We propose a family of exactly solvable quasiperiodic lattice models with analytical complex mobility edges, which can incorporate mosaic modulations as a straightforward generalization. By sweeping a potential tuning parameter $delta$, we demonstrate a kind of interesting butterfly-like spectra in complex energy plane, which depicts energy-dependent extended-localized transitions sharing a common exact non-Hermitian mobility edge. Applying Avila's global theory, we are able to analytically calculate the Lyapunov exponents and determine the mobility edges exactly. For the minimal model without mosaic modulation, a compactly analytic formula for the complex mobility edges is obtained, which, together with analytical estimation of the range of complex energy spectrum, gives the true mobility edge. The non-Hermitian mobility edge in complex energy plane is further verified by numerical calculations of fractal dimension and spatial distribution of wave functions. Tuning parameters of non-Hermitian potentials, we also investigate the variations of the non-Hermitian mobility edges and the corresponding butterfly spectra, which exhibit richness of spectrum structures.
{"title":"Non-Hermitian butterfly spectra in a family of quasiperiodic lattices","authors":"Li Wang, Zhenbo Wang, Shu Chen","doi":"arxiv-2404.11020","DOIUrl":"https://doi.org/arxiv-2404.11020","url":null,"abstract":"We propose a family of exactly solvable quasiperiodic lattice models with\u0000analytical complex mobility edges, which can incorporate mosaic modulations as\u0000a straightforward generalization. By sweeping a potential tuning parameter\u0000$delta$, we demonstrate a kind of interesting butterfly-like spectra in\u0000complex energy plane, which depicts energy-dependent extended-localized\u0000transitions sharing a common exact non-Hermitian mobility edge. Applying\u0000Avila's global theory, we are able to analytically calculate the Lyapunov\u0000exponents and determine the mobility edges exactly. For the minimal model\u0000without mosaic modulation, a compactly analytic formula for the complex\u0000mobility edges is obtained, which, together with analytical estimation of the\u0000range of complex energy spectrum, gives the true mobility edge. The\u0000non-Hermitian mobility edge in complex energy plane is further verified by\u0000numerical calculations of fractal dimension and spatial distribution of wave\u0000functions. Tuning parameters of non-Hermitian potentials, we also investigate\u0000the variations of the non-Hermitian mobility edges and the corresponding\u0000butterfly spectra, which exhibit richness of spectrum structures.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140610921","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}
We study the dynamics of the generalized Lotka-Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us to describe the fixed points of the model in terms of a few simple order parameters. We extend the analysis even for diverging abundances, using a mapping to the replicator model. With this we present a unified approach for both cooperative and competitive systems that display complementary behaviors. In particular we show the central role of an order parameter called the critical degree, $g_c$. In the competitive regime $g_c$ serves to distinguish high degree nodes that are more likely to go extinct, while in the cooperative regime it has the reverse role, it will determine the low degree nodes that tend to go relatively extinct.
{"title":"Heterogeneous mean-field analysis of the generalized Lotka-Volterra model on a network","authors":"Fabián Aguirre-López","doi":"arxiv-2404.11164","DOIUrl":"https://doi.org/arxiv-2404.11164","url":null,"abstract":"We study the dynamics of the generalized Lotka-Volterra model with a network\u0000structure. Performing a high connectivity expansion for graphs, we write down a\u0000mean-field dynamical theory that incorporates degree heterogeneity. This allows\u0000us to describe the fixed points of the model in terms of a few simple order\u0000parameters. We extend the analysis even for diverging abundances, using a\u0000mapping to the replicator model. With this we present a unified approach for\u0000both cooperative and competitive systems that display complementary behaviors.\u0000In particular we show the central role of an order parameter called the\u0000critical degree, $g_c$. In the competitive regime $g_c$ serves to distinguish\u0000high degree nodes that are more likely to go extinct, while in the cooperative\u0000regime it has the reverse role, it will determine the low degree nodes that\u0000tend to go relatively extinct.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140610926","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}
We study fluctuation properties in the energy spectra of finite-size honeycomb lattices, graphene billiards, subject to the Haldane-model onsite potential and next-nearest neighbor interaction at critical points, referred to as Haldane graphene billiards in the following. The billiards had the shapes of a rectangular billiard with integrable dynamics, one with chaotic dynamics, and one whose shape has, in addition, threefold rotational symmetry. It had been shown that the spectral properties of the graphene billiards coincide with those of the nonrelativistic quantum billiard with the corresponding shape, both at the band edges and in the region of low energy excitations around the Dirac points at zero energy. There, the dispersion relation is linear and, accordingly, the spectrum is described by the same relativistic Dirac equation for massless half-spin particles as relativistic neutrino billiards, whose spectral properties agree with those of nonrelativistic quantum billiards with violated time-reversal invariance. Deviations from the expected behavior are attributed to differing boundary conditions and backscattering at the boundary, which leads to a mixing of valley states corresponding to the two Dirac points, that are mapped into each other through time reversal. We employ a Haldane model to introduce a gap at one of the two Dirac points so that backscattering is suppressed in the energy region of the gap and demonstrate that there the correlations in the spectra comply with those of the neutrino billiard of the corresponding shape.
{"title":"Haldane graphene billiards versus relativistic neutrino billiards","authors":"Dung Xuan Nguyen, Barbara Dietz","doi":"arxiv-2404.07679","DOIUrl":"https://doi.org/arxiv-2404.07679","url":null,"abstract":"We study fluctuation properties in the energy spectra of finite-size\u0000honeycomb lattices, graphene billiards, subject to the Haldane-model onsite\u0000potential and next-nearest neighbor interaction at critical points, referred to\u0000as Haldane graphene billiards in the following. The billiards had the shapes of\u0000a rectangular billiard with integrable dynamics, one with chaotic dynamics, and\u0000one whose shape has, in addition, threefold rotational symmetry. It had been\u0000shown that the spectral properties of the graphene billiards coincide with\u0000those of the nonrelativistic quantum billiard with the corresponding shape,\u0000both at the band edges and in the region of low energy excitations around the\u0000Dirac points at zero energy. There, the dispersion relation is linear and,\u0000accordingly, the spectrum is described by the same relativistic Dirac equation\u0000for massless half-spin particles as relativistic neutrino billiards, whose\u0000spectral properties agree with those of nonrelativistic quantum billiards with\u0000violated time-reversal invariance. Deviations from the expected behavior are\u0000attributed to differing boundary conditions and backscattering at the boundary,\u0000which leads to a mixing of valley states corresponding to the two Dirac points,\u0000that are mapped into each other through time reversal. We employ a Haldane\u0000model to introduce a gap at one of the two Dirac points so that backscattering\u0000is suppressed in the energy region of the gap and demonstrate that there the\u0000correlations in the spectra comply with those of the neutrino billiard of the\u0000corresponding shape.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140610918","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}
We investigate the addition of applied stress to a random block matrix model introduced by Parisi to study the Hessian matrix of soft spheres near the jamming point. In the infinite dimensional limit the applied stress translates the spectral distribution to the left, leading to a stability constraint. With negative stress, as in the case of a random network of stretched elastic springs, the spectral distribution is translated to the right, and the density of states has a peak before the plateau.
{"title":"A random matrix model for the density of states of jammed soft spheres with applied stress","authors":"Mario Pernici","doi":"arxiv-2404.07064","DOIUrl":"https://doi.org/arxiv-2404.07064","url":null,"abstract":"We investigate the addition of applied stress to a random block matrix model\u0000introduced by Parisi to study the Hessian matrix of soft spheres near the\u0000jamming point. In the infinite dimensional limit the applied stress translates\u0000the spectral distribution to the left, leading to a stability constraint. With\u0000negative stress, as in the case of a random network of stretched elastic\u0000springs, the spectral distribution is translated to the right, and the density\u0000of states has a peak before the plateau.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573718","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}
Unraveling dynamic heterogeneity in supercooled liquids from structural information is one of the grand challenges of physics. In this work, we introduce an unsupervised machine learning approach based on a time-lagged autoencoder (TAE) to elucidate the effect of structural features on the long-term dynamics of supercooled liquids. The TAE uses an autoencoder to reconstruct features at time $t + Delta t$ from input features at time $t$ for individual particles, and the resulting latent space variables are considered as order parameters. In the Kob-Andersen system, with a $Delta t$ about a thousand times smaller than the relaxation time, the TAE order parameter exhibits a remarkable correlation with the long-time propensity. We find that short-range radial features correlate with the short-time dynamics, and medium-range radial features correlate with the long-time dynamics. This shows that fluctuations of medium-range structural features contain sufficient information about the long-time dynamic heterogeneity, consistent with some theoretical predictions.
{"title":"Unsupervised machine learning for supercooled liquids","authors":"Yunrui Qiu, Inhyuk Jang, Xuhui Huang, Arun Yethiraj","doi":"arxiv-2404.04473","DOIUrl":"https://doi.org/arxiv-2404.04473","url":null,"abstract":"Unraveling dynamic heterogeneity in supercooled liquids from structural\u0000information is one of the grand challenges of physics. In this work, we\u0000introduce an unsupervised machine learning approach based on a time-lagged\u0000autoencoder (TAE) to elucidate the effect of structural features on the\u0000long-term dynamics of supercooled liquids. The TAE uses an autoencoder to\u0000reconstruct features at time $t + Delta t$ from input features at time $t$ for\u0000individual particles, and the resulting latent space variables are considered\u0000as order parameters. In the Kob-Andersen system, with a $Delta t$ about a\u0000thousand times smaller than the relaxation time, the TAE order parameter\u0000exhibits a remarkable correlation with the long-time propensity. We find that\u0000short-range radial features correlate with the short-time dynamics, and\u0000medium-range radial features correlate with the long-time dynamics. This shows\u0000that fluctuations of medium-range structural features contain sufficient\u0000information about the long-time dynamic heterogeneity, consistent with some\u0000theoretical predictions.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573689","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}
The real-space renormalisation group method can be applied to the Chalker-Coddington model of the quantum Hall transition to provide a convenient numerical estimation of the localisation critical exponent, $nu$. Previous such studies found $nusim 2.39$ which falls considerably short of the current best estimates by transfer matrix ($nuapprox 2.593$) and exact-diagonalisation studies ($nu=2.58(3)$). By increasing the amount of data $500$ fold we can now measure closer to the critical point and find an improved estimate $nuapprox 2.51$. This deviates only $sim 3%$ from the previous two values and is already better than the $sim 7%$ accuracy of the classical small-cell renormalisation approach from which our method is adapted. We also study a previously proposed mixing of the Chalker-Coddington model with a classical scattering model which is meant to provide a route to understanding why experimental estimates give a lower $nusim 2.3$. Upon implementing this mixing into our RG unit, we find only further increases to the value of $nu$.
{"title":"Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics","authors":"Syl Shaw, Rudolf A. Römer","doi":"arxiv-2404.00660","DOIUrl":"https://doi.org/arxiv-2404.00660","url":null,"abstract":"The real-space renormalisation group method can be applied to the\u0000Chalker-Coddington model of the quantum Hall transition to provide a convenient\u0000numerical estimation of the localisation critical exponent, $nu$. Previous\u0000such studies found $nusim 2.39$ which falls considerably short of the current\u0000best estimates by transfer matrix ($nuapprox 2.593$) and\u0000exact-diagonalisation studies ($nu=2.58(3)$). By increasing the amount of data\u0000$500$ fold we can now measure closer to the critical point and find an improved\u0000estimate $nuapprox 2.51$. This deviates only $sim 3%$ from the previous two\u0000values and is already better than the $sim 7%$ accuracy of the classical\u0000small-cell renormalisation approach from which our method is adapted. We also\u0000study a previously proposed mixing of the Chalker-Coddington model with a\u0000classical scattering model which is meant to provide a route to understanding\u0000why experimental estimates give a lower $nusim 2.3$. Upon implementing this\u0000mixing into our RG unit, we find only further increases to the value of $nu$.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573494","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}
G. V. Afonin, J. C. Qiao, A. S. Makarov, R. A. Konchakov, E. V. Goncharova, N. P. Kobelev, V. A. Khonik
We performed calorimetric measurements on 30 bulk metallic glasses differing with their mixing entropies DSmix. On this basis, the excess entropies DS and excess enthalpies DH of glasses with respect to their maternal crystalline states are calculated. It is found that the excess entropy DS on the average decreases with increasing mixing entropy DSmix. This means that so-called "high-entropymetallic glasses" (i.e. the glasses having high DSmix) actually constitute glasses with low excess entropy DS. We predict that such glasses should have reduced relaxation ability. We also found that the excess enthalpy DH of glass linearly increases with its excess entropy DS, in line with a general thermodynamic estimate.
{"title":"High entropy metallic glasses, what does it mean?","authors":"G. V. Afonin, J. C. Qiao, A. S. Makarov, R. A. Konchakov, E. V. Goncharova, N. P. Kobelev, V. A. Khonik","doi":"arxiv-2403.20115","DOIUrl":"https://doi.org/arxiv-2403.20115","url":null,"abstract":"We performed calorimetric measurements on 30 bulk metallic glasses differing\u0000with their mixing entropies DSmix. On this basis, the excess entropies DS and\u0000excess enthalpies DH of glasses with respect to their maternal crystalline\u0000states are calculated. It is found that the excess entropy DS on the average\u0000decreases with increasing mixing entropy DSmix. This means that so-called\u0000\"high-entropymetallic glasses\" (i.e. the glasses having high DSmix) actually\u0000constitute glasses with low excess entropy DS. We predict that such glasses\u0000should have reduced relaxation ability. We also found that the excess enthalpy\u0000DH of glass linearly increases with its excess entropy DS, in line with a\u0000general thermodynamic estimate.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573623","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}
Venkat Venkatasubramanian, N Sanjeevrajan, Manasi Khandekar, Abhishek Sivaram, Collin Szczepanski
Despite the stunning progress recently in large-scale deep neural network applications, our understanding of their microstructure, 'energy' functions, and optimal design remains incomplete. Here, we present a new game-theoretic framework, called statistical teleodynamics, that reveals important insights into these key properties. The optimally robust design of such networks inherently involves computational benefit-cost trade-offs that are not adequately captured by physics-inspired models. These trade-offs occur as neurons and connections compete to increase their effective utilities under resource constraints during training. In a fully trained network, this results in a state of arbitrage equilibrium, where all neurons in a given layer have the same effective utility, and all connections to a given layer have the same effective utility. The equilibrium is characterized by the emergence of two lognormal distributions of connection weights and neuronal output as the universal microstructure of large deep neural networks. We call such a network the Jaynes Machine. Our theoretical predictions are shown to be supported by empirical data from seven large-scale deep neural networks. We also show that the Hopfield network and the Boltzmann Machine are the same special case of the Jaynes Machine.
{"title":"Arbitrage equilibrium and the emergence of universal microstructure in deep neural networks","authors":"Venkat Venkatasubramanian, N Sanjeevrajan, Manasi Khandekar, Abhishek Sivaram, Collin Szczepanski","doi":"arxiv-2405.10955","DOIUrl":"https://doi.org/arxiv-2405.10955","url":null,"abstract":"Despite the stunning progress recently in large-scale deep neural network\u0000applications, our understanding of their microstructure, 'energy' functions,\u0000and optimal design remains incomplete. Here, we present a new game-theoretic\u0000framework, called statistical teleodynamics, that reveals important insights\u0000into these key properties. The optimally robust design of such networks\u0000inherently involves computational benefit-cost trade-offs that are not\u0000adequately captured by physics-inspired models. These trade-offs occur as\u0000neurons and connections compete to increase their effective utilities under\u0000resource constraints during training. In a fully trained network, this results\u0000in a state of arbitrage equilibrium, where all neurons in a given layer have\u0000the same effective utility, and all connections to a given layer have the same\u0000effective utility. The equilibrium is characterized by the emergence of two\u0000lognormal distributions of connection weights and neuronal output as the\u0000universal microstructure of large deep neural networks. We call such a network\u0000the Jaynes Machine. Our theoretical predictions are shown to be supported by\u0000empirical data from seven large-scale deep neural networks. We also show that\u0000the Hopfield network and the Boltzmann Machine are the same special case of the\u0000Jaynes Machine.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150761","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}
We introduce a family of complex networks that interpolates between the Apollonian network and its binary version, recently introduced in [Phys. Rev. E textbf{107}, 024305 (2023)], via random removal of nodes. The dilution process allows the clustering coefficient to vary from $C=0.828$ to $C=0$ while maintaining the behavior of average path length and other relevant quantities as in the deterministic Apollonian network. Robustness against the random deletion of nodes is also reported on spectral quantities such as the ground-state localization degree and its energy gap to the first excited state. The loss of the $2pi / 3$ rotation symmetry as a tree-like network emerges is investigated in the light of the hub wavefunction amplitude. Our findings expose the interplay between the small-world property and other distinctive traits exhibited by Apollonian networks, as well as their resilience against random attacks.
{"title":"Random Apollonian networks with tailored clustering coefficient","authors":"Eduardo M. K. Souza, Guilherme M. A. Almeida","doi":"arxiv-2403.18615","DOIUrl":"https://doi.org/arxiv-2403.18615","url":null,"abstract":"We introduce a family of complex networks that interpolates between the\u0000Apollonian network and its binary version, recently introduced in [Phys. Rev. E\u0000textbf{107}, 024305 (2023)], via random removal of nodes. The dilution process\u0000allows the clustering coefficient to vary from $C=0.828$ to $C=0$ while\u0000maintaining the behavior of average path length and other relevant quantities\u0000as in the deterministic Apollonian network. Robustness against the random\u0000deletion of nodes is also reported on spectral quantities such as the\u0000ground-state localization degree and its energy gap to the first excited state.\u0000The loss of the $2pi / 3$ rotation symmetry as a tree-like network emerges is\u0000investigated in the light of the hub wavefunction amplitude. Our findings\u0000expose the interplay between the small-world property and other distinctive\u0000traits exhibited by Apollonian networks, as well as their resilience against\u0000random attacks.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315040","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}
Gui-Juan Liu, Jia-Ming Zhang, Shan-Zhong Li, Zhi Li
We investigate the properties of mobility edge in an Aubry-Andr'e-Harper model with non-reciprocal long-range hopping. The results reveal that there can be a new type of mobility edge featuring both strength-dependent and scale-free properties. By calculating the fractal dimension, we find that the positions of mobility edges are robust to the strength of non-reciprocal long-range hopping. Furthermore, through scale analysis of the observables such as fractal dimension, eigenenergy and eigenstate, etc., we prove that four different specific mobility edges can be observed in the system. This paper extends the family tree of mobility edges and hopefully it will shed more light on the related theory and experiment.
{"title":"Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model","authors":"Gui-Juan Liu, Jia-Ming Zhang, Shan-Zhong Li, Zhi Li","doi":"arxiv-2403.16739","DOIUrl":"https://doi.org/arxiv-2403.16739","url":null,"abstract":"We investigate the properties of mobility edge in an Aubry-Andr'e-Harper\u0000model with non-reciprocal long-range hopping. The results reveal that there can\u0000be a new type of mobility edge featuring both strength-dependent and scale-free\u0000properties. By calculating the fractal dimension, we find that the positions of\u0000mobility edges are robust to the strength of non-reciprocal long-range hopping.\u0000Furthermore, through scale analysis of the observables such as fractal\u0000dimension, eigenenergy and eigenstate, etc., we prove that four different\u0000specific mobility edges can be observed in the system. This paper extends the\u0000family tree of mobility edges and hopefully it will shed more light on the\u0000related theory and experiment.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300500","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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