Quantum phase transition in XXZ central spin model

summary

Video file (mp4)

The gist

The gist: The central spin model exhibits a normal-to-superradiant phase transition in the limit where the ratio of the transition frequency of the central spin to that of the bath spins and the

In short

This work investigates a normal-to-superradiant quantum phase transition in a central spin model, where one spin interacts with many bath spins. The study shows that this transition occurs in specific limits of system parameters and reveals how the longitudinal interaction affects the ground state's excitation number and coherence. It also connects these qubit systems to qubit-field systems for enhanced quantum sensing.

Key concepts

Central Spin Model
This model describes a single spin-1/2 particle (the central spin) coupled to N other spin-1/2 particles (bath spins). It is used as a platform to study quantum phase transitions, particularly when the bath spins are treated as a field.
Normal-to-Superradiant Phase Transition
This is a specific type of quantum phase transition observed in the model. It describes a change in the system's state where it moves from a normal phase to a superradiant phase, which is characterized by enhanced macroscopic excitations of the bath spins.
Quantum Fisher Information (QFI)
QFI is a tool used to characterize quantum phase transitions and measure precision in quantum sensing. It quantifies how sensitive the system's ground state is to small changes in its parameters, allowing for the illustration of practical measurement schemes.
Longitudinal Interaction ($\Delta$)
This interaction term significantly influences the ground state properties. The paper finds that it enhances both excitation number and coherence when $\Delta$ is negative but suppresses them when $\Delta$ is positive, highlighting its critical role in determining the system's behavior.

Terminology used across episodes

This episode discusses

The paper

Quantum phase transition in XXZ central spin model · Read on arXiv

Lei Shao, *Xiaoguang Wang

Zhejiang Institute of Modern Physics · Department of Physics, Zhejiang University · Department of Maths and Physics, Hunan Institute of Engineering

DOI: 10.1103/PhysRevA.107.013714

Transcript

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

Kai: Today's paper: "Quantum phase transition in XXZ central spin model".

Mira: The gist:

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

Title and authors: Kai: So we're talking about "Quantum phase transition in XXZ central spin model," and the authors are Lei Shao, Rui Zhang, Wangjun Lu, Zhucheng Zhang, and Xiaoguang Wang <ref:2207.04191#pg1>.

Mira: They look at this setup where you have a spin one/two particle coupled to N bath spins <ref:2207.04191#pg3>, which is also called the qubit-big spin model in reference twenty-six <ref:2207.04191#pg2>.

Lev: And they're interested in how the longitudinal interaction, delta k squared sigma k z sigma zero z, and the transverse interaction Ak squared sigma k x sigma zero x plussigma (k) y sigma(zero) y affect this transition <ref:2207.04191#pg2>.

Kai: They specifically look at the case where you simplify it by setting Ak equal to A and delta k equals delta, which makes the Hamiltonian look like Eq. (two) <ref:2207.04191#pg3>.

Mira: And they are interested in how this setup relates to other systems, like quantum dots or NV centers, because the bath spins can be thought of as a big spin or a quantum reference frame for quantum metrology <ref:2207.04191#pg2>.

Lev: So what's the main takeaway here is that they are using this model to probe how coupling strengths and interactions change the behavior of these large spin systems <ref:2207.04191#pg3>.

The paper's summary: Kai: They summarize that for the XXZ central spin model, the QPT happens when you take N to infinity and the ratio of transition frequencies goes to infinity <ref:2207.04191#pg1>. This is the key condition they are focusing on <ref:2207.04191#pg2>.

Mira: And they show that for the case where delta is less than omega, there's a critical point similar to the JC model, but then they say that for delta less than omega, it's actually different from the JC model one <ref:2207.04191#pg3>.

Lev: So if you were trying to build an error correction scheme based on this, you have to know that the underlying physics is modified by those longitudinal interactions even in this limit <ref:2207.04191#pg3>.

Kai: They use a low-energy effective Hamiltonian approach to solve this, which is a Holstein-Primakoff transformation and a Schrieffer-Wolff transformation using an anti-Hermitian operator S = lambda a†S− -aS+ / omega e0 <ref:2207.04191#pg3>.

Mira: This leads to the normal phase effective Hamiltonian, which is Henp = -omega e0 two −ω j + omega e one−g˜ two a† a, where a and a† are the bosonic annihilation and creation operators <ref:2207.04191#pg8>.

Lev: That structure of the effective Hamiltonian tells us that even in the normal phase, we're dealing with some sort of bosonic excitation description <ref:2207.04191#pg8>.

The paper's improvements: Kai: One improvement they point out is how the longitudinal interaction delta k squared sigma k z sigma zero z significantly influences the excitation number and coherence of the ground state <ref:2207.04191#pg1>.

Mira: They note that this influence is remarkably enhanced for negative longitudinal interaction, specifically when negative delta is between minus omega and zero <ref:2207.04191#pg3>.

Lev: So for practical implementation, that means if we can engineer a negative interaction strength in our system, we could potentially boost the coherence of the ground state significantly <ref:2207.04191#pg3>.

Kai: Conversely, they mention that this effect is suppressed when you have a positive longitudinal interaction <ref:2207.04191#pg3>.

Mira: For the case where delta equals zero, the excitation number of the ground state is zero for g equal to one, but for g greater than one, it's given by ng = eta / (4g squared - g-two) <ref:2207.04191#pg3>.

Lev: That formula for ng gives us a concrete number to work with when we consider the excitation number of the bath spins in that regime <ref:2207.04191#pg3>.

Conclusion: Kai: So to wrap up on "Quantum phase transition in XXZ central spin model," they show that you can characterize this QPT using quantum Fisher information, or QFI <ref:2207.04191#pg6>.

Mira: The QFI is used because it captures the abrupt change of the ground state around the critical point, which they show happens at g c equal to one <ref:2207.04191#pg6>.

Lev: And they give us a way to get a measurement scheme for this, and then use an error propagation formula Fg˜ = (∂g˜hσxi)two / (one-hσxi2) to calculate the precision of the coupling strength <ref:2207.04191#pg6>.

Kai: And they also mention that controlling the longitudinal interaction delta has a significant influence on where you get your maximum and minimum values for Fg, meaning you can change the coupling strength g at which you achieve maximum precision <ref:2207.04191#pg6>.

Mira: So this work suggests that we can use different longitudinal interactions to tune the system into a regime where quantum sensing gets enhanced by this criticality <ref:2207.04191#pg6>.

Lev: From my side, having that low-energy effective Hamiltonian from the Schrieffer-Wolff transformation gives us a new way to explain the transition, showing how the nonlinear term from that longitudinal interaction affects things compared to just looking at the JC model <ref:2207.04191#pg9>.

Kai: So in short, this paper on "Quantum phase transition in XXZ central spin model" gives us a new perspective on how these large spin systems exhibit quantum criticality and hints at using that criticality for enhanced quantum sensing <ref:2207.04191#pg6>.

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