Free-particle descriptions of topological quantum matter and many-body localisation

Lead Research Organisation: University of Leeds
Department Name: Physics and Astronomy


The notion of a free particle is at the heart of theoretical physics. This simple notion allows us to describe a wide variety of systems in nature: for example, we explain atoms as collections of free electrons, and electromagnetic radiation as a set of free harmonic oscillators. But in real world, particles also interact with one another. Interactions have particularly striking effects in quantum systems, where they lead to long-range correlations and quantum entanglement. This makes the theoretical description of quantum many-particle systems very challenging.

At the same time, there is growing interest in using interactions as a resource that could revolutionise technology. Modern technology has been based on quantum materials such as semiconductors, superconductors and magnets, which form the building blocks of lasers, transistors, computers, etc. In recent years, there has been a shift towards making such devices more powerful by exploiting the full power of quantum physics, which will be achieved by utilising quantum correlations and entanglement. Thus, at this stage, there is a compelling theoretical and practical need to understand and manipulate the effects of interactions in quantum systems.

This proposal will investigate two physical systems of current interest where interactions lead to novel physical phenomena:

(1) Topological phases of matter, which include Majorana and parafermion spin chains, spin liquids and fractional quantum Hall states. These phases form as a result of "non-perturbative" effects of interactions, and cannot be described as a collection of free electrons. This gives them unique properties such as robustness under arbitrary, but sufficiently weak, perturbations. Because of this special rigidity, topological quantum matter is being used as a building block of more robust quantum technologies, designed to be resilient to environmental perturbations.

(2) Non-equilibrium dynamics and thermalisation in quantum many-particle systems. Typical quantum systems are ergodic: they quickly reach thermal equilibrium because the interactions between their constituent particles quickly erase the memory of the system's initial condition. However, recent work on "many-body localisation" shows that there exist large classes of strongly-disordered, interacting quantum systems which fail to reach thermal equilibrium. These systems are thus non-ergodic, which means that quantum effects in them can persist for unusually long times, thus providing another route of protection for quantum technology.

In this proposal we will develop a new approach to describe interaction effects in strongly-correlated phenomena including topological phases of matter and many-body localisation. We will advance the modelling of many-body systems in random environments using state-of-the-art numerical simulations. Our theoretical investigation on the effects of topology and many-body localisation in quantum matter will impact several experiments on cold atoms, trapped ions, defects in solids, etc. Finally, we will explore the possibility of realising phases with topological order in random environments, and propose schemes for quantum information storage and processing with an enhanced stability against thermalisation.

Planned Impact

Our interdisciplinary research programme on interaction effects in quantum systems will have immediate impact on quantum information, AMO, condensed matter and statistical physics community. To achieve these goals and maximise impact, we have assembled a team of six Project Partners and Visitors from the leading institutions in the UK, US, China, and Switzerland. These researchers span fundamental theory, experiment and industry. Their continuous participation in the project will maximise the dissemination of our results in the communities of photonic quantum simulations, solid-state experiments, strongly-correlated and topological quantum systems.

To generate impact across academia, we will closely collaborate with our experimental Project Partners in the UK (Sir Michael Pepper, UCL; NQIT, Oxford) and overseas (Gang-Can Guo, Hefei). By developing state-of-the-art computer algorithms that combine machine learning with tensor networks, we will introduce a new research direction in the UK that connects many-body physics with computer science. These efforts will promote Leeds (and the UK) to a global centre for topology and many-body localisation (MBL) in quantum systems. As key players in recent developments in topological phases and MBL, the PI and Co-I are ideally placed to achieve this at a critical time when the UK research on MBL is gaining momentum (Nottingham, Lancaster, UCL, Oxford, experiments in Cambridge and UCL), and the topic has become nationally visible due to the recent Royal Society meeting (02/2017), organised by the Co-I.

In the longer term (five to ten years), impact will be generated by our novel approach that brings together interactions, topology and non-ergodicity to create robust quantum technologies. Our approach thus ties in with two of EPSRC's Grand Challenges -- `Quantum Physics for New Quantum Technologies' and `Emergence and Physics Far From Equilibrium'. Our end goal (non-ergodic topological quantum memories) is closely aligned with our Project Partner, the Oxford Hub NQIT and the UK Quantum Technology Programme. Our approach, which exploits exotic phases of matter and non-equilibrium physics to achieve protection of quantum information, is complementary to the Quantum Hubs. Thus, our proposal will generate impact as a link between Quantum Hubs and condensed matter physics community. Further connections with industry will ensue from collaboration with our Visiting Researcher, Sonika Johri (Intel Research). Support from the University of Leeds Research and Innovation Service, including the High Value Engineering and Commercialisation teams, will assist with making new industry contacts in addition to those already engaged with quantum technologies in the UK (e.g., Toshiba in Cambridge) and internationally (e.g., Intel, Microsoft and IBM in the US).

Finally, we will also use the following mechanisms to reach out to wider audience: (1) publications in high-profile journals, including a review article; (2) open-source software repository; (3) talks at major domestic and international conferences; (4) organisation of three Symposia (including a workshop and an international conference) which will showcase our results and bring high-profile researchers with complementary expertise to Leeds, e.g., Duncan Haldane (Princeton), Ignacio Cirac (Max Planck), Mikhail Lukin (Harvard), etc.; (5) training of a PDRA in scientific and transferrable skills, and engagement of roughly twenty MPhys/BSc students and ten students on Summer Research Placement; (6) outreach activities, which we will perform with consideration for the Responsible Innovation Framework of EPSRC. The Co-I, as a School Liaison Officer, will use the existing outreach infrastructure and boost it with additional programmes (e.g., "Disorder Day") based on this proposal. We will continue to promote our research in the media and bridge the gap with the humanities and arts community, with our planned physics/dance performances.
Description Topological edge currents are probably the most striking manifestation of topological phases of matter. We recently analysed the physics of currents in Haldane's honeycomb lattice that can be implemented in the laboratory with optical lattices. We found that the direction of the edge currents depends on the sign of both the Chern number of the model as well as the applied chemical potential that breaks the particle-hole symmetry of the model. Alongside the edge currents, transverse currents can emerge in the bulk of the system whenever the chemical potential is varied in space, even if it does not cause a phase transition. The interplay between edge and bulk currents produced by the harmonic trapping of the atomic cloud produces unique signatures that can be revealed in time-of-flight images.
Exploitation Route Mainly scientific advances and collaborations.
Sectors Digital/Communication/Information Technologies (including Software),Energy

Description Recently I have my Inaugural lecture for my professorship. My lecture was open to the public and it had more than 150 people in the audience including students from schools. There I presented in a pedagogical way my recent findings of my research.
First Year Of Impact 2018
Impact Types Cultural

Title Supporting Data for Fractional Quantum Hall Effect in Monolayer WSe2 
Description Source data for the figures in the manuscript "Odd- and even-denominator fractional quantum Hall states in monolayer WSe2" 
Type Of Material Database/Collection of data 
Year Produced 2020 
Provided To Others? Yes  
Title Supporting data for "Many-body Hilbert space scarring on a superconducting processor" 
Type Of Material Database/Collection of data 
Year Produced 2022 
Provided To Others? Yes