Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions

Piotr Sierant; Xhek Turkeshi

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Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions

Piotr Sierant, Xhek Turkeshi

Statistical Mechanics · Submitted 14 Sep 2021

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

The authors' main claim The sub-leading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being constant non-zero in the error correcting phase and vanishing in the quantum Zeno phase.

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arXiv ID2109.06882 (version 3)

Pith IDJU3HKHKO, Pith's permanent record of this paper and its review

CitationPiotr Sierant, Xhek Turkeshi. "Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions." arXiv:2109.06882 (2021). https://pith.science/paper/JU3HKHKO

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We investigate the structure of many-body wave functions of 1D quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropy indicates a model dependent multifractal scaling of the wave-functions at any non-zero measurement rate. The sub-leading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being constant non-zero in the error correcting phase and vanishing in the quantum Zeno phase. We provide robust numerical evidence investigating a variety of quantum many-body systems, and provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D.

background contribution method result interpretation main claim

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 investigate the structure of many-body wave functions of 1D quantum circuits with local measurements employing the participation entropies.	contribution 0.90	0.94	0.03	asserted 0.85
s1	The leading term in system size dependence of participation entropy indicates a model dependent multifractal scaling of the wave-functions at any non-zero measurement rate.	result 1.00	0.81	0.12	hedged possibility 0.56
s2	The sub-leading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being constant non-zero in the error correcting phase and vanishing in the quantum Zeno phase.	result 0.81	0.87	0.70	asserted 1.00
s3	We provide robust numerical evidence investigating a variety of quantum many-body systems, and provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D.	contribution 0.95	0.96	0.18	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.61 · evidence from simulation or computation 1.00.

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arXiv listing abstract v3

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The paper

Original abstract

We investigate the structure of many-body wave functions of 1D quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropy indicates a model dependent multifractal scaling of the wave-functions at any non-zero measurement rate. The sub-leading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being constant non-zero in the error correcting phase and vanishing in the quantum Zeno phase. We provide robust numerical evidence investigating a variety of quantum many-body systems, and provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D.

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References

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84 later papers cite it

Evidence: some. 50 of the citing papers share no author with it, and 2 of those carry a confident label from Pith's citation classifier.

Pith read 11 of the 118 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool.

Uses its method or tool 2 of 5 papers with this label · 1 by the same authors

Extracted the linear coefficient and subleading term using the procedure explained in this paper.

Quantifying nonstabilizerness of matrix product states (2022) · 1.00 · paraphrased: the licence does not allow quoting

By the same authors

Following this paper, parameterized the dependence of the averaged participation entropy on the system size.

Universality in Anderson localization on random graphs with varying connectivity (2022) (same authors) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

3 arXiv papers cite this in 3 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 · 2 sentences without a confident label

Cites it as background 1 paper

In this section we will mainly be interested in a particular class of entanglement transitions, known as measurement-induced transitions [ref] .

Quantum simulation using noisy unitary circuits and measurements · Measurement-induced entanglement transitions in hybrid quantum circuits · 0.92

What it cites · 9 sentences without a confident label

Uses the method or tool of 1 paper

Stabilizer circuits are simulated in time polynomial in $L$ (up to $L≤880$) using the package Stim [ref] and employing the ideas in [ref] .

The Heisenberg Representation of Quantum Computers · Introduction · 1.00

Compares with 1 paper

This should be compared with systems of up to $L=8$ sites considered in the recent experiment [ref] .

Observation of measurement-induced quantum phases in a trapped-ion quantum computer · S7 Experimental proposal on quantum processors · 0.95

Cites as background 26 papers

In the many-body framework, this competition gives rise to dynamical phases captured by non-linear functions of the density matrix separated by so-called measurement-induced phase transitions (MIPTs) [ref] .

Conformal invariance and quantum non-locality in critical hybrid circuits · Introduction · 0.83
In the many-body framework, this competition gives rise to dynamical phases captured by non-linear functions of the density matrix separated by so-called measurement-induced phase transitions (MIPTs) [ref] .

Classical Models of Entanglement in Monitored Random Circuits · Introduction · 0.83
In the many-body framework, this competition gives rise to dynamical phases captured by non-linear functions of the density matrix separated by so-called measurement-induced phase transitions (MIPTs) [ref] .

Topological order and criticality in (2+1)D monitored random quantum circuits · Introduction · 0.83

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