Kuwahara Tomotaka, Saito Keiji
Mathematical Science Team, RIKEN Center for Advanced Intelligence Project (AIP), 1-4-1 Nihonbashi, Chuo-Ku, Tokyo, 103-0027, Japan.
Interdisciplinary Theoretical & Mathematical Sciences Program (iTHEMS) RIKEN 2-1, Hirosawa, Wako, Saitama, 351-0198, Japan.
Nat Commun. 2020 Sep 8;11(1):4478. doi: 10.1038/s41467-020-18055-x.
The area law for entanglement provides one of the most important connections between information theory and quantum many-body physics. It is not only related to the universality of quantum phases, but also to efficient numerical simulations in the ground state. Various numerical observations have led to a strong belief that the area law is true for every non-critical phase in short-range interacting systems. However, the area law for long-range interacting systems is still elusive, as the long-range interaction results in correlation patterns similar to those in critical phases. Here, we show that for generic non-critical one-dimensional ground states with locally bounded Hamiltonians, the area law robustly holds without any corrections, even under long-range interactions. Our result guarantees an efficient description of ground states by the matrix-product state in experimentally relevant long-range systems, which justifies the density-matrix renormalization algorithm.
纠缠的面积定律提供了信息论与量子多体物理之间最重要的联系之一。它不仅与量子相的普适性有关，还与基态的高效数值模拟有关。各种数值观测结果使人们坚信，面积定律对于短程相互作用系统中的每个非临界相都是成立的。然而，长程相互作用系统的面积定律仍然难以捉摸，因为长程相互作用会导致与临界相类似的关联模式。在这里，我们表明，对于具有局部有界哈密顿量的一般非临界一维基态，即使在长程相互作用下，面积定律也能稳健地成立，无需任何修正。我们的结果保证了在实验相关的长程系统中，通过矩阵乘积态对基态进行有效描述，这为密度矩阵重整化算法提供了依据。
