Few-body systems capture many-body physics: Tensor network approach
Shi-Ju Ran,^1,* Angelo Piga,¹ Cheng Peng,² Gang Su,^2,3 and Maciej Lewenstein^1,4
1ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
²Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, School of Physical Sciences,
University of Chinese Academy of Sciences, Beijing 100049, China
³Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
⁴ICREA, Passeig Lluis Companys 23, 08010 Barcelona, Spain
(Received 10 April 2017; revised manuscript received 29 September 2017; published 13 October 2017)

Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing the few-body models that can be easily accessed by theoretical or experimental means, to accurately capture the ground-state properties of infinite many-body systems in higher dimensions. The general idea is to embed a small bulk of the infinite model in an “entanglement bath” so that the many-body effects can be faithfully mimicked. The approach we propose is efficient, simple, flexible, sign-problem free, and it directly accesses the thermodynamic limit. The numerical results of the spin models on honeycomb and simple cubic lattices show that the ground-state properties including quantum phase transitions and the critical behaviors are accurately captured by only O(10) physical and bath sites. Moreover, since the few-body Hamiltonian only contains local interactions among a handful of sites, our work provides different ways of studying the many-body phenomena in the infinite strongly correlated systems by mimicking them in the few-body experiments using cold atoms/ions, or developing quantum devices by utilizing the many-body features.