Electronic structure and dynamics in quasi-disordered systems, from quasiperiodic potentials to quantum spin ice
Lead Research Organisation:
University of Cambridge
Department Name: Physics
Abstract
Condensed matter physics is traditionally concerned with long-range ordered systems living on crystalline lattices, and this is the domain where the central tools of the field, such as Bloch's theorem, are applicable. This picture was changed by the work of Anderson and Mott who realised that disorder and strong interactions can result in localisation, contradicting the Bloch's theorem picture of extended electronic eigenstates. Understanding the connection between disorder, strong interactions, and localisation has since led to important developments in condensed matter physics, most recently to the discovery of many-body localisation.
My project is concerned with the rich physics of "quasi-disordered" systems, that is, phases of matter between the limits of perfect order and complete, uncorrelated disorder. I focus on two examples:
1. Quasicrystals are, in fact, long-range ordered; unlike crystals, however, this order is aperiodic, and so Bloch's theorem does not apply. As such, they emerge as a middle ground between periodic crystals and disordered systems, with unique localisation and topological properties. I investigate Anderson localisation transitions of one- and two-dimensional quasicrystals which display novel kinds of critical behaviour.
2. Frustrated magnets have massively degenerate ground states: although these are disordered, the form of interactions result in subtle and unusual long-range correlated disorder and unique spin liquid phases. In particular, I investigate novel methods to understand the spin dynamics and electronic structure of spin ice systems.
My project is concerned with the rich physics of "quasi-disordered" systems, that is, phases of matter between the limits of perfect order and complete, uncorrelated disorder. I focus on two examples:
1. Quasicrystals are, in fact, long-range ordered; unlike crystals, however, this order is aperiodic, and so Bloch's theorem does not apply. As such, they emerge as a middle ground between periodic crystals and disordered systems, with unique localisation and topological properties. I investigate Anderson localisation transitions of one- and two-dimensional quasicrystals which display novel kinds of critical behaviour.
2. Frustrated magnets have massively degenerate ground states: although these are disordered, the form of interactions result in subtle and unusual long-range correlated disorder and unique spin liquid phases. In particular, I investigate novel methods to understand the spin dynamics and electronic structure of spin ice systems.
Organisations
People |
ORCID iD |
| Claudio Castelnovo (Primary Supervisor) | |
| Attila Szabo (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509620/1 | 01/10/2016 | 30/09/2022 | |||
| 1948693 | Studentship | EP/N509620/1 | 01/10/2017 | 31/03/2021 | Attila Szabo |
| Description | An important open question in the quantum physics of materials is whether disorder, which is extremely efficient at arresting the motion of individual particles, still causes insulating behaviour for many interacting particles, which is a more realistic picture of matter. I contributed to understanding this problem by designing a two-dimensional model that allows single-particle motion only in a few isolated channels: this establishes an interesting middle ground in the study of such many-body localisation, which has roused the interest of the community, and recently has established a collaboration to understand the interplay of disorder, interactions, and topology in similar models. I have also studied frustrated magnetic systems, in which competing interactions lead to exotic forms of disorder and excitations, creating a unique environment to study, both theoretically and experimentally, the consequences of strong interactions and correlations in quantum materials. I have established techniques to model a class of such systems on a computer using classical physics, making simulations more efficient and enabling access to aspects of the physics at an unprecented level of detail. I have recently started working on using neural networks to efficiently represent the complexity inherent in quantum physics. I have found that deep neural networks can prove surprisingly inadequate at representing quantum systems with substantial interference effects, and mitigated this problem by designing a novel neural network architecture that overcomes this problem in certain systems. I am now working on extending this approach into one which can reliably be used on a wider variety of problems. |
| Exploitation Route | The disordered model developed by us is experimentally realisable and provides a useful platform for studying many-body localisation in higher dimensions, both theoretically and experimentally. Our studies of quantum spin liquids also bear experimental importance in the frustrated magnetism community. The field of neural quantum states is newly arising, therefore, several important pathways are yet to be explored; these promise robust and efficient approaches to solving a variety of challenging problems in many-body quantum physics. |
| Sectors | Other |
| URL | http://www.tcm.phy.cam.ac.uk/profiles/as2372/ |