量子自旋玻璃链中的信息置乱与蝴蝶速度
Information scrambling and butterfly velocity in quantum spin glass chains
AI总结：
本研究将零维SY和球形量子p-自旋玻璃模型推广到一维，分析顺磁与自旋玻璃相中信息置乱动力学的交叉，揭示了两种模型中混沌指标随温度、量子参数的不同演化规律及玻璃化复杂度与涨落的关联。
摘要：
我们将两种知名的零维量子自旋玻璃模型——Sachdev-Ye（SY）模型和球形量子p-自旋玻璃模型——推广到一维晶格体系，以研究顺磁（PM）相和自旋玻璃（SG）相中，由玻璃化转变、复杂动力学以及量子与热涨落导致的非局域置乱动力学的交叉行为。在由量子点构成的SY链中，每个量子点由N个自旋为S的SU(M)自旋的无穷程随机海森堡模型描述，我们在大N、M极限下采用玻色自旋子表示，得到了跨越PM-SG相界的量子李雅普诺夫指数λ_L和蝴蝶速度v_B随温度T和量子参数S的变化关系。具体而言，我们提取了在相区深处以及靠近复本对称破缺SG转变的不同区域中，λ_L和v_B的渐近T与S依赖关系（例如幂律关系）。我们发现，几乎在整个相图上混沌都不是最大的。对于p-自旋玻璃链，我们得到了混沌指标随温度和合适的量子参数Γ变化的极为相似的结果，但存在一些重要的定性差异。具体而言，在p-自旋玻璃模型的PM相中，λ_L和v_B随T和Γ变化时会出现一个最大值，该最大值与复杂玻璃化弛豫的起始点重合，且位于玻璃化转变温度之上。相比之下，在SY模型的PM相中，该最大值仅随S变化时出现，而不随温度变化出现。该最大值源于玻璃化能景中最大复杂度导致的混沌增强。因此，SY模型的结果表明，玻璃化复杂度随量子涨落和热涨落的演化方式存在显著差异。
英文摘要：
We make lattice generalization of two well-known zero-dimensional models of quantum spin glass, Sachdev-Ye (SY) and spherical quantum $p$-spin glass model, to one dimension for studying crossovers in non-local scrambling dynamics due to glass transition, complex dynamics, and quantum and thermal fluctuations in paramagnetic (PM) and spin glass (SG) phases. In the SY chain of quantum dots, each described by infinite-range random Heisenberg model of $N$ spin-$S$ $SU(M)$ spins, we obtain the quantum Lyapunov exponent $λ_\mathrm{L}$ and butterfly velocity $v_B$ as a function of temperature $T$ and the quantum parameter $S$ across the PM-SG phase boundary using a bosonic spinon representation in the large $N,M$ limit. In particular, we extract asymptotic $T$ and $S$ dependence, e.g., power laws, for $λ_\mathrm{L}$ and $v_B$ in different regions deep inside the phases and near the replica symmetry breaking SG transition. We find the chaos to be non-maximal almost over the entire phase diagram. Very similar results for chaos indicators are found for the $p$-spin glass chain as a function of temperature and a suitable quantum parameter $Γ$, with some important qualitative differences. In particular, $λ_\mathrm{L}$ and $v_B$ exhibit a maximum, coinciding with onset of complex glassy relaxation, above the glass transition as a function of $T$ and $Γ$ in the PM phase of the $p$-spin glass model. In contrast, the maximum is only observed as a function of $S$, but not with temperature, in the PM phase of SY model. The maximum originates from enhanced chaos due to maximal complexity in the glassy landscape. Thus, the results in the SY model indicate very different evolution of glassy complexity with quantum and thermal fluctuations.
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