Critical level statistics at the many-body localization transition region

Rao, Wen-Jia

doi:10.1088/1751-8121/abe0d5

Cited by 15 publications

(5 citation statements)

References 45 publications

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“…In an MBL system driven by random disorder such as Eq. ( 1), the distribution of t S near the transition region will deviate from a Gaussian function -a manifestation of Griffiths regime -which results in a peak of V S at the transition point [45][46][47] . Therefore, we can compute the evolution of V S to locate the transition.…”

Section: Revealing the Griffiths Regimementioning

confidence: 99%

Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition

Rao

2021

Preprint

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We employ singular value decomposition to study the eigenvalue spectrums of random spin systems. It's shown the singular values λ k of the sample matrix in the ergodic phase contain two branches that both follow power-law behavior but with different power exponents α. By analyzing the singular vectors, it is verified the higher part of λ k with k > kTh are universal that follows random matrix theory, where kTh estimates the Thouless energy. We further demonstrate that α corresponds only to the exponential part of the level spacing distribution while is insensitive to the level repulsion, or equivalently the system's symmetry. Consequently, the power exponent α gives an underestimation for the many-body localization transition point, which, however, reveals the Griffiths regime in a transparent way.

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Section: Revealing the Griffiths Regimementioning

confidence: 99%

Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition

Rao

2021

Preprint

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“…where R is given in table 2. Equation ( 23) yields the fidelity for O, U and S-RPE (equation ( 10), 14,18) for respective values of β. For very short time, average fidelity of β-RPE decays as ⟨R(t)⟩ ∼ 1 − βσ 2 t 2 .…”

Section: β-Rpementioning

confidence: 99%

“…Such dynamical signatures can be measured experimentally and can identify various quantum mechanical phases [10][11][12]. While the integrable and chaotic limits are well characterized, the evidence of intermediate statistics have generated considerable interest in the context of many-body localization transition [13][14][15][16][17]. This necessitates exploring dynamical signatures of random matrix ensembles beyond the WDE.…”

Section: Introductionmentioning

confidence: 99%

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

Das,

Ghosh

2023

J. Phys. A: Math. Theor.

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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.

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“…Besides the level statistics deep in the thermal/MBL phase, there are also significant amount of works on the spectral statistics right at the critical point, or even along the whole phase diagram [25][26][27][28][29][30][31][32] . Notably, the two-parameter β − h model, recently proposed in Ref.…”

Section: Introductionmentioning

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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Critical level statistics at the many-body localization transition region

Cited by 15 publications

References 45 publications

Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition

Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition

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

Random Matrix Model for Eigenvalue Statistics in Random Spin Systems

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