Alvaro Alhambra

OS Mathematical Physics November 11 16:00

Quantum states at equilibrium: thermal states, tensor networks and area laws

The thermal or Gibbs state is one of the most ubiquitous states of quantum matter, which appears when quantum systems come to equilibrium with their surrounding environment. Beyond its wide interest for physics, it also notably appears in the study of computational complexity and algorithms.

The most interesting and complex of these occur when the system at hand is composed of a large number of particles, such as in a regular lattice. In this talk, we will discuss how these states can be described classically, most notably through tensor network methods. Their effectiveness is related to how correlations are distributed in these systems at equilibrium. We also describe these through the so-called area law, which states that these correlations are localized within the system at hand. In doing so, we will illustrate one of the more successful ways of efficiently describing quantum states via classical algorithms.