论文标题
部分可观测时空混沌系统的无模型预测
Field theory approach to eigenstate thermalization in random quantum circuits
论文作者
论文摘要
我们使用现场理论方法来探索大型Floquet随机量子电路家族的Floquet Operator的本征算法的统计数据。计算准本征征的相关功能并显示为显示随机矩阵圆形单一集合统计，这与Berry猜想的量子电路的类似物一致。该数量确定了量子混乱的所有关键指标，例如光谱形式和任意可观察到的期望值的热依赖性。它还使我们能够明确表明本地操作员的矩阵元素满足特征态热假说（ETH）；即，在系统大小中，此类运算符的非对角矩阵元素的方差成倍小。这些结果代表了在严格的物理水平上为Floquet随机量子电路家族提供的ETH证明。对于此和大多数其他Sigma模型计算，一个出色的开放问题是数学上严格证明大N极限中鞍点近似的有效性的证明。
We use field-theoretic methods to explore the statistics of eigenfunctions of the Floquet operator for a large family of Floquet random quantum circuits. The correlation function of the quasienergy eigenstates is calculated and shown to exhibit random matrix circular unitary ensemble statistics, which is consistent with the analogue of Berry's conjecture for quantum circuits. This quantity determines all key metrics of quantum chaos, such as the spectral form factor and thermalizing time-dependence of the expectation value of an arbitrary observable. It also allows us to explicitly show that the matrix elements of local operators satisfy the eigenstate thermalization hypothesis (ETH); i.e., the variance of the off-diagonal matrix elements of such operators is exponentially small in the system size. These results represent a proof of ETH for the family of Floquet random quantum circuits at a physical level of rigor. An outstanding open question for this and most of other sigma-model calculations is a mathematically rigorous proof of the validity of the saddle-point approximation in the large-N limit.
