Entanglement entropy across the dynamical phase transition in the quantum O(N) model

summary

The gist

The gist The dynamical phase transition of the quantum O(N) model at large N leaves universal fingerprints in the infrared structure of the entanglement spectrum.

In short

This study investigates how a dynamical phase transition (DPT) in a large-N quantum O(N) model affects its entanglement spectrum far from equilibrium. The research found that while entanglement entropy follows standard volume laws, the critical point generates unique logarithmic corrections to this law. These corrections are governed by the transition's scaling properties and reveal universal fingerprints in the system's low-energy structure.

Key concepts

Dynamical Phase Transition (DPT): This is a change in behavior of a quantum system when it is suddenly changed (quenched) from one state to another. In this large-N O(N) model, the transition occurs when a mass parameter is quenched below a critical value, leading to different long-term dynamical regimes.
Entanglement Spectrum: This refers to the set of energy levels associated with entanglement in a quantum system. Analyzing this spectrum helps reveal how correlations develop over time after a quench. The paper uses it to find universal signatures of the DPT by looking at how these modes behave.
Logarithmic Corrections: These are specific, slow corrections that appear in the long-time behavior of entanglement entropy, taking the form of $\ln(t)$. These terms are not present in standard volume laws and are crucial because their scaling exponent is determined by the critical point of the phase transition.
Entanglement Dispersion: This describes how entanglement spreads or propagates through space and time. The paper examines a specific measure called the entanglement dispersion ($\omega_{0}q_{\parallel}$), which shows different scaling behaviors (like $q^{1/2}$ or $q^{1/4}$) depending on whether the system is above, at, or below the critical point.

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This episode discusses

The paper

Entanglement entropy across the dynamical phase transition in the quantum O(N) model · Read on arXiv

Laboratoire Kastler Brossel, Sorbonne University, CNRS, ENS-PSL Research University, Collège de France · Laboratoire de Physique Th࠵eorique et Mod࠵eles Statistiques · Ecole Normale Sup࠹erieure de Lyon

We demonstrate that the dynamical phase transition of the quantum O(N) model at large N leaves universal fingerprints in the infrared structure of the entanglement spectrum. While the leading contribution to the entanglement entropy at long time follows the conventional volume law associated with ballistic entanglement spreading, its subleading behavior sharply distinguishes the different dynamical regimes. Specifically, quenches at and below the critical point generate gapless low-energy entanglement modes together with logarithmic corrections to the long-time entanglement entropy, whose scaling is governed by the scaling exponent of the transition. Using an infinite-slab bipartition geometry and exact numerical correlation functions in the large- N limit, we characterize these scaling laws across the dynamical phase diagram and relate them to the emergence of long-range correlations during the post-quench dynamics. We further show that the entanglement eigenmodes themselves reveal characteristic signatures of the dynamical phase transition through their spatio-temporal structure and degeneracy properties.

DOI: 10.1103/mjx8-8vj6

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: We're looking at the paper: "Entanglement entropy across the dynamical phase transition in the quantum O(N) model".

Mira: The gist The dynamical phase transition of the quantum O(N) model at large N leaves universal fingerprints in the infrared structure of the entanglement spectrum.

Kai: First, who's behind it and why it matters.

Paper summary: Kai: We're looking at the paper "Entanglement entropy across the dynamical phase transition in the quantum O(N) model" again. To recap, it focuses on how this Dynamical Phase Transition of the quantum O(N) model at large N leaves universal fingerprints in the infrared structure of its entanglement spectrum.

Mira: The central thesis is that while leading order entanglement entropy follows the conventional volume law from ballistic spreading, subleading behavior sharply distinguishes different dynamical regimes.

Lev: Specifically, quenches at and below the critical point generate gapless low-energy entanglement modes together with logarithmic corrections to the long-time entanglement entropy.

Kai: These corrections scale according to the scaling exponent alpha governing correlations around this transition. They use an infinite-slab bipartition geometry and exact numerical correlation functions in the large N limit for this study.

Mira: And they show how these scaling laws relate to the emergence of long-range correlations during the post-quench dynamics, which is what makes it relevant for understanding many-body systems far from equilibrium.

Lev: The paper also investigates entanglement quasi-particles characterized by an entanglement dispersion omega q(t). For quenches below or at the critical point, they find an entanglement dispersion of the form omega 0q proportional to q(one/two) in the long time limit <ref:2605.23600#pg3>.

Conclusion: Kai: So we're wrapping up this discussion on "Entanglement entropy across the dynamical phase transition in the quantum O(N) model." The main point is that there are clear, universal fingerprints left in the low-energy entanglement spectrum at late times.

Mira: These fingerprints show up as those subleading, time-dependent logarithmic corrections to the leading volume-law contribution to entanglement entropy.

Lev: These corrections originate from the late-time scaling properties of the lowest entanglement mode, and that universal leading time-dependent logarithmic contribution probes the transition through its dependence on that scaling exponent alpha.

Kai: It's a bit subtle because you can only see these effects when you look at the entanglement spectrum itself rather than just calculating the total entropy.

Mira: The implications are that we have a way to probe dynamical phase transitions using entanglement properties in this model, which is representative of many systems far from equilibrium.

Lev: The paper does show some limitations, though, they mention that sharp regulators can make extracting universal features of the DPT more difficult due to persistent finite-size effects at long times.

Kai: So in a nutshell, the dynamics of the entanglement spectrum are where you find these critical scaling laws when studying this quantum O(N) model.

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