Nonergodic extended states in the 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math>
 ensemble

Das, Adway Kumar; Ghosh, Anandamohan

doi:10.1103/physreve.105.054121

Cited by 16 publications

(7 citation statements)

References 95 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, a convenient matrix representation of β-ensemble can be found at the cost of canonical invariance, where the relevant ensemble consists of random real symmetric tridiagonal matrices [63]. Such a matrix model hosts three distinct phases separated by two 2nd order critical points [80,81]. We can further generalize β-ensemble if we let the relative strength of diagonal and off-diagonal elements to vary.…”

Section: β-Rpementioning

confidence: 99%

“…The crossover curves get steeper with N and tend to intersect each other around γ = 2. Using the 2nd order phase transition ansatz [80], we are able to collapse the s 2 data from all system sizes, as shown in the respective insets. Therefore, short-range energy correlations for RPE from all the three symmetry classes show a 2nd order phase transition at γ = 2, which was previously established using ratio of level spacing [37].…”

Section: Rpe For Large Nmentioning

confidence: 99%

“…In (d), (e) and (f), the 2nd moment of NNS is shown for varying N. In (g), (h) and (i), we show the time evolution of the fidelity of N 4 δ-localized states with energy closest to 0 for various γ and N = 4096. Dashed lines denote the equilibrium values and markers denote the Thouless and relaxation times.In (j), (k) and (l), κ, the relative depth of the correlation hole is shown for varying N. The insets of (d), (e), (f), (j), (k) and (l) show the collapsed data using 2nd order phase transition ansatz, γ ′ = (γ − 2)(log N) 1 ν[80]. The estimated critical exponent ν ≈ 1.2025, 0.988, 0.9765 for ⟨ s 2 ⟩ and ν ≈ 1.0102, 1.0745, 1.1414 for κ from the three symmetry classes, respectively.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Dynamical signatures of Chaos to integrability crossover in 2×2 generalized random matrix ensembles

Das,

Ghosh

2023

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

We introduce a two-parameter ensemble of generalized 2 × 2 real symmetric random matrices called the β-Rosenzweig–Porter ensemble (β-RPE), parameterized by β, a fictitious inverse temperature of the analogous Coulomb gas model, and γ, controlling the relative strength of disorder. β-RPE encompasses RPE from all of the Dyson’s threefold symmetry classes: orthogonal, unitary and symplectic for β = 1 , 2 , 4 . Firstly, we study the energy correlations by calculating the density and 2nd moment of the nearest neighbor spacing (NNS) and robustly quantify the crossover among various degrees of level repulsions. Secondly, the dynamical properties are determined from an exact calculation of the temporal evolution of the fidelity enabling an identification of the characteristic Thouless and the equilibration timescales. The relative depth of the correlation hole in the average fidelity serves as a dynamical signature of the crossover from chaos to integrability and enables us to construct the phase diagram of β-RPE in the γ-β plane. Our results are in qualitative agreement with numerically computed fidelity for N ≫ 2 matrix ensembles. Furthermore, we observe that for large N the 2nd moment of NNS and the relative depth of the correlation hole exhibit a second order phase transition at γ = 2.

show abstract

Section: β-Rpementioning

confidence: 99%

Section: Rpe For Large Nmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Dynamical signatures of Chaos to integrability crossover in 2×2 generalized random matrix ensembles

Das,

Ghosh

2023

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Thus we have obtained the Hamiltonians, H(k, λ) such that S(k, λ) is maximum subjected to the constraints in (10). Moreover (13) implies that such Hamiltonians can be expressed as,…”

Section: J Stat Mech (2022) 063101mentioning

confidence: 99%

“…In many physical systems, the spectral property of the governing Hamiltonian is intermediate between completely integrable and chaotic [8][9][10], a behavior demonstrated in many phenomenological models as well [11][12][13][14]. Often in such matrix models, it is possible to control the extent of integrability by varying the coupling strength as in Rosenzweig-Porter ensemble (RPE) [15,16] or the range of coupling as in power law banded random matrix [12] or introducing inhomogeneous coupling as in β-ensemble [13].…”

Section: Introductionmentioning

confidence: 99%

Chaos due to symmetry-breaking in deformed Poisson ensemble

Das¹,

Ghosh²

2022

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

The competition between strength and correlation of coupling terms in a Hamiltonian defines numerous phenomenological models exhibiting spectral properties interpolating between those of Poisson (integrable) and Wigner–Dyson (chaotic) ensembles. It is important to understand how the off-diagonal terms of a Hamiltonian evolve as one or more symmetries of an integrable system are explicitly broken. We introduce a deformed Poisson ensemble to demonstrate an exact mapping of the coupling terms to the underlying symmetries of a Hamiltonian. From the maximum entropy principle we predict a chaotic limit which is numerically verified from the spectral properties and the survival probability calculations.

show abstract

KPZ scaling from the Krylov space

Gorsky,

Nechaev,

Valov

2024

J. High Energ. Phys.

View full text Add to dashboard Cite

Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems, such as Heisenberg spin chains, has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis. We focus on the Heisenberg time scale, which approximately corresponds to the ramp–plateau transition for the Krylov complexity in systems with a large but finite number degrees of freedom. Two frameworks are under consideration: i) the system with growing Lanczos coefficients and an artificial cut-off, and ii) the system with the finite Hilbert space. In both cases via numerical analysis, we observe the transition from Gaussian to KPZ-like scaling, or equivalently, the diffusion-superdiffusion transition at the critical Euclidean time $$ {t}_E^{\ast } $$ t E ∗ = ccrK, for the Krylov chain of finite length K, and ccr = O(1). In particular, we find a scaling ~ K1/3 for fluctuations in the one-point correlation function and a dynamical scaling ~ K−2/3 associated with the return probability (Loschmidt echo) corresponding to autocorrelators in physical space. In the first case, the transition is of the 3rd order and can be considered as an example of dynamical quantum phase transition (DQPT), while in the second, it is a crossover. For case ii), utilizing the relationship between the spectrum of tridiagonal matrices at the spectral edge and the spectrum of the stochastic Airy operator, we demonstrate analytically the origin of the KPZ scaling for the particular Krylov chain using the results of the probability theory. We argue that there is interesting outcome of our study for the double scaling limit of matrix models. For the case of topological gravity, the white noise term of order O (1/N) is identified, which should be taken into account in the controversial issue of ensemble averaging in 2D/1D holography.

show abstract

Nonergodic extended states in the β ensemble

Cited by 16 publications

References 95 publications

Dynamical signatures of Chaos to integrability crossover in 2×2 generalized random matrix ensembles

Dynamical signatures of Chaos to integrability crossover in 2×2 generalized random matrix ensembles

Chaos due to symmetry-breaking in deformed Poisson ensemble

KPZ scaling from the Krylov space

Contact Info

Product

Resources

About