The quantum many body problem has been at the heart of much of theoretical and experimental physics over the past few decades. Even though we have understood the fundamental laws that govern the behavior of elementary particles for almost a century, the issue is that many interesting phenomena are the result of the complex collective behavior of many interacting quantum particles. In the words of condensed matter theorist Philip W. Anderson: “More is different.”
Since simulating models with this many degrees of freedom exactly is entirely intractable computationally, approximations such as perturbation theory have been widely used to gain insight into their behavior. However, this approach requires that the theory is close to non-interacting, which renders it unusable in many cases of physical interest.
More recently, an approach based on insights from quantum information theory has shown great promise for tackling these non-perturbative regimes. It was understood that the low-energy quantum states of local models display relatively little entanglement compared to generic quantum states, a feature that is exploited in tensor network methods.