Questions tagged [anderson-localization]

An insulated state in a non-interacting system arising from the destructive interference among multiple-scattering paths in a condensed matter system.

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Scale invariance beyond the critical point

Using Anderson localization as an example, I understand how scale invariance comes into play at a critical point - at a critical point, the localization length $\xi$ (the average "radius" of ...
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How to understand averages in Anderson localizaition

Consider the lattice $\hat{H}=\sum_{i}\epsilon_{i}\hat{a}^{\dagger}_{i}\hat{a}_{i}+V_{i+1,i}\hat{a}^{\dagger}_{i+1}\hat{a}_{i}$. The disorder is for on-site energy $\epsilon_{i}$. In this brief ...
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Phase transition vs. critical phenomena

Just trying to get some clarity in terminology: is phase transitions synonymous with critical phenomena? At the first glance they mean the same thing, but I am not sure whether phase transitions ...
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What is the meaning or definition of 'correlation length' in the context of Anderson localization?

I was reading a paper that talks about Anderson localization. It mentions the quantity called 'correlation length' or 'localization length' but no formal definition is given as to what it actually ...
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Proof that the self-energy is an inverse lifetime

My question concerns the self-energy of a diagonal propagator for a single-particle lattice problem. The context is Anderson Localisation, but really it's a problem of complex analysis. I would like ...
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Does Anderson localisation occur if the potential are equal in pairs?

Consider the Anderson model given by the Hamiltonian $H \in B(l^2( \mathbb{Z}^d)) $ defined by $H = - \Delta + V$ where the potential $V$ acts on a unit vector $ \mid {x} \rangle  \in l^2( \mathbb{Z}^...
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What is the meaning of Thouless energy?

Wikipedia article says "a measure of the sensitivity of energy levels to a change in the boundary conditions of the system", which I don't really understand. Thouless energy is defined as $$...
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Divergences in resolvent expansion of Anderson hamiltonian

I'm reading these lecture notes on Anderson localization, and I cannot understand how the resonant regions contribute to the divergence of the resolvent expansion (sections 3.1 and 3.2). The relevant ...
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A quadratic Hamiltonian is a model of independent particles - why?

I'm reading some notes on the Anderson Hamiltonian: $$ H=\sum h_i c_i^\dagger c_i -q\sum_{\langle i,j\rangle}(c_i^\dagger c_j+c_j^\dagger c_i)$$ Where the $c_i/c_i^\dagger$ are fermionic annihilation/...
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What are the prerequistes for system to exhibit Anderson Localisation(AL)?

The existence of a localized phase in a disordered system tells us that system starting in a given initial superposition of energy eigen states continues to remain in that state in long time limit. ...
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Complete localization in 2D

The two-dimensional Anderson model is the model $$ H = T + \lambda V_\omega $$ where $T$ is nearest-neighbor hopping on $\mathbb{Z}^2$ and $V_\omega$ is a random potential. $\lambda > 0$ is the ...
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What is known about the density of states of the Anderson model?

This question was posted a week ago on MathOverflow without an answer: https://mathoverflow.net/questions/369156/what-is-known-about-the-density-of-states-for-the-anderson-model The Anderson Model is ...
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Small time solution to Fokker-Planck equation

In reference to this note, a specific Focker-Planck equation with initial condition $W(\rho, t=0)=\delta(\rho-1)$ have the solution $$W\left(\rho,t\right)=\dfrac{e^{-\frac{t}{4}}}{\sqrt{\pi}t^{\frac{3}...
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Analog of Anderson localization caused by random hopping

Consider the tight-binding Hamiltonian: $$ H = \sum_i \epsilon_i a^\dagger_i a_i + \sum_i V_i (a^\dagger_i a_{i+1} + a^\dagger_{i+1} a_i) $$ Random on-site energy $\epsilon_i$ leads to the famous ...
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When I will see the weak localization effect?

I understand the origin of weak localization (WL) effect but I have a doubt that when I will see the WL effect, assuming that I am at low temperature and I have quasi 2D sample.
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How to apply Wick's theorem in Anderson model

I'm trying to solve the non-interacting single impurity Anderson model where we consider free electrons in a conduction band: $$H_{cond} =\sum_k \varepsilon_k c_k^\dagger c_k$$ and an impurity with ...
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The notion of "Mobility Gaps" in the context of Anderson Localization

In the context of Anderson Localization, I heard statements such as the following: "Due to disorder, there is a broadening of the bands. Although spectral gaps between continuous bands may shrink or ...
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Heat transfer between a common material and a non-thermalizable one?

I've read that some systems cannot reach equilibrium (page 15 of the book Selected Scientific Papers of Sir Rudolf Peierls: With Commentary or R. Peierls, “Zur kinetischen Theorie der Wärmeleitung in ...
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Oscillatory part of Anderson localized wavefunction

In the context of Anderson localization, wavefunctions are localized on a scale of the localization length $\zeta$: $$ |\psi(r)| = A\; exp(-|r|/\zeta) $$ What is the oscillatory part of this ...
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What tools from quantum information can we use to detect the ergodic to many body localization phase trasnsition?

So is there any specific quantity which depends on the density matrix of the excited eigenstates can detect the ergodic to MBL phase transition? Can anything other than half chain entanglement entropy ...
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Can I use time evolving block decimation (TEBD) to simulate the dynamics for many body localized systems?

In the many-body localized phase, the system is described by quasi-local integrals of motion ("l-bits"). The entanglement does grow logarithmically with time. So if I use TEBD to get the real-time ...
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What is motivation behind understanding many body localization?

I'm reading about many body localization which consider both interaction and disorder. But I don't know why this topic has gained so much attention? What is harder part of this localization that makes ...
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How to generate random potential in tight binding model?

Tight binding model exhibit Anderson localization. In Anderson localization there is no interaction b/w particles. But in order to generate random potential in tight binding model if we switch on time ...
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How is Anderson Localization a quantum-mechanical phenomenon? How to compare it with classical case? [duplicate]

I was reading book of 50 Years of Anderson localization, which mentions that it highlights wave particle duality. What does it mean? About this localization I have also read that we can understand it ...
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What is the broken symmetry in a phase transition into Anderson localisation?

Anderson localisation is a state of matter where there is no diffusion of particles because of randonmness in the potential landscape. The wavefunction is localised, i.e. exponentially dropping to ...
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What is the relationship between the integrability of a quantum many-body system and thermalization?

If a quantum many-body system is integrable, does it imply the system would always thermalized or many-body localized?
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Difference between Anderson localization and weak localization

I have read that weak localization is a precursor to Anderson localization. Weak localization happens due to the constructive interference between paths that loop around in opposite direction, on ...
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Single-electron propagator in disordered media: higher moments?

The known result that the impurity-averaged single electron propagator takes the form $ \langle G_0(r) \rangle \sim e^{-|r|/\ell} $, for $\ell$ the mean free path is frequently quoted by papers on ...
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Localization length in Anderson localized systems

In Anderson localized systems, a great portion of the system's properties are governed by the localization length. These phenomena are well understood and have been studied for ages. However, I could ...
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Inuitive analogy for localization?

I'm looking for a plain English analogy for electron/wave localization. And in particular weak localization and Anderson/strong localization. Is it possible to describe these phenomena in simple terms ...
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Is interaction a relevant perturbation for 1d Anderson localization of fermions?

Disorder is a relevant perturbation in 1d, which drives the system to Anderson localization. My question is if I am already at the Anderson localization fixed point, how to analyze the scaling ...
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scaling theory of Anderson localization

Initially, Anderson studied the eigenstates of the tight-binding Hamiltonian $$ H = \sum_n \epsilon_n a_n^\dagger a_n + V \sum_{m,n} a_m^\dagger a_n . $$ His question was whether the eigenstates ...
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How to derive Eq.(1) in Prof. A Leggett's lecture note?

I came across a lecture note on weak localisation by Prof. A. J. Leggett. In this note, he wrote down his first equation as follows: $$\sigma = \lim_{\omega\rightarrow 0} \lim_{q\rightarrow 0} \frac{1}...
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What is many body localization?

Is there any good definition of many body localization? It is the property of one state or it is the property of a Hamiltonian? Why does disorder play an important role in many body localization? ...
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What is Anderson localization? Could someone give an example worked out in detail?

What is Anderson localization, for someone with no previous knowledge on the subject? I tried to read Anderson's original paper, but it was too terse for me. I have seen a couple of intuitive ...
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Introduction to Anderson localization

I find Anderson's original paper too terse. I am looking for something that introduces me gently to the subject so that I can understand Anderson's paper and other literature. What references are out ...