Quantum thermal states on the lattice: correlations, area laws and tensor network representations

January 14, 2021
4:00pm to 5:00pm


Specialist level
Alvaro Martín Alhambra
Max-Planck-Institut fur Quantenoptik, Garching



In the past couple of decades, one of the biggest triumphs of quantum information theory has been the characterization of correlations of ground states of quantum many-body systems. This usually takes the form of area laws for the entanglement entropy, which can be rigorously linked to the efficient classical simulability of ground states. A similar intuition applies to thermal states, which are known to obey an area law for the quantum mutual information. Here, we will present the tightest area laws known for quantum thermal states on lattices, with an improved dependence on the temperature. These involve the mutual information, as well as other information-theoretic measures of correlations, such as the entanglement of purification. While the direct connection between thermal area laws and simulability is still unknown, we show how the same techniques that lead to improved area laws also lead to provably efficient tensor network algorithms for thermal states. In doing so, we provide the first rigorous quasilinear-time algorithm for one-dimensional models, which closely matches what is found in heuristic numerical approaches.