Tensor Networks: a quantum-information perspective on numerical renormalization groups

TL;DR

This paper discusses how tensor networks, inspired by quantum information theory, provide efficient variational representations for many-body quantum states, enhancing numerical methods for complex quantum problems.

Contribution

It introduces a perspective connecting tensor networks with quantum information, highlighting their role in improving numerical renormalization group techniques for quantum many-body problems.

Findings

Tensor networks effectively represent quantum states with entanglement.

Quantum-information tools enhance numerical approaches to condensed matter.

Tensor networks facilitate addressing many-body quantum correlations.

Abstract

Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful strategy to work around this obstacle was to develop numerical methods based on the well-known theoretical renormalization group. In recent years, it was realized that quantum states engineered via numerical renormalization allow a variational representation in terms of a tensor network picture. The discovery provided a further boost to the effectiveness of these techniques, not only due to the increased flexibility and manipulability, but also because tensor network states embed a direct interface to the entanglement they carry, so that one can directly address many-body quantum correlations within these variational ansatz states. This lead to the application of several numerical tools, originally developed in the field of quantum-information, to approach condensed matter problems.