Quantum

Optimal Disorder Strength for Approximate Unitary $k$-Designs in Spin Chains

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Briefings

This preprint investigates the optimal disorder strength for approximating unitary $k$-designs in interacting XXZ spin chains. The study identifies a non-monotonic crossover where the moment gap $ abla^{(k)}$ scales logarithmically as $- abla^2$ at weak disorder and $-1/ abla$ at strong disorder, with the optimal crossover occurring at the energy scale of the non-random interaction. Numerical simulations confirm these theoretical predictions and demonstrate that multi-quench protocols can suppress the gap exponentially.

Key points

• The optimal disorder strength for approximating unitary $k$-designs in interacting XXZ chains is determined by a non-monotonic crossover between weak and strong disorder regimes.
• At weak disorder, the moment gap scales logarithmically as $\ln \Delta^{(k)} \sim -\sigma^2$, while at strong disorder it scales as $\ln \Delta^{(k)} \sim -1/\sigma$.

Context and limitations

The findings apply specifically to the full spectrum of the interacting XXZ chain in a fixed-magnetization sector; results for other spin chains or different magnetization sectors are not covered.

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