strongly anomalous features, pointing to a global asymptotic slowdown at large times and to the emergence of localization phenomena. Using theoretical modeling and very-large-scale computer simulations, we demonstrate that the spectral dimension is not defined in such systems and that the observed anomalous dynamical features stem from the existence of Lifshitz tails in the lower spectral edge of the Laplacian matrix. We are able to derive the correct scaling laws relating the spectral density of states and anomalous dynamics, emphasizing the fundamental role played by the Lifshitz dimension. Our work contributes to establishing a theoretical framework for anomalous dynamical features, such as activity localization and frustrated synchronization in hierarchical and hierarchical-modular networks and helps contextualize previous observations of sub-diffusive behavior and rare-region effects in brain networks. More in general, our results, help shedding light on the relation between structure and function in biological information-processing complex networks.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73520698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-21DOI: 10.1103/physrevb.102.134206
S. E. Skipetrov
We demonstrate that a weak disorder in atomic positions introduces spatially localized optical modes in a dense three-dimensional ensemble of immobile two-level atoms arranged in a diamond lattice and coupled by the electromagnetic field. The frequencies of the localized modes concentrate near band edges of the unperturbed lattice. Finite-size scaling analysis of the percentiles of Thouless conductance reveals two mobility edges and yields an estimation $nu = 0.8$--1.1 for the critical exponent of the localization length. The localized modes disappear when the disorder becomes too strong and the system starts to resemble a fully disordered one where all modes are extended.
{"title":"Localization of light in a three-dimensional disordered crystal of atoms","authors":"S. E. Skipetrov","doi":"10.1103/physrevb.102.134206","DOIUrl":"https://doi.org/10.1103/physrevb.102.134206","url":null,"abstract":"We demonstrate that a weak disorder in atomic positions introduces spatially localized optical modes in a dense three-dimensional ensemble of immobile two-level atoms arranged in a diamond lattice and coupled by the electromagnetic field. The frequencies of the localized modes concentrate near band edges of the unperturbed lattice. Finite-size scaling analysis of the percentiles of Thouless conductance reveals two mobility edges and yields an estimation $nu = 0.8$--1.1 for the critical exponent of the localization length. The localized modes disappear when the disorder becomes too strong and the system starts to resemble a fully disordered one where all modes are extended.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79711804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-23DOI: 10.1142/9789811216220_0001
J. Ruiz-Lorenzo
Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low temperature phase have been proposed: droplet, replica symmetry breaking and chaotic pairs. We present analytical studies of critical properties of spin glasses, in particular, critical exponents at and below the phase transition, existence of a phase transition in a magnetic field, computation of the lower critical dimension (in presence/absence of a magnetic field). We also introduce some rigorous results based on the concept of metastate. Finally, we report some numerical results regarding the construction of the Aizenman-Wehr metastate, scaling of the correlation functions in the spin glass phase and existence of a phase transition in a field, confronting these results with the predictions of different theories.
{"title":"Nature of the Spin Glass Phase in Finite Dimensional (Ising) Spin Glasses","authors":"J. Ruiz-Lorenzo","doi":"10.1142/9789811216220_0001","DOIUrl":"https://doi.org/10.1142/9789811216220_0001","url":null,"abstract":"Spin glasses are the paradigm of complex systems. These materials present really slow dynamics. However, the nature of the spin glass phase in finite dimensional systems is still controversial. Different theories describing the low temperature phase have been proposed: droplet, replica symmetry breaking and chaotic pairs. We present analytical studies of critical properties of spin glasses, in particular, critical exponents at and below the phase transition, existence of a phase transition in a magnetic field, computation of the lower critical dimension (in presence/absence of a magnetic field). We also introduce some rigorous results based on the concept of metastate. Finally, we report some numerical results regarding the construction of the Aizenman-Wehr metastate, scaling of the correlation functions in the spin glass phase and existence of a phase transition in a field, confronting these results with the predictions of different theories.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83441584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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