Thermalization of dilute impurities in one dimensional spin chains

Anatoli Polkovnikov; Dries Sels

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Thermalization of dilute impurities in one dimensional spin chains

Dries Sels, Anatoli Polkovnikov

Quantum Physics · Submitted 19 May 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim However, this is a transient effect and the eventual delocalization can be understood in terms of a flowing localization length.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.53 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.39 · compares with prior results 0.09 · mentions code or data availability 0.01.

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We analyze a crossover between ergodic and non-ergodic regimes in an interacting spin chain with a dilute density of impurities, defined as spins with a strong local field. The dilute limit allows us to unravel some finite size effects and propose a mechanism for the delocalization of these impurities in the thermodynamic limit. In particular we show that impurities will always relax by exchanging energy with the rest of the chain. The relaxation rate only weakly depends on the impurity density and decays exponentially, up to logarithmic corrections, with the field strength. We connect the relaxation to fast operator spreading and show that the same mechanism destabilizes the recursive construction of local integrals of motion at any impurity density. In the high field limit, impurities will appear to be localized, and the system will be non-ergodic, over a wide range of system sizes. However, this is a transient effect and the eventual delocalization can be understood in terms of a flowing localization length.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We analyze a crossover between ergodic and non-ergodic regimes in an interacting spin chain with a dilute density of impurities, defined as spins with a strong local field.	contribution 0.98	0.88	0.09	asserted 0.89
s1	The dilute limit allows us to unravel some finite size effects and propose a mechanism for the delocalization of these impurities in the thermodynamic limit.	contribution 0.79	0.90	0.16	asserted 0.67
s2	In particular we show that impurities will always relax by exchanging energy with the rest of the chain.	result 1.00	0.90	0.39	asserted 1.00
s3	The relaxation rate only weakly depends on the impurity density and decays exponentially, up to logarithmic corrections, with the field strength.	result 1.00	0.90	0.16	asserted 1.00
s4	We connect the relaxation to fast operator spreading and show that the same mechanism destabilizes the recursive construction of local integrals of motion at any impurity density.	interpretation 0.49	0.91	0.21	asserted 1.00
s5	In the high field limit, impurities will appear to be localized, and the system will be non-ergodic, over a wide range of system sizes.	result 0.98	0.81	0.12	asserted 0.95
s6	However, this is a transient effect and the eventual delocalization can be understood in terms of a flowing localization length.	interpretation 0.91	0.81	0.28	asserted 0.93

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.63.

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Original abstract

We analyze a crossover between ergodic and non-ergodic regimes in an interacting spin chain with a dilute density of impurities, defined as spins with a strong local field. The dilute limit allows us to unravel some finite size effects and propose a mechanism for the delocalization of these impurities in the thermodynamic limit. In particular we show that impurities will always relax by exchanging energy with the rest of the chain. The relaxation rate only weakly depends on the impurity density and decays exponentially, up to logarithmic corrections, with the field strength. We connect the relaxation to fast operator spreading and show that the same mechanism destabilizes the recursive construction of local integrals of motion at any impurity density. In the high field limit, impurities will appear to be localized, and the system will be non-ergodic, over a wide range of system sizes. However, this is a transient effect and the eventual delocalization can be understood in terms of a flowing localization length.

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20 arXiv papers cite this in 32 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 25 sentences without a confident label

Cites it as background 7 papers

There has been a recent debate about the existence of MBL even in static systems [ref] .

Many-Body Localization with Quasiperiodic Driving · Discussion · 0.84
Recently, claims have been made that this localization phenomenology may not be stable in the thermodynamic limit due to thermal inclusions [ref] .

Pair localization in dipolar systems with tunable positional disorder · Introduction · 0.81
In general, the actual stability of an MBL (and hence a DTC) phase in the thermodynamic limit is a matter of considerable debate [ref] , though the stability of a DTC over experimentally relevant length and time-scale has been established already [ref] .

Slow Dynamics and Kohlrausch Relaxation in Isolated Disordered Many-Body Systems · Introduction · 0.80

What it cites · 17 sentences without a confident label

Compares with 2 papers

The latter was recently observed in other systems with slightly broken integrability [ref] .

Eigenstate thermalization hypothesis through the lens of autocorrelation functions · Fidelity Susceptibility · 0.92
The latter was recently observed in other systems with slightly broken integrability [ref] .

Universality in the onset of quantum chaos in many-body systems · Fidelity Susceptibility · 0.92

Cites as support 1 paper

Exponential enhancement of the fidelity susceptibility implies an exponential (in $L$) enhancement of spectral weight at low frequency from $O(1)$ to $O(exp(S(L)))$, accompanied by exponentially slow (in $L$) relaxation [ref] .

Dynamical obstruction to localization in a disordered spin chain · Fidelity Susceptibility · 0.96

Cites as background 3 papers

We note, however, that very recently, after the first version of this paper was completed, a series of numerical papers, based on newly developed approaches, appeared [ref] .

Avalanches and many-body resonances in many-body localized systems · Introduction · 0.92
We note, however, that very recently, after the first version of this paper was completed, a series of numerical papers, based on newly developed approaches, appeared [ref] .

Markovian baths and quantum avalanches · Introduction · 0.92
We note, however, that very recently, after the first version of this paper was completed, a series of numerical papers, based on newly developed approaches, appeared [ref] .

Challenges to observation of many-body localization · Introduction · 0.92

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