纯量子态的回归关系及其对高效计算的启示
Regression relation for pure quantum states and its implications for efficient computing
摘要：
我们得到了孤立多体量子系统纯量子态中量子力学算符期望值的Onsager回归关系的一个修正形式。我们使用从这种关系中获得的见解表明，在多体量子系统中的高温时间关联函数可以可控地计算，而无需完全对角化的哈密顿量，而是使用随机采样的纯态的薛定谔方程的直接积分。这种方法也适用于量子猝灭和其他可由含时多体哈密顿描述的情况。与完全对角化相比，该方法意味着计算机内存需求的指数减少。我们通过数值计算无限温度下的关联函数的自旋不变海森堡链高达29 1/2的方法来说明。因此，我们还检验了自旋扩散假设，并发现它与数值结果是令人满意的一致。修正回归关系的推导和计算方法的论证都是基于量子典型性的概念。
英文摘要：
We obtain a modified version of the Onsager regression relation for the expectation values of quantum-mechanical operators in pure quantum states of isolated many-body quantum systems. We use the insights gained from this relation to show that high-temperature time correlation functions in many-body quantum systems can be controllably computed without complete diagonalization of the Hamiltonians, using instead the direct integration of the Schroedinger equation for randomly sampled pure states. This method is also applicable to quantum quenches and other situations describable by time-dependent many-body Hamiltonians. The method implies exponential reduction of the computer memory requirement in comparison with the complete diagonalization. We illustrate the method by numerically computing infinite-temperature correlation functions for translationally invariant Heisenberg chains of up to 29 spins 1/2. Thereby, we also test the spin diffusion hypothesis and find it in a satisfactory agreement with the numerical results. Both the derivation of the modified regression relation and the justification of the computational method are based on the notion of quantum typicality.
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