Quantum criticality in Ising chains with random hyperuniform couplings

Crowley, Philip J. D.; Laumann, Chris R.; Gopalakrishnan, Sarang

doi:10.1103/physrevb.100.134206

Cited by 18 publications

(10 citation statements)

References 81 publications

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“…For uncorrelated disorder, l FS ∼ δh −2 while l ∼ δh −1 , and thus ν = 2. As in the infinite-randomness case, hyperuniform correlations in the disorder can reduce the exponent controlling the divergence of l FS while leaving the exponent of l unchanged [79]. When the disorder is sufficiently hyperuniform that l is the most divergent length scale, the exponent is thus ν = 1.…”

Section: Discussionmentioning

confidence: 97%

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Avalanche induced coexisting localized and thermal regions in disordered chains

Crowley

Chandran

2020

Phys. Rev. Research

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We investigate the stability of an Anderson localized chain to the inclusion of a single finite interacting thermal seed. This system models the effects of rare low-disorder regions on many-body localized chains. Above a threshold value of the mean localization length, the seed causes runaway thermalization in which a finite fraction of the orbitals are absorbed into a thermal bubble. This "partially avalanched" regime provides a simple example of a delocalized, nonergodic dynamical phase. We derive the hierarchy of length scales necessary for typical samples to exhibit the avalanche instability, and show that the required seed size diverges at the avalanche threshold. We introduce a dimensionless statistic that measures the effective size of the thermal bubble, and use it to numerically confirm the predictions of avalanche theory in the Anderson chain at infinite temperature.

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Section: Discussionmentioning

confidence: 97%

“…The points (faded colors) are a random subsample of the data prior to window averaging [Eq. (79)]. Data are shown for chain lengths L = 3 .…”

Section: B Thermalization Of L-bits With Exponentially Weak Couplingmentioning

confidence: 99%

Avalanche induced coexisting localized and thermal regions in disordered chains

Crowley

Chandran

2020

Phys. Rev. Research

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“…For uncorrelated disorder, l FS ∼ δh −2 while l ∼ δh −1 , and thus ν = 2. As in the infinite randomness case, hyperuniform correlations in the disorder can reduces the exponent controlling the divergence of l FS while leaving the exponent of l unchanged [76]. When the disorder is sufficiently hyper-uniform that l is the most divergent length scale, the exponent is thus ν = 1.…”

Section: Discussionmentioning

confidence: 97%

Avalanche induced co-existing localised and thermal regions in disordered chains

Crowley,

Chandran

2019

Preprint

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We investigate the stability of an Anderson localised chain to the inclusion of a single finite interacting thermal seed. This system models the effects of rare low-disorder regions on many-body localised chains. Above a threshold value of the mean localisation length, the seed causes runaway thermalisation in which a finite fraction of the orbitals are absorbed into a thermal bubble. This 'partially avalanched' regime provides a simple example of a delocalised, non-ergodic dynamical phase. We derive the hierarchy of length scales necessary for typical samples to exhibit the avalanche stability, and show that the required seed size diverges at the avalanche threshold. We introduce a new dimensionless statistic that measures the effective size of the thermal bubble, and use it to numerically confirm the predictions of avalanche theory in the Anderson chain at infinite temperature.

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“…II B for exact mathematical definitions. Hyperuniformity is an emerging field, playing vital roles in a number of fundamental and applied contexts, including glass formation [19,20], jamming [21][22][23][24][25], rigidity [26,27], bandgap structures [28][29][30], biology [31,32], localization of waves and excitations [33][34][35], self-organization [36][37][38], fluid dynamics [39,40], quantum systems [41][42][43][44][45], random matrices [43,46,47] and pure mathematics [48][49][50][51][52]. Because disordered hyperuniform two-phase media are states of matter that lie between a crystal and a typical liquid, they can be endowed with novel properties [12,18,[53][54][55][56][57][58][59][60][61][62][63]…”

Section: Introductionmentioning

confidence: 99%

Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability

Wang,

Torquato

2021

Preprint

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Time-dependent interphase diffusion processes in multiphase heterogeneous media arise ubiquitously in physics, chemistry and biology. Examples of heterogeneous media include composites, geological media, gels, foams and cell aggregates. The recently developed concept of spreadability, S(t), provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales [Torquato, S., Phys. Rev. E., 104 054102 (2021)]. To investigate the capability of S(t) to probe microstructures of real heterogeneous media, we explicitly compute S(t) for well-known two-dimensional and three-dimensional idealized model structures that span across nonhyperuniform and hyperuniform classes. Among the former class, we study fully penetrable spheres and equilibrium hard spheres, and in the latter class, we examine sphere packings derived from "perfect glasses", uniformly randomized lattices (URL), disordered stealthy hyperuniform point processes and Bravais lattices. Hyperuniform media are characterized by an anomalous suppression of volume fraction fluctuations at large length scales compared to that of any nonhyperuniform medium. We further confirm that the small-, intermediate-and long-time behaviors of S(t) sensitively capture the small-, intermediate-and large-scale characteristics of the models. In instances in which the spectral density χV (k) has a power-law form B|k| α in the limit |k| → 0, the long-time spreadability provides a simple means to extract the value of the coefficients α and B that is robust against noise in χV (k) at small wavenumbers. For typical nonhyperuniform media, the intermediate-time spreadability is slower for models with larger values of the coefficient B = χV (0). Interestingly, the excess spreadability S(∞) − S(t) for URL packings has nearly exponential decay at small to intermediate t, but transforms to a power-law decay at large t, and the time for this transition has a logarithmic divergence in the limit of vanishing lattice perturbation. Our study of the aforementioned models enables us to devise an algorithm that efficiently and accurately extracts large-scale behaviors from diffusion data alone. Lessons learned from such analyses of our models are used to determine accurately the large-scale structural characteristics of a sample Fontainebleau sandstone, which we show is nonhyperuniform. Our study demonstrates the practical applicability of the diffusion spreadability to extract crucial microstructural information from real data across length scales and provides a basis for the inverse design of materials with desirable time-dependent diffusion properties.

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Quantum criticality in Ising chains with random hyperuniform couplings

Cited by 18 publications

References 81 publications

Avalanche induced coexisting localized and thermal regions in disordered chains

Avalanche induced coexisting localized and thermal regions in disordered chains

Avalanche induced co-existing localised and thermal regions in disordered chains

Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability

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