An insulated state in a non-interacting system arising from the destructive interference among multiple-scattering paths in a condensed matter system.
Questions tagged [anderson-localization]
47 questions
28
votes
1 answer
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?
What is the relation between Anderson localization…
hehuan0430
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16
votes
3 answers
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 there that introduce Anderson localization?…
a06e
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13
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2 answers
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 are localized or extended.
But in the paper by the…
kaiser
- 1,227
12
votes
2 answers
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 explanations, e.g. 50 years of Anderson localization on…
a06e
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6
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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 disorder strength. Taking the normalization of $T$ so…
PPR
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6
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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 Anderson localization.
I wonder if there's an analog…
liwt31
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5
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1 answer
Experimental detection of Anderson localization of light in 3D vs 2D
I have a question about the experimental realization of Anderson localization of light. I am a theorist, and have not worked much in optics, so please bear with me.
Anderson localization of light in 3D has a turbulent history. Notable experimental…
MOOSE
- 537
5
votes
3 answers
Phase transitions 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 really include such phenomena as Anderson localization…
Roger V.
- 68,984
5
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1 answer
What is known about the density of states of the Anderson model?
This question was posted a week ago on MathOverflow https://mathoverflow.net/q/369156/
The Anderson Model is given by the random Hamiltonian (as an operator on $l^2(\mathbb{Z}^d)$)
$$
H_\omega = - \Delta + V(\omega)
$$
where $V(\omega) \mid x…
5
votes
1 answer
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 evolution will it be efficient? Or it will not work…
Sayandip Dhara
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5
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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 account of guaranteed identity of phases accumulated…
symanzik138
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4
votes
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Diagrammatic Calculation of Anderson localization
I'm current following Piers Coleman's Many-Body Physics to understand the diagrammatic method for Anderson localization (weak localization)
The diagrams are as follows.
where the dashed line is the impurity scattering $n_i |u(\mathbf{p} -…
Jason Chen
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4
votes
1 answer
Weak localization, strong localization, and localization without a metal-insulator transition
As I begin to read literature on Anderson localization by disorder, authors are distinguishing between cases that are unfamiliar to me, namely weak localization, strong localization, and localization without a metal-insulator transition.
Can anyone…
BGreen
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4
votes
1 answer
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 even vanish, one still has mobility gap between…
Peter Wildemann
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4
votes
1 answer
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 not find an (even approximate) formula for the…
Hagadol
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