Introduction and Perspective on Tensor Network Methods for Quantum Many-Body Physics

Modeling the behavior of strongly correlated electrons calls for new paradigms in computational physics. Approaches based on single-electron physics can fail dramatically for systems with strong correlation, requiring a truly many-body perspective. Tensor networks offer a way forward, by representing the entire many-electron wavefunction, but in a compressed form which makes computations efficient. After reviewing the basics of tensor networks in mathematical language, I will discuss the settings where they are known to succeed, based on locality of interactions and limited entanglement. These arguments surprisingly extend even to finite-temperature systems, which can be accessed by recently develop tensor network algorithms, leading to an interesting hybrid quantum-classical picture and frontier results on challenging two-dimensional systems.