Understanding the behaviour of many-body quantum systems is one of the great challenges in physics. Both at and out of equilibrium, besides few exactly solvable cases, our understanding relies on numerical simulations. Unfortunately, simulating many-body quantum systems is a hard-computational problem. The standard lore is that this problem is exponentially hard in the case of simulating many-body quantum systems out-of-equilibrium. Even for simple systems, such as 1D spin chains, the current algorithms, based on the time-dependent density matrix renormalization group, are exponentially expensive in the amount of entanglement in the system. In generic out-of-equilibrium scenarios, the amount of entanglement grows linearly with time, resulting in exponentially expensive simulations. In the last years, however, the developments of the experimental techniques for controlling many-body quantum systems have pushed the exploration of out-of-equilibrium many-body quantum systems further. A critical assessment of the scope and limitations of classical numerical simulations that could help to both validate and understand the new experiments is thus necessary.;In this thesis we address this issue by unveiling the real role entanglement has in limiting our ability to simulate many-body quantum systems out-of-equilibrium. In particular, we first develop the tools for numerical computations. We build a comprehensive library for the manipulation of Fermionic Gaussian States with the programming language Julia. Then, we proceed to design and characterize a specific algorithm that allows to systematically approximate the equilibration value of local operators after a quantum quench. At the core of this algorithm there is the idea of transforming entanglement between distant parts of the system into mixture, while at the same time preserving the local reduced density matrices. Finally, we show that, for the Ising model, during the out-of-equilibrium evolution the entanglement spectrum allows us to obtain universal information. This information encodes the data of the underlying conformal field theory describing the system at the critical point, suggesting that it should be possible to adopt an analytical approach based on conformal field theories to obtain information about the out-of-equilibrium dynamics.
|Date of Award||4 Dec 2020|
- University Of Strathclyde
|Sponsors||EPSRC (Engineering and Physical Sciences Research Council)|
|Supervisor||Gian-Luca Oppo (Supervisor) & Gordon Robb (Supervisor)|