Statistical diagonalization of a random biased Hamiltonian: the case of the eigenvectors

Ithier, G.; Ascroft, Saeed

doi:10.1088/1751-8121/aae800

Cited by 6 publications

(4 citation statements)

References 88 publications

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“…We remark that this result also comprises, as special cases, the previous findings from Refs. [35,68], which were obtained by means of completely different approximations and under quite substantial additional restrictions. Yet another, and in fact more general, such approach will be elaborated in the subsequent Sec.…”

Section: Consequently We Obtainmentioning

confidence: 99%

“…By means of yet another approach, based on a Lippman-Schwinger-type equation, Ithier and Ascroft evaluated special cases of the eigenvector overlap moments in Deutsch's random matrix ensemble up to fourth order [24], which are needed in the last two factors in (92) when evaluating the ensemble average of that equation.…”

Section: Connections To Pertinent Previous Workmentioning

confidence: 99%

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Typical relaxation of perturbed quantum many-body systems

Dabelow¹,

Reimann²

2021

J. Stat. Mech.

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We substantially extend our relaxation theory for perturbed many-body quantum systems from ((2020) Phys. Rev. Lett. 124 120602) by establishing an analytical prediction for the time-dependent observable expectation values which depends on only two characteristic parameters of the perturbation operator: its overall strength and its range or band width. Compared to the previous theory, a significantly larger range of perturbation strengths is covered. The results are obtained within a typicality framework by solving the pertinent random matrix problem exactly for a certain class of banded perturbations and by demonstrating the (approximative) universality of these solutions, which allows us to adopt them to considerably more general classes of perturbations. We also verify the prediction by comparison with several numerical examples.

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Section: Consequently We Obtainmentioning

confidence: 99%

Section: Connections To Pertinent Previous Workmentioning

confidence: 99%

Typical relaxation of perturbed quantum many-body systems

Dabelow¹,

Reimann²

2021

J. Stat. Mech.

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“…This will be investigated in a further publication. In addition, in the case of a random interaction like the Gaussian Unitary or Gaussian Orthogonal ensembles, the calculation of the MBDoS with interactions can be done from the non interacting MBDoS, by considering the subordination property between their Stieltjes transforms [11,39]: m H0+W (z) = m H0 (z + σ 2 w m H (z)), with m H (z) = Tr((H − z) −1 )) where σ 2 w m H (z) can be considered as a many body self energy.…”

Section: Generalizationmentioning

confidence: 99%

Many body density of states of a system of non interacting spinless fermions

2023

Self Cite

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The modeling of out-of-equilibrium many-body quantum systems requires to go beyond low-energy physicsand single or few bodies densities of states. Many-body localization, presence or lack of thermalizationand quantum chaos are examples of phenomena in which states at different energy scales, including highly excitedones, contribute to dynamics and therefore affect the system's properties. Quantifying these contributions requiresthe Many-Body Density of States (MBDoS), a function whose calculation becomes challenging even for non-interactingidentical particles due to the difficulty to enumerate accessible states while enforcing the exchangesymmetry. In the present work, we introduce a new approach to evaluate the MBDoS in the general case of non-interacting systems of identical quantum particles. The starting point of our method is the principal component analysis of a filling matrix $F$ describinghow $N$ particles can be distributed into $L$ single-particle energy levels. We show thatthe many body spectrum can be expanded as a weighted sum of singular vectors of the filling matrix.The weighting coefficients only involve renormalized energies obtained from the single body spectrum.We illustrate our method in two classes of problems that are mapped into spinless fermions:(i) non-interacting electrons in a homogeneous tight-binding model in 1D and 2D,and (ii) interacting spins in a chain under a transverse field.

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“…Important open questions remain surrounding relaxation time-scales and the route to equilibrium of complex quantum systems [20][21][22][23][24][25][26][27][28], as well as the emergence of thermodynamical laws [29][30][31][32]. A useful approach to the description of generic non-integrable quantum systems can be developed from quantum chaos [33,34] and the eigenstate thermalization hypothesis (ETH), which in turn can be derived from an underlying random matrix theory (RMT) [24,35], based on Deutsch's model [25,[36][37][38] for non-integrable systems.…”

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confidence: 99%

Taking snapshots of a quantum thermalization process: Emergent classicality in quantum jump trajectories

Nation

Porras

2020

Phys. Rev. E

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We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to nonintegrable quantum systems that the set of outcomes of the measurement of a macroscopic observable evolve in time like stochastic variables, whose variance satisfies the celebrated Einstein relation for Brownian diffusion. Our results show how to extend the framework of eigenstate thermalization to the prediction of properties of quantum measurements on an otherwise closed quantum system. We show numerically the validity of the random matrix approach in quantum chain models.

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Statistical diagonalization of a random biased Hamiltonian: the case of the eigenvectors

Cited by 6 publications

References 88 publications

Typical relaxation of perturbed quantum many-body systems

Typical relaxation of perturbed quantum many-body systems

Many body density of states of a system of non interacting spinless fermions

Taking snapshots of a quantum thermalization process: Emergent classicality in quantum jump trajectories

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