Extended states with Poisson spectral statistics

Mondal, Triparna; Sadhukhan, Suchetana; Shukla, Pragya

doi:10.1103/physreve.95.062102

Cited by 7 publications

(8 citation statements)

References 19 publications

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“…4). Thus our analysis shows that the eigenstate localization property is not necessarily indicative of the degree of repulsion present in the energy spectrum as also observed in certain structured matrix ensembles [65,66].…”

Section: Properties Of Energy Levelsmentioning

confidence: 57%

Non-ergodic extended states in $β$-ensemble

Das,

Ghosh

2021

Preprint

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Matrix models showing chaotic-integrable transition in the spectral statistics are important for understanding Many Body Localization (MBL) in physical systems. One such example is the βensemble, known for its structural simplicity. However, eigenvector properties of β-ensemble remain largely unexplored, despite energy level correlations being thoroughly studied. In this work we numerically study the eigenvector properties of β-ensemble and identify the ergodic transition point (γET = 0) and localization transition point (γAT = 1) where we express the repulsion parameter as β = N −γ . Thus other than Rosenzweig-Porter ensemble (RPE), β-ensemble is another example where Non-Ergodic Extended (NEE) states are observed over a finite interval of parameter values (0 < γ < 1). We find that the chaotic-integrable transition coincides with the ergodic transition unlike the RPE or the 1-D disordered spin-1/2 Heisenberg model where this coincidence occurs at the localization transition. As a result, the dynamical time-scales in the NEE regime of β-ensemble behave differently than the former models.

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Section: Properties Of Energy Levelsmentioning

confidence: 57%

Non-ergodic extended states in $β$-ensemble

Das,

Ghosh

2021

Preprint

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“…. But, as discussed in [24] for the case of chiral circulant matrices, Poisson spectral statistics appears along with delocalized eigenfunctions. This indicates the influence of constraints on the relation between eigenvalue and eigenfunction statistics which is further confirmed by the present study of other four cases.…”

Section: Numerical Analysismentioning

confidence: 95%

“…Herafter this case will be referred as the column-constraint chiral matrix with circulant off diagonal blocks. The spectral properties of this case was considered in detail in [24] and is included here for comparison with other cases. As discussed in [24], all eigenvectors of H Case 2: Toeplitz matrix: Next we consider C as a N × N toeplitz matrix with real elements [27], defined as…”

Section: Hermitian Matrices With Chirality and Other Constraintsmentioning

confidence: 99%

“…The spectral properties of this case was considered in detail in [24] and is included here for comparison with other cases. As discussed in [24], all eigenvectors of H (i.e O n , n = 1, . .…”

Section: Hermitian Matrices With Chirality and Other Constraintsmentioning

confidence: 99%

“…Similarly the fully localized case shows a behavior typical of a set of uncorrelated random levels, that is, exponential decay for P (s), also referred as Poisson distribution, P (s) = e −s , and Σ 2 (r) = r[1][2][3]. But, as discussed in[24] for the case of chiral circulant matrices, Poisson spectral statistics appears along with delocalized eigenfunctions. This indicates the influence of constraints on the relation between eigenvalue and eigenfunction statistics which is further confirmed by the present study of other four cases.…”

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confidence: 99%

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Statistical analysis of chiral structured ensembles: Role of matrix constraints

Mondal

Shukla

2019

Phys. Rev. E

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We numerically analyze the statistical properties of complex system with conditions subjecting the matrix elements to a set of specific constraints besides symmetry, resulting in various structures in their matrix representation. Our results reveal an important trend: while the spectral statistics is strongly sensitive to the number of independent matrix elements, the eigenfunction statistics seems to be affected only by their relative strengths. This is contrary to previously held belief of one to one relation between the statistics of the eigenfunctions and eigenvalues (e.g. associating Poisson statistics to the localized eigenfunctions and Wigner-Dyson statistics to delocalized ones).

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Spectral and strength statistics of chiral Brownian ensemble

Shukla¹

2021

J. Phys. A: Math. Theor.

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Multi-parametric chiral random matrix ensembles are important tools to analyze the statistical behavior of generic complex systems with chiral symmetry. A recent study (Mondal and Shukla 2020 Phys. Rev. E 102 032131) of the former maps them to the chiral Brownian ensemble (Ch-BE) that appears as a non-equilibrium state of a single parametric crossover between two stationary chiral Hermitian ensembles. This motivates us to pursue a detailed statistical investigation of the spectral and strength fluctuations of the Ch-BE, with a focus on their behavior near zero energy region. The information can then be used for a wide range of complex systems with chiral symmetry. Our analysis also reveals connections of Ch-BE to generalized Calogero Sutherland Hamiltonian (CSH) and Wishart ensembles. This along with already known connections of complex systems without chirality to CSH strongly hints the later to be the ‘backbone’ Hamiltonian governing the spectral dynamics of complex systems.

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Extended states with Poisson spectral statistics

Cited by 7 publications

References 19 publications

Non-ergodic extended states in $β$-ensemble

Non-ergodic extended states in $β$-ensemble

Statistical analysis of chiral structured ensembles: Role of matrix constraints

Spectral and strength statistics of chiral Brownian ensemble

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