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Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

Published 15 Jun 2023 in quant-ph | (2306.09333v2)

Abstract: Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution, $P(\mathcal{M})$, of the magnetization transferred across the chain's center. The first two moments of $P(\mathcal{M})$ show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.

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Citations (45)
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Summary

  • The paper demonstrates that higher moments of magnetization distribution deviate from KPZ predictions, suggesting a novel universality class.
  • The experimental method employs a 46-qubit superconducting array with high-fidelity fSim gates to capture precise Floquet dynamics.
  • The findings impact quantum simulation by challenging conventional spin transport theories and paving the way for exploring new quantum dynamics regimes.

Dynamics of Magnetization at Infinite Temperature in a Heisenberg Spin Chain

The paper "Dynamics of magnetization at infinite temperature in a Heisenberg spin chain" offers a comprehensive study of the magnetization dynamics in a one-dimensional (1D) Heisenberg spin chain at an infinite temperature. This study was conducted using a system of 46 superconducting qubits. The Heisenberg spin chain is a fundamental model in quantum magnetism and statistical mechanics, and understanding its dynamical properties is crucial for addressing unresolved problems in quantum dynamics and universality classes.

Summary of Research

The study focuses on the spin dynamics of the Heisenberg model, which is characterized by nearest-neighbor exchange interactions in spin-1/2 systems. The Heisenberg model is an integrable system with a simple SU(2) symmetry at its isotropic point (Δ = 1). While previous conjectures suggested that the model's spin dynamics belong to the Kardar-Parisi-Zhang (KPZ) universality class due to observed superdiffusive behavior, the results observed in this paper challenge that notion.

Experimental Approach and Findings

  • Experimental Setup: The experiment utilizes a chain of 46 superconducting qubits operated in a Floquet setting using high-fidelity two-qubit gates known as fSim gates. The setup allows for a precise study of spin transport and dynamic properties in various anisotropy regimes.
  • Observations: The authors investigated the distribution of magnetization transfer, P(M)P(\mathcal{M}), across the chain's center and measured its moments. The first two moments exhibited superdiffusive behavior, a trait associated with KPZ universality. However, the skewness (third moment) and kurtosis (fourth moment) contradicted the KPZ conjecture at certain scales.
  • Results on Universality Classes: The authors found that higher moments of the distribution do not align with the KPZ predictions. Notably, they suggest a distinctive dynamical behavior that could imply the spin chain belongs to a yet to be discovered universality class. In particular, they observe that the skewness vanishes near the infinite-temperature equilibrium point, which contradicts the KPZ predictions.

Theoretical and Practical Implications

This research impacts both theoretical investigations into the universality classes of quantum dynamics and practical development in quantum computing and simulation:

  • Universal Behavior of Quantum Systems: The results emphasize the importance of considering higher-order moments in determining dynamic universality classes, providing a benchmark for validating quantum models' theoretical predictions.
  • Quantum Simulation: The study highlights how quantum processors can test theoretical predictions that are challenging to explore through numerical simulations alone, demonstrating an application of quantum simulation beyond classical reach.
  • Potential for New Universal Classes: The discrepancies observed challenge the existing classification of the Heisenberg spin chain's universality class, pointing to the potential existence of new dynamic universal behaviors.

Future Directions

In light of these findings, speculating future developments involves expanding analytical and numerical techniques to potentially discover new universality classes. Increased understanding of quantum entanglement and its effects in quantum statistical models will be critical. Moreover, developing experimental methods that can push the quantum system's time evolution further could uncover dynamic regimes not yet accessible, offering deeper insights into quantum non-equilibrium dynamics.

In conclusion, this research represents a significant contribution to the field of quantum dynamics, leveraging state-of-the-art quantum hardware to probe the complexities of quantum spin chains, underscoring both the potential and challenges in achieving a comprehensive understanding of universal quantum systems.

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