连续量子系统的密度矩阵重整化群
Density-Matrix Renormalization Group for Continuous Quantum Systems
摘要：
我们介绍了一个通用的和实用的框架应用矩阵乘积态技术的连续量子系统。我们将空间划分为多个部分，并为每个部分中的多体状态生成连续的基函数。通过将这种映射与现有的数值密度矩阵重整化群例程相结合，我们展示了如何可以准确地获得基态波函数，空间相关性，和空间纠缠熵直接在连续。对于一个典型的强相互作用玻色子介观系统，我们证明了比标准的基于网格的离散化更快的收敛。我们说明了我们的方法的力量，通过研究超流绝缘体过渡的外部潜力。我们概述了如何可以直接应用或推广这种技术的各种实验相关的问题，在凝聚态物理和量子场论。
英文摘要：
We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each segment. By combining this mapping with existing numerical Density-Matrix Renormalization Group routines, we show how one can accurately obtain the ground-state wave function, spatial correlations, and spatial entanglement entropy directly in the continuum. For a prototypical mesoscopic system of strongly-interacting bosons we demonstrate faster convergence than standard grid-based discretization. We illustrate the power of our approach by studying a superfluid-insulator transition in an external potential. We outline how one can directly apply or generalize this technique to a wide variety of experimentally relevant problems across condensed matter physics and quantum field theory.
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