Area law of noncritical ground states in 1D long-range interacting systems

Tomotaka Kuwahara () and Keiji Saito
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Tomotaka Kuwahara: RIKEN Center for Advanced Intelligence Project (AIP)
Keiji Saito: Keio University

Nature Communications, 2020, vol. 11, issue 1, 1-7

Abstract: Abstract 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.

Date: 2020
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DOI: 10.1038/s41467-020-18055-x

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