Theory of quantum matter in and out of equilibrium

Lead Research Organisation: University of Oxford
Department Name: Oxford Physics


The student [Samuel Garratt] will study topical problems in the theory of quantum matter in and out of equilibrium. In the initial phase, his work will focus on simple lattice models of chaotic quantum many-body systems. In later phases, his work may include studies of spin liquids.

The near-term aim of the work is to use analytically tractable models and numerical calculations to examine the validity and limitations of the Ergodic Thermalisation Hypothesis. A specific objective is to relate the phenomenon of operator spreading to eigenstate correlations, and to discover whether there are potential measurement protocols that would expose these correlations in experiment.

Longer-term objectives may include understanding theoretically the experimental signatures of spin liquid phases as studied in inelastic neutron scattering experiments of geometrically frustrated magnets.

The work addresses the EPSRC Grand Challenge theme of Emergence and Physics Far from Equilibrium. It is within the Physical Sciences research theme and relates to questions that arise in the research areas of Cold atoms and molecules, and of Condensed matter: magnetism and magnetic materials.

There are currently no companies or collaborators outside Oxford University involved in this project.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509711/1 01/10/2016 30/09/2021
1946484 Studentship EP/N509711/1 01/10/2017 31/03/2121 Samuel Joshua Garratt
Description Quantum mechanical systems can be completely characterised by the set of states which do not change with time. As a concrete example, we could think about the state of a hydrogen atom, composed of one electron and one proton. The stationary states in this case were historically visualised as a specific set of orbits of the electron around the proton. If we prepare the electron in one of these so-called stationary states, it will remain in that state for all time, and this has implications for the outcomes of measurements. In fact, knowledge of these stationary states allows for exact predictions of a system's behaviour.

In practice, few quantum systems are as simple as the hydrogen atom, and in the description of physical matter such as metals we should think about collections of many interacting quantum particles. Physically, we can restrict ourselves to thinking about systems which are 'local'. That is, systems composed of particles which can only interact with particles which are nearby in space.

We have explored the effect of local interactions on the properties of stationary states, and have discovered detailed correlations between them. Our work fits within the broader theme of understanding how quantum mechanical systems can reach an equilibrium (in the same sense as the temperature of a cup of coffee decreasing with time), and our result has implications for the rate at which different properties of these systems equilibrate.
Exploitation Route To give an example, the analysis techniques developed in the publication "Goldstone modes in the emergent gauge fields of a frustrated magnet" could be applied to a large number of materials which exhibit spin liquid phases and at low temperatures freeze into glass phases. This would allow for predictions of thermal properties of these systems (for example, the heat capacity) as well as the results of low-energy neutron scattering experiments.
Sectors Education,Other

Title Hydrodynamic theory of spin waves in frustrated magnets 
Description We have developed and applied a combination of methods to model the low-energy dynamics of a class of magnets. Our approach amounts to a set of analysis techniques for the numerical data generated from a well-established calculation technique, linear spin-wave theory. 
Type Of Material Computer model/algorithm 
Year Produced 2019 
Provided To Others? Yes  
Impact From our analysis we have been able to make predictions for the behaviour of a class of magnets known to host so-called spin liquid phases, and have offered interpretations of pre-existing experimental data. 
Description Rudolf Peierls Centre for Theoretical Physics 
Organisation University of Oxford
Department Rudolf Peierls Centre for Theoretical Physics
Country United Kingdom 
Sector Academic/University 
PI Contribution I have worked on a number of problems in theoretical condensed matter physics. These have broadly been between two areas to date: frustrated magnetism and many-body quantum chaos. In order to tackle these problems, I have learnt a wide range of mathematical and numerical techniques, ranging from field theory to parallel programming. I have also prepared and delivered a number of talks and poster presentations, both locally and at conferences.
Collaborator Contribution The Rudolf Peierls Centre for Theoretical Physics has provided me with IT equipment, a shared office, and access to the high performance compute cluster Hydra. This department has organised seminars, which have exposed me to a wide field of research, and has also provided many opportunities for academic discussion.
Impact Through this partnership I have published a paper in Physical Review B with my supervisor, "Goldstone modes in the emergent gauge fields of a frustrated magnet". There is also significant ongoing work on a class of models for chaotic quantum many-body systems.
Start Year 2017
Description Morning of Theoretical Physics 
Form Of Engagement Activity Participation in an open day or visit at my research institution
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Public/other audiences
Results and Impact The Rudolf Peierls Centre for Theoretical Physics hosts outreach events for alumni of the University of Oxford's physics department, under the name of Saturday Mornings of Theoretical Physics. The majority of these alumni have left physics following their first degrees, although have maintained an interest in the years or decades since graduation; one of the purposes of the event is to keep these people up to date on modern developments in the science. The particular event which I attended featured a series of lectures showcasing work on superfluids and superconductors, as well as several breaks for discussions with the attendees. For those of us still working within the university, these discussions are very useful for understanding the different sectors which trained physicists find themselves in. On the other hand, the attendees were all very interested in hearing about the particulars of our research in theoretical physics.

Throughout the day I spoke to the alumni about their own career paths following a first degree in physics, and explained the ideas behind my own research.
Year(s) Of Engagement Activity 2017