Scaling of the reduced energy spectrum of random matrix ensemble

Rao, Wen-Jia; Chen, M. N.

doi:10.1140/epjp/s13360-020-01067-3

Cited by 7 publications

(3 citation statements)

References 43 publications

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“…Formally, a r-th order reduced energy spectrum E (r) i is comprised of every (r + 1)-th level of the original spectrum {E i }, which is mathematically achieved by tracing out every r levels in between. This construction is very similar to that of the reduced density matrix where we trace out the degrees of freedom in a subsystem, hence we suggest to call E (r) i the "reduced energy spectrum" 41 . It is proved in Ref.…”

Section: Model and Methodsmentioning

confidence: 92%

Critical Level Statistics at the Many-Body Localization Transition Region

Rao

2021

Preprint

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We study the critical level statistics at the many-body localization (MBL) transition region in random spin systems. By employing the inter-sample randomness as indicator, we manage to locate the MBL transition point in both orthogonal and unitary models. We further count the n-th order gap ratio distributions at the transition region up to n = 4, and find they fit well with the short-range plasma model (SRPM) with inverse temperature β = 1 for orthogonal model and β = 2 for unitary. These critical level statistics are argued to be universal by comparing results from systems both with and without total Sz conservation. We also point out that these critical distributions can emerge from the spectrum of a Poisson ensemble, which indicates the thermal-MBL transition point is more affected by the MBL phase rather than thermal phase.

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Section: Model and Methodsmentioning

confidence: 92%

Critical Level Statistics at the Many-Body Localization Transition Region

Rao

2021

Preprint

Self Cite

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“…Formally, an rth order reduced energy spectrum E (r) i is comprised of every (r + 1)-th level of the original spectrum {E i }, which is mathematically achieved by tracing out every r levels in between. This construction is very similar to that of the reduced density matrix where we trace out the degrees of freedom in a subsystem, hence we suggest to call E (r) i the 'reduced energy spectrum' [41]. It is proved in reference [43] that the energy spectrum of SRPM with k = 1 and inverse temperature β has the same structure as the β-th order reduced energy spectrum of a Poisson ensemble (which is named 'Daisy model' by the authors).…”

Section: Model and Methodsmentioning

confidence: 94%

Critical level statistics at the many-body localization transition region

Rao

2021

J. Phys. A: Math. Theor.

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We study the critical level statistics at the many-body localization (MBL) transition region in random spin systems. By employing the inter-sample randomness as indicator, we manage to locate the MBL transition point in both orthogonal and unitary models. We further count the nth order gap ratio distributions at the transition region up to n = 4, and find they fit well with the short-range plasma model with inverse temperature β = 1 for orthogonal model and β = 2 for unitary. These critical level statistics are argued to be universal by comparing results from systems both with and without total S z conservation. We also point out that these critical distributions can emerge from the spectrum of a Poisson ensemble, which indicates the thermal-MBL transition point is more affected by the MBL phase rather than thermal phase.

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“…where the diagonals x i follow the normal distribution N (0, 2) and y k (k = 1, 2, ..., N −1) follows the χ distribution with parameter (N − k) β. For the β ensemble, analytical and strong numerical evidences support P r (n) to have the following compact form [36][37][38][39] P β, r…”

Section: Random Matrix Modelsmentioning

confidence: 99%

Random Matrix Model for Eigenvalue Statistics in Random Spin Systems

Rao

2021

Preprint

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We numerically study the eigenvalue statistics along the thermal to many-body localization (MBL) transition in random spin systems, and compare them to two random matrix (RM) models, namely the mixed ensemble and Gaussian β ensemble. We show both RM models are capable of capturing the lowest-order level correlations during the transition, while the deviations become non-negligible when fitting higher-order ones. Specifically, the mixed ensemble will underestimate the longer-range level correlations, while the opposite is true for β ensemble. Strikingly, a simple average of these two models gives nearly perfect description of the eigenvalue statistics at all disorder strengths, even around the critical region, which indicates the interaction range and strength between eigenvalue levels are responsible for the phase transition.

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Scaling of the reduced energy spectrum of random matrix ensemble

Cited by 7 publications

References 43 publications

Critical Level Statistics at the Many-Body Localization Transition Region

Critical Level Statistics at the Many-Body Localization Transition Region

Critical level statistics at the many-body localization transition region

Random Matrix Model for Eigenvalue Statistics in Random Spin Systems

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