论文标题
量子混乱和量子远距离链链的合奏不等于
Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
论文作者
论文摘要
我们使用大尺度的精确对角线化来研究横向场中的量子链链，并具有与指数$α$衰变的远程幂律相互作用。我们在数值上研究了量子混乱和特征态热化{on}特征值和本征态的各种探针。级别间距统计数据在所有值$α> 0 $的值中产生了明显的符号，因此要在Wigner-dyson分布中，因此产生了量子混乱。但是，对于$α<1 $，我们发现微型熵熵是非凸。这是由于以下事实：这些频谱以$α<1 $的能量分离的多重组进行了组织。虽然量子混沌行为在单个多重组中发展，但正如我们在分析和数值上争论的那样，许多多重行为不会重叠，也不会相互混合。我们的发现表明，一小部分的多重组可能会以$α\ ll 1 $的价格持续，甚至对于大$ n $，也会导致整体不等值。
We use large-scale exact diagonalization to study the quantum Ising chain in a transverse field with long-range power-law interactions decaying with exponent $α$. We numerically study various probes for quantum chaos and eigenstate thermalization {on} the level of eigenvalues and eigenstates. The level-spacing statistics yields a clear sign towards a Wigner-Dyson distribution and therefore towards quantum chaos across all values of $α>0$. Yet, for $α<1$ we find that the microcanonical entropy is nonconvex. This is due to the fact that the spectrum is organized in energetically separated multiplets for $α<1$. While quantum chaotic behaviour develops within the individual multiplets, many multiplets don't overlap and don't mix with each other, as we analytically and numerically argue. Our findings suggest that a small fraction of the multiplets could persist at low energies for $α\ll 1$ even for large $N$, giving rise to ensemble inequivalence.
