Statistical analysis of chiral structured ensembles: Role of matrix constraints

Mondal, Triparna; Shukla, Pragya

doi:10.1103/physreve.99.022124

Cited by 9 publications

(5 citation statements)

References 43 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: 59%

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: 59%

Non-ergodic extended states in $β$-ensemble

Das,

Ghosh

2021

Preprint

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“…It should be noted that |N − 2k| number of eigenvalues of such H k− are exactly 0 while the rest comes in ± pairs, a property known as chirality. Ensemble of H k− with normally distributed entries is known as the chiral orthogonal ensemble of topological order k (ChOE(k)) [20,28]. In deformed ensemble, H k− from ChOE(k) is added to a direct sum of two GOE blocks to tune the presence of a symmetry.…”

Section: Orthogonal Operatorsmentioning

confidence: 99%

Chaos due to symmetry-breaking in deformed Poisson ensemble

Das¹,

Ghosh²

2022

J. Stat. Mech.

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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.

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“…Rather in the L-ensemble formalism beginning with (2.1) the matrix elements L (M) (x, y) are a prescribed functional form. For works which do address random Toeplitz matrices, as a non-exhaustive list we draw attention to [35][36][37][38][39].…”

Section: Remark 22mentioning

confidence: 99%

Circulant L-ensembles in the thermodynamic limit

Forrester¹

2021

J. Phys. A: Math. Theor.

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L-ensembles are a class of determinantal point processes which can be viewed as a statistical mechanical systems in the grand canonical ensemble. Circulant L-ensembles are the subclass which are locally translationally invariant and furthermore subject to periodic boundary conditions. Existing theory can very simply be specialised to this setting, allowing for the derivation of formulas for the system pressure, and the correlation kernel, in the thermodynamic limit. For a one-dimensional domain, this is possible when the circulant matrix is both real symmetric, or complex Hermitian. The special case of the former having a Gaussian functional form for the entries is shown to correspond to free fermions at finite temperature, and be generalisable to higher dimensions. A special case of the latter is shown to be the statistical mechanical model introduced by Gaudin to interpolate between Poisson and unitary symmetry statistics in random matrix theory. It is shown in all cases that the compressibility sum rule for the two-point correlation is obeyed, and the small and large distance asymptotics of the latter are considered. Also, a conjecture relating the asymptotic form of the hole probability to the pressure is verified.

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Statistical analysis of chiral structured ensembles: Role of matrix constraints

Cited by 9 publications

References 43 publications

Non-ergodic extended states in $β$-ensemble

Non-ergodic extended states in $β$-ensemble

Chaos due to symmetry-breaking in deformed Poisson ensemble

Circulant L-ensembles in the thermodynamic limit

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