Spectral properties of three-dimensional Anderson model

Šuntajs, Jan; Prosen, Tomaž; Vidmar, Lev

doi:10.1016/j.aop.2021.168469

Cited by 41 publications

(32 citation statements)

References 62 publications

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“…One may argue that τ max quantitatively resembles the scaling of the Thouless time t Th obtained from the spectral form factor [26]. Intriguingly, the criterion t Th ≈ t H provides an accurate tool to pinpoint the Anderson localization tran- sition in three dimensions studied by the spectral form factor [35,81]. Despite this similarity, we note that τ max was introduced as a fitting parameter of the phenomenological model in Eqs.…”

Section: B Fitting Results For Disorder Averagesmentioning

confidence: 84%

Phenomenology of spectral functions in disordered spin chains at infinite temperature

Vidmar,

Krajewski,

Bonca

et al. 2021

Preprint

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Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a manybody localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here we introduce a phenomenological theory that may explain some of those features. We develop a theory based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. In particular, we argue that the proximity to the local integrals of motion of the Anderson insulator substantially impacts the dynamical properties in finite interacting systems. Taking the spin imbalance as an exemplary observable, we show that our theory quantitatively describes its integrated spectral function for a wide range of disorders.

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Section: B Fitting Results For Disorder Averagesmentioning

confidence: 84%

Phenomenology of spectral functions in disordered spin chains at infinite temperature

Vidmar,

Krajewski,

Bonca

et al. 2021

Preprint

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“…The 3D Anderson model exhibits a delocalization-localization transition at the critical disorder W c ≈ 16.5 (see, e.g., Refs. [161][162][163][164] for reviews). Our focus here is on disorder strengths well below this transition, W W c .…”

Section: B Quantum-chaotic Quadratic Modelmentioning

confidence: 99%

Volume-law entanglement entropy of typical pure quantum states

Bianchi,

Hackl,

Kieburg

et al. 2021

Preprint

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We introduce and discuss known results for the volume-law entanglement entropy of typical pure quantum states in which the number of particles is not fixed and derive results for the volumelaw entanglement entropy of typical pure quantum states with a fixed number of particles. For definiteness, we consider lattice systems of fermions in an arbitrary dimension and present results for averages over all states as well as over the subset of all Gaussian states. For quantum states in which the number of particles is not fixed, the results for the average over all states are well known since the work of Page, who found that in the thermodynamic limit the leading term follows a volume law and is maximal. The associated variance vanishes exponentially fast with increasing system size, i.e., the average is also the typical entanglement entropy. The corresponding results for Gaussian states are more recent. The leading term is still a volume law, but it is not maximal and depends on the ratio between the volumes of the subsystem and the entire system. Moreover, the variance is independent of the system size, i.e., the average also gives the typical entanglement entropy. We prove that while fixing the number of particles in pure quantum states does not qualitatively change the behavior of the leading volume-law term in the average entanglement entropy, it can fundamentally change the nature of the subleading terms. In particular, subleading corrections appear that depend on the square root of the volume. We unveil the origin of those corrections. Finally, we discuss the connection between the entanglement entropy of typical pure states and recent analytical results obtained in the context of random matrix theory, as well as numerical results obtained for physical Hamiltonians.

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“…We stress that we refer to Hamiltonians of interacting systems of which the many-body spectrum exhibits quantum chaos as quantum-chaotic interacting Hamiltonians, and to quadratic Hamiltonians for which the single-particle spectrum exhibits quantum chaos as quantum-chaotic quadratic Hamiltonians [60]. Examples of quantum-chaotic quadratic models in a lattice include the three-dimensional Anderson model below the localization transition [61][62][63][64][65][66] and the quadratic SYK2 model [60,67,68]. For the latter, the agreement with the RMT predictions is guaranteed by construction.…”

Section: Introductionmentioning

confidence: 99%

Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians

Łydżba,

Zhang,

Rigol

et al. 2021

Preprint

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We study the matrix elements of local and nonlocal operators in the single-particle eigenstates of two paradigmatic quantum-chaotic quadratic Hamiltonians; the quadratic Sachdev-Ye-Kitaev (SYK2) model and the three-dimensional Anderson model below the localization transition. We show that they display eigenstate thermalization for normalized observables. Specifically, we show that the diagonal matrix elements exhibit vanishing eigenstate-to-eigenstate fluctuations, and a variance proportional to the inverse Hilbert space dimension. We also demonstrate that the ratio between the variance of the diagonal and the off-diagonal matrix elements is 2, as predicted by the random matrix theory. We study distributions of matrix elements of observables and establish that they need not be Gaussian. We identify the class of observables for which the distributions are Gaussian.

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Spectral properties of three-dimensional Anderson model

Cited by 41 publications

References 62 publications

Phenomenology of spectral functions in disordered spin chains at infinite temperature

Phenomenology of spectral functions in disordered spin chains at infinite temperature

Volume-law entanglement entropy of typical pure quantum states

Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians

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