Quantum Quenches that Resemble Operator Growth

summary

The gist

The gist: Growth quenches are local quenches that may gradually destabilize a false vacuum in certain kinetic constrained quantum lattice models, and this study points out a formal analogy with the

In short

This study maps local quantum quenches to operator growth dynamics using a formal analogy involving vectorization in Hilbert space. It applies recursion methods to analyze these quenches, revealing Krylov and Fock space localization depending on parameters like $ u$ and $ u_m$. The results connect conserved charges, transport properties, and non-equilibrium coherent phenomena in many-body systems.

Key concepts

Growth Quenches: These are local quantum disturbances in kinetic constrained models that destabilize a false vacuum. The paper treats them as an analogue to how local operators evolve over time, allowing researchers to study complex dynamics by mapping them onto known operator growth problems.
Krylov Space Localization: This refers to the confinement of dynamics within a specific subspace defined by Lanczos coefficients. When $| u| > 2ar{eta}$, the dynamics are localized here, which implies localization in Fock space because the quench fails to spread there due to quantum coherent effects.
Fock Space Cage States: In 1D growth quenches, these states are interpreted as conserved charges. They exhibit ballistic transport in simpler models. The paper uses this interpretation to link the structure of Fock space states directly to physical conservation laws and their motion.
Lyapunov Exponent ($ar{ u}$): This quantity bounds the spread complexity of the dynamics, acting as a measure of how fast quantum information scrambles or spreads. The paper derives a bound $ar{ u}_L ext{ } ext{≤ } ar{ u}^2 - 4ar{eta}^2$ for certain regimes, helping to characterize the localization behavior.

Terminology used across episodes

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This episode discusses

The paper

Quantum Quenches that Resemble Operator Growth · Read on arXiv

Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université Paris CitǨ · CNRS · Sorbonne Universit⠼ Paris Cit⠼

DOI: 10.1103/4k2f-xvq3

Transcript

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

Kai: We're looking at the paper: "Quantum Quenches that Resemble Operator Growth".

Mira: The gist: Growth quenches are local quenches that may gradually destabilize a false vacuum in certain kinetic constrained quantum lattice models,

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

Title and authors: Kai: So, we’re looking at this paper, "Quantum Quenches that Resemble Operator Growth." It's about growth quenches, which are local disturbances that can destabilize a false vacuum in certain kinetic constrained quantum lattice models like the East-West model.

Mira: And what they really point out is a formal analogy between these growth quenches and the dynamics of a local operator in the Heisenberg picture.

Lev: That means they're trying to map something about how operators evolve to something about these actual physical quenches, which is important for thinking about how we model things in quantum computation.

Kai: Exactly, it connects the abstract math of operator growth to the actual behavior of systems under a quench.

Mira: And it suggests that by using the tools from one area, like operator dynamics, we can get new results about these physical quenches.

The paper's summary: Kai: So, this paper explores how growth quenches behave by mapping them onto the evolution of local operators in a doubled Hilbert space using something called vectorization or the Choi-Jamio lkowski map.

Mira: They set up an identity where the identity operator acts like that false vacuum, and a local operator is defined as a specific kind of initial state that only differs from that vacuum at just a few sites.

Lev: That mapping is what connects things like return amplitudes to Green functions, and expectation values to out-of-time order correlation functions, which are all different physical ways of looking at the same dynamics.

Kai: And they apply the recursion method here to growth quenches by treating them like a one-dimensional semiinfinite Krylov chain defined by Lanczos coefficients.

Mira: The main results they get there are about how these Lanczos coefficients grow, conjecturing that the diagonal ones grow as am ∼ nu m diagonal, and the off-diagonal ones grow as bm ∼ alpha m off-diagonal.

The paper's improvements: Kai: Now they look at what this analogy lets them predict. They investigate localization in Krylov space, finding that when the parameter nu is greater than two alpha, the dynamics in that space are localized.

Mira: And this Krylov space localization implies a localization in Fock space because the quench dynamics doesn't spread there and is confined by quantum coherent effects.

Lev: That’s interesting because it sets a clear condition for when we expect confinement, which is what we need to figure out how error correction overhead actually lands on real hardware.

Kai: They also derive a bound for the growth quench analogue of the Lyapunov exponent, lambda L less than or equal to the square root of four alpha squared minus nu squared when nu is less than two alpha.

Mira: And they show that in large N solvable models inspired by Sachdev-Ye-Kitaev models, this bound on the Lyapunov exponent gets saturated in the large-q SYK grow quench.

Conclusion: Kai: To wrap up, the paper shows that growth quench dynamics are localized in general and slowly and intermediately delocalized at a special point in deformed East-West models.

Mira: The existence of Fock localization due to a linear onsite potential in the Krylov space is a novelty here, which they realize in mean field models.

Lev: So what this means for us is that growth quenches are a promising way to realize non-equilibrium coherent phenomena in many-body systems.

Kai: It gives us tools to study things that happen when a system is being pushed away from equilibrium locally, using established methods from operator dynamics.

Mira: We should keep an eye on how this idea of Fock localization due to the Krylov space potential shows up in more complex kinetic models.

Lev: And for the hardware side, understanding these localization transitions could help us predict how quickly chaos spreads in systems we're actually trying to build.

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