Periodic Reporting for period 1 - quasiTENS (Quantum Systems Investigated through Tensor Network States)
Reporting period: 2017-10-01 to 2019-09-30
This project gives important new insights into MBL systems and their ability to store quantum information: In the first part of the project, the length scales over which heat locally propagates in effectively one-dimensional MBL systems were calculated. In the second part, it was shown mathematically rigorously that MBL systems with certain symmetries are able to protect quantum information at non-zero temperature. Finally, the third part sheds light on the hotly debated question on whether MBL exists in effectively two dimensions. These insights will help to quantify the practical importance of MBL systems for technological applications. Moreover, novel analytical and numerical tensor network methods are developed for the description of MBL systems, further establishing the high relevance of tensor network techniques for the description of quantum matter.
1. We obtained an algorithm to exactly calculate quantities which describe how far heat can locally propagate in small MBL systems. We also found an approach to approximately determine those quantities for larger MBL systems, partially improving over previous methods.
2. Dr Wahl showed mathematically rigorously that effectively one-dimensional MBL systems with certain symmetries can protect quantum information at arbitrary temperature.
3. A code was written and used to simulate two-dimensional MBL systems. The strict existence of MBL in effectively two dimensions is debated, with theoretical work refuting it, whereas optical lattice experiments are affirmative. This apparent contradiction is resolved by the insight that strongly disordered two-dimensional systems might be perfect heat insulators (i.e. have MBL) on all experimentally relevant time scales, whereas in the theoretical limit of infinite observation times, they do conduct heat over arbitrary distances. Dr Wahl's code describes the behaviour of such systems on experimental time scales, which is the practically most relevant issue. On the available time scales, we obtained a transition from a heat-conducting regime to a heat-insulating regime as the disorder strength is increased, just as experimentally observed. The extracted transition point is consistent with the latest experiments.
All results were published and presented at various conferences and seminars.
2. Dr Wahl provided a mathematical proof for the stability of symmetry-protected topological MBL systems. This is a major advancement, as rigorous proofs are extremely rare in the field of MBL, and it further emphasises the versatility of tensor network methods.
3. A specific tensor network approach - two dimensional quantum circuits - provided the first simulations of optical lattice experiments which display two-dimensional MBL. Our results constitute the first theoretical piece of evidence for the existence of MBL in two dimensions on experimental time scales.