AI 中文总结
本研究提出双参数拟设统一ETH违反的两种机制，通过含无序和线性势的自旋-1/2 J₁-J₂链验证，发现观测到的ETH违反符合受限遍历性，为ETH连续过渡提供了理论框架。
AI 中文摘要
本征态热化假设（ETH）是理解孤立多体系统中量子热化与遍历性的主流框架，但尚无通用理论描述ETH在常规状态与完全破坏之间的连续过渡。本文提出一种用于ETH违反的双参数拟设，统一并区分两种机制：渐弱遍历性与受限遍历性。渐弱遍历性对应已确立的遍历性破缺路径，受限遍历性则描述有限系统中ETH被违反、热力学极限下恢复的独特场景。我们在含在位无序和线性势的自旋-1/2 J₁-J₂链中测试该框架，发现观测到的ETH违反与受限遍历性一致。
英文摘要
The eigenstate thermalization hypothesis (ETH) provides the prevailing framework for understanding quantum thermalization and ergodicity in isolated many-body systems. Yet, no general theory describes the continuous onset of ETH violation between the conventional ETH and its complete breakdown. Here, we introduce a two-parameter ansatz for the ETH violation that unifies and distinguishes two mechanisms: fading ergodicity and trapped ergodicity. While fading ergodicity captures the established route to ergodicity breaking, trapped ergodicity describes a distinct scenario in which ETH is violated in finite systems but restored in the thermodynamic limit. We test this framework in the spin-1/2 $J_1$-$J_2$ chains with on-site disorder and linear potential. In both cases, we find that the observed ETH violation is consistent with trapped ergodicity.
