# Few-body systems capture many-body physics: tensor network approach

## TL;DR

This paper introduces a tensor network-based method that constructs small, manageable models mimicking infinite many-body systems, enabling accurate analysis of ground states and phase transitions in higher dimensions.

## Contribution

A novel scheme using an entanglement bath to accurately simulate infinite many-body systems with few-body models, facilitating experimental and theoretical studies.

## Key findings

- Accurately captures ground-state properties and phase transitions.
- Efficient and sign-problem-free approach.
- Applicable to higher-dimensional lattices.

## Abstract

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 $\mathcal{O}(10)$ physical and bath sites. Moreover, since the few-body Hamiltonian only contains local interactions among a handful of sites, our work provides new 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 novel quantum devices by utilizing the many-body features.