Research Project Summaries

Supervisor: Peter Haynes

The simulation of quantum materials and molecules have been identified as promising early applications of quantum computers due to the equivalence of entanglement and the correlation of the motion of electrons [1]. The so-called era of Noisy Intermediate-Scale Quantum (NISQ) technology [2] is just around the corner and promises universal quantum computing with 50–100 qubits that are capable of performing tasks beyond classical computers but limited by noise in the number of quantum gates that can be connected into a circuit to execute a given quantum algorithm. Simulations of small molecules and simple models of materials were demonstrated on six-qubit hardware [3] and machines with over 100 qubits are now available. This project will involve a collaboration with Dr Johannes Lischner in Materials. We will explore quantum embedding as an approach [4] to study localised defects in crystals and apply emerging algorithms for quantum computers such as variational quantum eigensolvers to models parametrised by first-principles simulations on classical computers.

[1] Richard Feynman, Int. J. Theor. Physics 21, 467–488 (1982)
[2] John Preskill, arXiv:1801.00862
[3] Abhinav Kandala et al., Nature 459, 242–246 (2017)
[4] Christian Vorwerk et al., Nat. Comput. Sci. 2, 424 (2022).

Supervisor: Arash Mostofi

Materials underpin every modern technology and are ubiquitous in our lives, from components that make up jet aircraft, to transistors in computer chips. Our research group (www.mostofigroup.org) is dedicated to the application and development of theory and computational simulation tools for understanding and predicting the behaviour of materials from the atomic length-scale up. We use quantum mechanics to describe systems of interacting electrons and nuclei, an approach that is often called ab initio, or first-principles, and which is invaluable for providing microscopic insight into the macroscopic behaviour of materials.

A key focus of our work is to push towards developing predictive understanding of real materials and devices, i.e., structurally complex and heterogeneous systems that correspond more closely to reality. Current lines of research in the group span a broad range of phenomena and materials, including:

• complex oxides (multifunctional properties, symmetry-breaking, superconductivity)
• 2D materials (electronic and optical properties, defect and adsorbate engineering)
• Moire materials (strong electron correlations, superconductivity, excitons, topology)
• polymer nanocomposites (mechanical strength and failure mechanisms)
• development of methods and software for electronic structure simulations [ONETEP (www.onetep.org); Wannier90 (www.wannier.org)]

PhD project topics are available in all of the above areas. Interested candidates are encouraged to look at the group’s recent publications at www.mostofigroup.org and to contact a.mostofi@imperial.ac.uk to discuss projects and funding opportunities.

Supervisor: Matthew Foulkes

In 2020, working with collaborators from DeepMind Ltd., we helped introduce FermiNet [1], a new way to solve the Schrödinger equation for systems of many interacting electrons. The totally antisymmetric many-fermion wavefunction is represented as a neural network, the parameters of which are optimized according to the quantum mechanical variational principle without the use of externally generated data. This proved remarkably successful. We are now using neural wavefunctions to study larger molecules, investigate the Wigner crystallization of the interacting electron gas [2] , and look for quantum phase transitions in real solids. The aim of this project is to further develop the neural wavefunction approach and use it to investigate more strongly correlated systems, such as magnets and superconductors.

[1] D. Pfau et al., Phys. Rev. Research 2, 033429 (2020); J.S. Spencer et al., arXiv:2011.07125 (2020).
[2] G. Cassella et al., arXiv:2202.05183, accepted for publication in Phys. Rev. Lett. (2022).

Supervisor: Paul Tangney

Band theories break down when strong interactions cause strong correlations. The field of strongly-correlated electrons is among the most interesting and important areas of physics because strong correlation causes cooperative phenomena, such as superconductivity. Strongly interacting phonons are much less well studied because, until recently, we have lacked good sources of radiation in the terahertz energy range that phonons inhabit. This so-called "THz gap" is now closing and a vast array of THz devices is on the horizon if we can understand how THz radiation interacts with materials well enough to control it. Fortunately, we have found a way to study arbitrarily-strong phonon interactions with higher accuracy than has ever been possible for electrons. We can map the distribution of a solid or liquid's energy in reciprocal spacetime (frequency-space) and use it to study problems such as the breakdown of band theory in multiferroics, resonances in THz device components, and localized "rattler modes", which can decimate a material's thermal conductivity. In this project you will use this new method to solve one or more problems of fundamental and/or technological importance, and help to develop it further.

Supervisor: Kim Christensen

Project Summary: Atrial fibrillation (AF) is the most common cardiac arrhythmia but continues to suffer poor treatment success rates. One promising route to developing personalised, patient-specific treatment strategies is to augment computational models of the atria with clinical data derived from a patient. We have pioneered such a novel approach, combining theoretical physics techniques with clinical expertise, by studying how heart muscle fibres in the atria cluster. This project would advance these techniques further, focussing on the robustness of results, critical for the potential use of the approach to inform personalised clinical treatment of AF.

The challenge: There is an urgent need to master chronic diseases as the population ages. Among the greatest challenges is the disrupted cardiac electro-mechanics of the diseased heart causing atrial fibrillation. AF affects about 35M people worldwide and is the single biggest cause of stroke. Current treatment strategies involve destruction by heating (ablating) discrete areas of atrial heart muscle.  However, even with more than a decade of “learning-while-burning”, the target areas for ablation cannot be identified reliably. In patients with persistent AF, success rates remain at 30%. Failure to improve the success rate is due to the lack of mechanistic understanding of AF. Clinical ablation is still based on “sledgehammer”, “one-size-fits-all” empiricism, resulting in lengthy and risky procedures, with the ablation targeted toward fixed anatomical areas (pulmonary veins). There is an urgent need for a deeper understanding of the specific underlying AF mechanism in individual patients.

It has become evident that significant progress will come from understanding the intricate relationship between the electrical activity (function) and the underlying heart muscle architecture (structure). Uniting Imperial College’s
theoretical physics and clinical medical expertise, we have pioneered a novel approach to model AF where we integrated the dynamics on a network mimicking the branching structure of atrial heart muscle [1,2]. Recently, however, we
have managed to use the underlying heart muscle fibre maps derived directly from clinical measurements to develop a personalised AF risk map of the heart [3]. The proposed project will advance these techniques, focusing on the
robustness of predicting personalised AF risk areas from heart muscle fibre maps. Robustness is vital and necessary for a successful use in a personalised clinical treatment of AF.

[1] K. Christensen, K.A. Manani, and N.S. Peters "Simple Model for Identifying Critical Regions in Atrial Fibrillation" Phys. Rev. Lett. 114, 028104 (2015).
[2] M. Falkenberg, A.J. Ford, A.C. Li, R. Lawrence, A. Ciacci, N.S. Peters and K. Christensen, "Unified Mechanism of Local Drivers in a Percolation Model of Atrial Fibrillation" Phys. Rev. E 100, 062406 (2019).
[3] Falkenberg, Peters, Ng , Christensen et al., "Identifying locations susceptible to micro-anatomical re-entry using spatial network representations of atrial fibre maps", Computing in Cardiology (inC) (2019).

 Supervisor:  Kim Christensen

The increasing availability of empirical data has revealed important insights on the topology of real systems. Typically, real-world systems are characterized by irregular topologies where a small fraction of their components establish direct interactions while the remaining majority indirectly affect one another through chains of direct interactions. These
topological features can be mathematised by networks, a powerful modelling paradigm in the field of complex systems. The science of network has proven very successful for the investigation of phenomena in a variety of complex systems, but it has until recently been limited by studying only the pairwise interactions between system constituents. Higher-order networks allow for group interactions to be represented and it turns out that these more general networks can exhibit a richer and more realistic phenomenology than their simplistic pair-wise counterparts. There are many exciting areas in the study of for example social dynamics that are open for further investigation using higher-order networks, for example, in relation to social contagion in relation to opinion dynamics and consensus formation or the dynamics of epidemics. A PhD in this area would be co-supervised by Dr. Giovanni Petri, researcher at the Centre for Artificial Intelligence (CENTAI), Torino, Italy (https://lordgrilo.github.io/).

[1] Iacopo Iacopini, Giovanni Petri, Alain Barrat & Vito Latora, Simplicial Models of Social Contagion, Nature Communications 10 2485 (2019) 
[2] Iacopini, Petri, Barronchelli, Barrat, “Group interactions modulate critical mass dynamics in social convention”, Commun Phys. 5, 64 (2022) 

Supervisor: John Pendry

Most of optics is concerned with materials that may be elaborately structured in space but are static in time. Many new phenomena appear when the time dimension is added. This may not mean that the materials themselves move, just that their local properties change with time. A simple example might be a grating modulated in time so that it appears to move. Its velocity can be anything we like because there is no physical motion. When the velocity breaks the light barrier many novel phenomena appear such as squeezing light into intense pulses. Even in the absence of an external source of radiation these 'transluminal structures' as they are known can generate their own light through a quantum mechanical process akin to Hawking radiation. We are currently exploring with the EXSS group the possibility of experimental realisation. The aim of the PhD project is to further explore these new phenomena.

Supervisor: Frank Schindler

Recent years have seen numerous classical realizations of topological phases initially discovered in a quantum context. They rely on a direct analogy between the single-electron Schrödinger equation and the linearized differential equations governing waves in metamaterials and photonic crystals [1]. The Ph.D. project investigates topological phases in such platforms beyond the linear regime: This limit does not have a quantum analog and so warrants the development of an independent theoretical formalism. We will start by studying localized nonlinear excitations (solitary waves, breathers) in the presence of band topology [2]. This project is open-ended: all known intrinsically nonlinear phenomena (bifurcations, multi-stability, chaos, …) have an unexplored counterpart in topological systems, and there may exist new nonlinear effects enabled by topology. As labs worldwide are just beginning to explore nonlinear topological systems, this Ph.D. project is ideal for students interested in close contact with experiments.

[1] Kim, Minkyung, Zubin Jacob, and Junsuk Rho. "Recent advances in 2D, 3D and higher-order topological photonics." Light: Science & Applications 9 (2020): 130.
[2] Jürgensen, Marius, and Mikael C. Rechtsman. "Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps." Phys. Rev. Lett. 128 (2022): 113901.

Supervisor: Frank Schindler

Moiré materials like twisted bilayer graphene provide a highly tunable experimental platform for probing flat band systems at the intersection of topological band theory and strong correlations [1]. This Ph.D. project focuses on comprehensively understanding the bound state spectrum in such systems, e.g., that of excitons [2]. Like a hydrogen atom, an exciton is a bound state of a negatively charged electron and a positively charged hole. However, unlike the hydrogen problem, the kinetic term in the exciton Hamiltonian is set by the crystalline band structure, not the Schrödinger equation in vacuum. We will use analytical reasoning and numerics on simple toy models to explore the imprints that a topologically nontrivial kinetic term leaves on excitons and other bound states like trions and Cooper pairs. This project will be an entry point to one of the major open problems in condensed matter theory: the systematic understanding of topological effects in strongly interacting systems.

[1] Andrei, Eva Y., et al. "The marvels of moiré materials." Nature Reviews Materials 6 (2021): 201-206.
[2] Kwan, Yves H., et al. "Exciton band topology in spontaneous Quantum Anomalous Hall insulators: Applications to twisted bilayer graphene." Phys. Rev. Lett. 126 (2021): 137601.

Supervisor: Frank Schindler

This Ph.D. project lies at the intersection of condensed matter and quantum science. Besides the application of concepts from quantum information, such as entanglement entropy and contextuality, to condensed matter, we are witnessing the emergence of novel NISQ-era many-body systems like Rydberg atom arrays and digital quantum computers. These systems can be understood using tools from condensed matter physics. For instance, quantum circuits built from unitary gates display measurement-induced phase transitions that can be described by non-Hermitian Hamiltonians [1]. This observation allows us to realize intrinsically non-Hermitian "point gap" topology – a new paradigm for dynamical phases of matter without Hermitian counterparts [2] – in the context of quantum circuits. The Ph.D. project will be centered around systematically deriving this correspondence and testing it in real-world quantum simulators. An exciting follow-up question will be classifying the dynamical phases of quantum circuits by symmetry and topology.

[1] Fleckenstein, Christoph, et al. "Non-Hermitian topology in monitored quantum circuits." Phys. Rev.  Research 4 (2022): L032026.
[2] Okuma, Nobuyuki, et al. "Topological origin of non-Hermitian skin effects." Phys. Rev. Lett. 124 (2020): 086801.