Strongly-entangled topological matter

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

Abstract

This project will advance the theoretical understanding of the new type of matter called topological matter, which emerges in strongly-interacting quantum systems. By performing numerical simulations, the project will investigate fundamental properties of topological matter, such as its geometry and quantum entanglement. This will provide feedback to experiments on how to realise new topological matter in materials like bilayer graphene.

Topology is a branch of mathematics that describes properties of objects which do not change under local perturbations. For example, a soccer ball is the same as a rugby ball because we can slowly stretch one into the other. Curiously, in certain semiconductor materials (like the ones used to build transistors and solar cells) there are phases of matter which are also insensitive to local perturbations. This topological matter is very different from ordinary matter (like water or ice) because it represents a collective state that emerges when many quantum particles interact, similar to superfluids and superconductors.

Topological matter forms a very active field of modern condensed matter physics, for at least three reasons. First, topological matter has been seen in many beautiful experiments, starting with the original discovery of the fractional quantum Hall effect in the 1980s. Second, topological matter represents a major challenge for theoretical physics, because it cannot be explained by traditional solid state theories based on "symmetry breaking". Third, topological phases have very rich and unexpected properties, for example their low-energy excitations behave as "quasiparticles" which are more general than the Standard Model of particle physics (i.e., they are neither bosons nor fermions). Recent discovery of one such quasiparticle - the "Majorana fermion" - has attracted much public attention, and current research focuses on harnessing the power of the Majoranas to perform quantum computing. Thus, topological matter may have an important role to play in future quantum technologies.

This project will advance the understanding of topological matter in the systems of strongly interacting particles, where many fundamental problems remain open. The project will investigate the role of geometry in topological matter, which determines their elastic and thermal properties. Furthermore, the project will investigate quantum correlations ("entanglement") in topological matter, with the goal of understanding how topological order could be enabled to survive at high temperatures. This would represent an important practical advance as most of topological matter is currently realised only at cryogenic conditions. Finally, the project will establish close connection to experiments that seek to realise topological matter in new materials. By developing and applying new numerical algorithms, the project will identify interaction-driven topological phenomena that can be experimentally accessed in bilayer graphene, in particular the phases that host the Majorana fermions or even more exotic "parafermion" quasiparticles.

Planned Impact

Physics has traditionally been reductionist: to understand something, we divide it into smaller parts. However, some of the most interesting phenomena in modern condensed matter physics cannot be understood in this way because of interactions between particles. Topological phases of matter are such emergent phenomena. The research into topological matter currently lies at the frontier of modern physics; for example, this has been acknowledged by the EPSRC as one of the "Grand Challenges", and also by the international collaboration on the "Many-Electron Problem" supported by the Simons Foundation.

Apart from contributing to a fundamental challenge of theoretical physics, this project will also impact the experiments in two different ways, which may lead to technological applications in the long term. First, the project will benefit from being at the interface between condensed matter physics and quantum information. A synergy between these two areas is expected to be the key for designing robust quantum devices for real world applications. The proposal focuses on bilayer graphene, which connects with the UK's focus on graphene technology. Second, although the research in this proposal is theoretical, one of its goals is to perform extensive numerical modeling of real systems and thereby guide the experiments towards realising topological matter. In particular, the project aims to provide feedback to experiments on how to realise complex topological states whose quasiparticles (the parafermions) may be vital for designing fault-tolerant quantum computers which may revolutionise future technology.

The impact of this project will foremost be generated by establishing my group in Leeds as a hub for research on topological phenomena in strongly-interacting systems. In particular, this will be achieved by developing computational methods based on exact diagonalisation and tensor networks. This will strengthen the UK position in state-of-the-art numerical simulations of topological systems, which is currently not on the level of the US, Canada and Europe (particularly Germany).

The impact and visibility of this research will be achieved via the following routes.

1. The dissemination plan consists of several high-impact publications (of the level of Phys. Rev. Lett. or Phys. Rev. X). Additionally, a review article on topological phenomena in bilayer graphene, co-authored with at least one experimental colleague, is planned to maximise the impact.

2. Invited talks at workshops, conferences and academic institutions, in which I have extensive track-record. In February 2017, I am also co-organising a large international meeting funded by the Royal Society, together with colleagues at Oxford (Arijeet Pal, Steve Simon), Cambridge (Ulrich Schneider) and London (Sir Michael Pepper). This meeting will be an additional opportunity to generate international impact.

3. A project-dedicated webpage which will contain, on the one hand, a popular introduction and summaries to the publications. On the other hand, the page will be an interface to an open-source software repository. My existing software is GPL-licensed and available on my homepage.

4. Train a PDRA in both scientific and transferrable skills, and contribute to the education of students (especially via summer research projects).

5. Engage young audiences through UCAS School Open Days, by participating at Leeds Science Festival, and on a regular basis via social media (Twitter, Facebook pages).

6. Develop personal contacts and collaborations within the UK, and bring the international experts for shorter and longer term stays in Leeds. In the second year of the grant, I will organise a workshop on many-body topological phenomena. The workshop will fit naturally into the existing framework of the Leeds Symposia on Topological Quantum Computation (whose 19th session I have co-organised this year), which will also minimise its cost on this project.
 
Title Leeds Light Night 2018 
Description As part of Leeds Light Night 2018, Spanish artists Hotaru Visual Guerrilla have taken inspiration from our research into quantum chaos to explore the beauty of chaos using light, sound and movement. 
Type Of Art Artistic/Creative Exhibition 
Year Produced 2018 
Impact The performance was featured in national media: https://leeds-list.com/culture/21-events-to-make-this-years-light-night-the-best-one-yet/ https://www.yorkshireeveningpost.co.uk/news/leeds-light-night-makes-spectacular-return-to-city-centre-1-9381988 also mentioned on BBC 1 Yorkshire and North Midlands (https://article.signalmedia.co/0e680991-a473-38aa-8277-60f6a2d92abf?u=f9157888-8859-4dec-89cc-3ce73fc5de40?igin=docx), and regional radio stations such as Radio Aire and Magic FM. 
 
Description (1) The formulation of "generalized pseudopotentials" to describe anisotropic fractional quantum Hall states [Phys. Rev. Lett. 118, 146403 (2017)]. This is a key theoretical development that extends Haldane's seminal work in 1983 to allow for the microscopic description of fractional quantum Hall states in tilted magnetic fields and materials with band mass anisotropy. (2) The discovery of "interaction distance" -- a new method to quantify the effect of interactions on quantum many-body states including ones with topological order [Nature Communications 8, 14926 (2017)]. This work introduces a new theoretical concept to measure the complexity of quantum states according to "how interacting" they are, which will pave the way for a new theoretical perspective and more efficient numerical simulations of quantum many-body systems. (3) Experimental proposal for observing "anyons" (particles that form the building blocks of topological phases of matter) using scanning tunnelling microscopy [Phys. Rev. X 8, 011037 (2018)]. This proposal might lead to a direct experimental observation of anyons through their distinct STM signature, thus making key progress in the field of topological phases of matter and their use in quantum computation. (4) A discovery of the new physical phenomenon -- "quantum many-body scars" [Nature Physics 14, 745 (2018)]-- which explains the observed non-ergodic dynamics in recent quantum simulators built from Rydberg atoms.
Exploitation Route The key findings (1) and (2), which introduce new theoretical concepts, are already cited and being used by other researchers in academic community. The finding (3) is expected to motivate experimental search for anyons using STM techniques. If signatures of anyons are indeed detected, this will inspire efforts to controllably manipulate them and study their properties, paving the way for their use in fundamental research on quantum computation and applications to quantum technologies. The finding (4) has already inspired a variety of follow-up works by groups at Princeton, Harvard, Boston University, Maryland, Zurich.
Sectors Electronics

 
Description Our research on quantum many-body scars has been publicised in the media, both domestically and internationally, and it has inspired a Spanish artist's performance during Leeds Light Night 2018 [further details are given in the Arts section of the summary].
First Year Of Impact 2018
Sector Culture, Heritage, Museums and Collections
Impact Types Cultural

 
Description Free-particle descriptions of topological quantum matter and many-body localisation
Amount £466,889 (GBP)
Funding ID EP/R020612/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Academic/University
Country United Kingdom
Start 05/2018 
End 04/2021
 
Description Royal Society Research Grants
Amount £15,000 (GBP)
Funding ID RG160635 
Organisation The Royal Society 
Sector Academic/University
Country United Kingdom
Start 03/2017 
End 02/2018
 
Description Leeds 
Organisation University of Leeds
Country United Kingdom 
Sector Academic/University 
PI Contribution My group has contributed to developing a new theoretical framework to characterise interaction effects on quantum many-body systems.
Collaborator Contribution The group of Jiannis Pachos has initiated the project and continues to lead the main direction of the project.
Impact Christopher J. Turner, Konstantinos Meichanetzidis, Zlatko Papic, Jiannis K. Pachos, Nature Communications 8, 14926 (2017); Konstantinos Meichanetzidis, Christopher J. Turner, Ashk Farjami, Zlatko Papic, Jiannis K. Pachos, Phys. Rev. B 97, 125104 (2018); Jiannis K. Pachos, Zlatko Papic, SciPost Phys. Lect. Notes 4 (2018).
Start Year 2016
 
Description Princeton 
Organisation Princeton University
Department Department of Physics
Country United States 
Sector Academic/University 
PI Contribution An on-going collaboration which focuses on the investigation of theoretical properties of non-Abelian topological states in the fractional quantum Hall effect, and their experimental realization in graphene systems or experimental probes via techniques such as STM. I have proposed theoretical models of these phenomena and performed numerical simulations.
Collaborator Contribution Theoretical analysis has been performed jointly with other theory partners at Princeton University (Michael Zaletel) and University of Pittsburgh (Roger Mong), who have contributed expertise on independent numerical techniques (DMRG). More recently, we have made stronger connections with our experimental partners, who provided expertise on the physics of graphene (Andrea Young at UCSB) and STM techniques (Ali Yazdani at Princeton University).
Impact Maissam Barkeshli, Chetan Nayak, Zlatko Papic, Andrea Young, Michael Zaletel, Phys. Rev. Lett. 121, 026603 (2018); Zlatko Papic, Roger S. K. Mong, Ali Yazdani, Michael P. Zaletel, Phys. Rev. X 8, 011037 (2018); : Michael P. Zaletel, Scott Geraedts, Zlatko Papic, Edward H. Rezayi, Phys. Rev. B 98, 045113 (2018).
Start Year 2016
 
Description Princeton 
Organisation University of California, Berkeley
Department School of Public Health Berkeley
Country United States 
Sector Academic/University 
PI Contribution An on-going collaboration which focuses on the investigation of theoretical properties of non-Abelian topological states in the fractional quantum Hall effect, and their experimental realization in graphene systems or experimental probes via techniques such as STM. I have proposed theoretical models of these phenomena and performed numerical simulations.
Collaborator Contribution Theoretical analysis has been performed jointly with other theory partners at Princeton University (Michael Zaletel) and University of Pittsburgh (Roger Mong), who have contributed expertise on independent numerical techniques (DMRG). More recently, we have made stronger connections with our experimental partners, who provided expertise on the physics of graphene (Andrea Young at UCSB) and STM techniques (Ali Yazdani at Princeton University).
Impact Maissam Barkeshli, Chetan Nayak, Zlatko Papic, Andrea Young, Michael Zaletel, Phys. Rev. Lett. 121, 026603 (2018); Zlatko Papic, Roger S. K. Mong, Ali Yazdani, Michael P. Zaletel, Phys. Rev. X 8, 011037 (2018); : Michael P. Zaletel, Scott Geraedts, Zlatko Papic, Edward H. Rezayi, Phys. Rev. B 98, 045113 (2018).
Start Year 2016
 
Description Singapore 
Organisation Institute of High Performance Computing
Country Singapore 
Sector Public 
PI Contribution We have made a theoretical formalism for describing the anisotropic fractional quantum Hall effect.
Collaborator Contribution The partners in Singapore (Chinghua Lee, Bo Yang) have contributed to the theoretical formulation of the main idea.
Impact Bo Yang, Zi-Xiang Hu, Ching Hua Lee, Zlatko Papic, Phys. Rev. Lett. 118, 146403 (2017); Ching Hua Lee, Wen Wei Ho, Bo Yang, Jiangbin Gong, Zlatko Papic, Phys. Rev. Lett. 121, 237401 (2018).
Start Year 2016
 
Description Singapore 
Organisation National University of Singapore
Department Cancer Science Institute of Singapore (CSI)
Country Singapore 
Sector Academic/University 
PI Contribution We have made a theoretical formalism for describing the anisotropic fractional quantum Hall effect.
Collaborator Contribution The partners in Singapore (Chinghua Lee, Bo Yang) have contributed to the theoretical formulation of the main idea.
Impact Bo Yang, Zi-Xiang Hu, Ching Hua Lee, Zlatko Papic, Phys. Rev. Lett. 118, 146403 (2017); Ching Hua Lee, Wen Wei Ho, Bo Yang, Jiangbin Gong, Zlatko Papic, Phys. Rev. Lett. 121, 237401 (2018).
Start Year 2016
 
Description University of Geneva/IST Austria 
Organisation Institute of Science and Technology Austria
Country Austria 
Sector Public 
PI Contribution We are contributing to theoretical investigation on non-ergodic quantum many-body systems, in particular through the development of novel numerical methods to simulate such systems.
Collaborator Contribution The long-term collaborators at IST and Geneva provide theoretical expertise in different areas of condensed matter physics and insight into possible experimental realisations.
Impact Maksym Serbyn, Z. Papic, Dmitry A. Abanin, Phys. Rev. B 96, 104201 (2017); Dmitry A. Abanin and Zlatko Papic, DOI: 10.1002/andp.201700169 (review article); Alexios A. Michailidis, Marko Žnidaric, Mariya Medvedyeva, Dmitry A. Abanin, Tomaž Prosen, Z. Papic, Phys. Rev. B 97, 104307 (2018); Christopher J. Turner, Alexios A. Michailidis, Dmitry A. Abanin, Maksym Serbyn, Zlatko Papic, Nature Physics 14, 745-749 (2018); Christopher J. Turner, Alexios A. Michailidis, Dmitry A. Abanin, Maksym Serbyn, Zlatko Papic, Phys. Rev. B 98, 155134 (2018)
Start Year 2016
 
Description University of Geneva/IST Austria 
Organisation University of Geneva
Country Switzerland 
Sector Academic/University 
PI Contribution We are contributing to theoretical investigation on non-ergodic quantum many-body systems, in particular through the development of novel numerical methods to simulate such systems.
Collaborator Contribution The long-term collaborators at IST and Geneva provide theoretical expertise in different areas of condensed matter physics and insight into possible experimental realisations.
Impact Maksym Serbyn, Z. Papic, Dmitry A. Abanin, Phys. Rev. B 96, 104201 (2017); Dmitry A. Abanin and Zlatko Papic, DOI: 10.1002/andp.201700169 (review article); Alexios A. Michailidis, Marko Žnidaric, Mariya Medvedyeva, Dmitry A. Abanin, Tomaž Prosen, Z. Papic, Phys. Rev. B 97, 104307 (2018); Christopher J. Turner, Alexios A. Michailidis, Dmitry A. Abanin, Maksym Serbyn, Zlatko Papic, Nature Physics 14, 745-749 (2018); Christopher J. Turner, Alexios A. Michailidis, Dmitry A. Abanin, Maksym Serbyn, Zlatko Papic, Phys. Rev. B 98, 155134 (2018)
Start Year 2016
 
Description Zhejiang 
Organisation Zhejiang University
Department School of Medicine
Country China 
Sector Academic/University 
PI Contribution We have introduced the concept of geometric quench to probe bulk out-of-equilibrium dynamics of fractional quantum Hall phases of matter.
Collaborator Contribution Dr. Zhao Liu from Zhejiang University provided expertise in the numerical simulations of fractional Chern insulators.
Impact Zhao Liu, Andrey Gromov, Zlatko Papic, Phys. Rev. B 98, 155140 (2018)
Start Year 2018
 
Title Interaction distance 
Description The software evaluates the interaction distance which we introduced in [Nature Communications 8, 14926 (2017)] using as input the entanglement spectrum or energy spectrum of a quantum system. The software is written in Python and some documentation for it can be found at the website listed below. A review article introducing the method and further promoting the software is soon to be published. 
Type Of Technology Software 
Year Produced 2017 
Open Source License? Yes  
Impact Too early to say because we are just about to start promoting this software, which will happen after we complete the review article mentioned above. 
URL https://theory.leeds.ac.uk/interaction-distance/
 
Description 22nd Symposium on Quantum Information 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact International workshop promoting research at Theoretical Physics Group in Leeds, with participants from all over the UK, Switzerland, EU, Singapore, Australia.
Year(s) Of Engagement Activity 2018
URL https://theory.leeds.ac.uk/jiannis-pachos/symposia-on-topological-quantum-information/symposium-dec-...
 
Description 4th Northern Quantum Meeting 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Postgraduate students
Results and Impact Promoting research on quantum physics amongst Universities in Yorkshire area, networking and community building within the N8 group
Year(s) Of Engagement Activity 2019
URL https://theory.leeds.ac.uk/dr-almut-beige/northernquantum4/
 
Description Leeds Light 2018 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Public/other audiences
Results and Impact As part of Leeds Light Night 2018, Spanish artists Hotaru Visual Guerrilla have taken inspiration from our research into quantum chaos to explore the beauty of chaos using light, sound and movement.

https://leeds-list.com/culture/21-events-to-make-this-years-light-night-the-best-one-yet/
https://www.yorkshireeveningpost.co.uk/news/leeds-light-night-makes-spectacular-return-to-city-centre-1-9381988
also mentioned on BBC 1 Yorkshire and North Midlands (https://article.signalmedia.co/0e680991-a473-38aa-8277-60f6a2d92abf?u=f9157888-8859-4dec-89cc-3ce73fc5de40?igin=docx), and regional radio stations such as Radio Aire and Magic FM.
Year(s) Of Engagement Activity 2018
 
Description Physics Sixth Form Conference 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Schools
Results and Impact I have co-organised a one-day event at University of Leeds which involved 120 students from local schools. The purpose of this event was for A-level students to hear about the new and exciting areas of research happening at the University of Leeds, and the opportunities available to both pre-university and undergraduate students to not just learn physics, but DO physics. The event showcased the research performed by postgraduate students at the University of Leeds, who presented their posters and explained their work to the participants. In addition, the event featured several lectures, in particular one focusing on quantum physics and technology.
Year(s) Of Engagement Activity 2017
URL https://physicalsciences.leeds.ac.uk/events/event/301/physics_sixth_form_conference
 
Description Press Quantum Scars 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact Our Nature Physics paper on quantum scars was featured in several news outlets:

Photonics Online: https://www.photonicsonline.com/doc/insight-into-quantum-chaos-may-be-the-key-to-quantum-computers-0001
Nanotechnology News: http://www.nanotech-now.com/news.cgi?story_id=55131
Digital Journal: http://www.digitaljournal.com/tech-and-science/science/key-to-quantum-computing-is-understanding-quantum-chaos/article/522261
Space Daily: http://www.spacedaily.com/reports/Deeper_understanding_of_quantum_chaos_may_be_the_key_to_quantum_computers_999.html
Phys.org: https://phys.org/news/2018-05-deeper-quantum-chaos-key.html
University of Leeds press release: https://www.leeds.ac.uk/news/article/4231/insight_into_quantum_chaos_may_be_the_key_to_quantum_computers
Year(s) Of Engagement Activity 2018
URL https://www.leeds.ac.uk/news/article/4231/insight_into_quantum_chaos_may_be_the_key_to_quantum_compu...
 
Description Royal Society Conference 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact Co-organised a major international conference on many-body localisation and related phenomena in quantum systems. The conference boosted the visibility of this new topic in the UK, in academic circles as well as among broader audience.
Year(s) Of Engagement Activity 2017
URL https://royalsociety.org/science-events-and-lectures/2017/02/ergodicity-in-quantum-systems/
 
Description UCAS/School Open Days 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Public/other audiences
Results and Impact I have regularly been giving a popular lectures during UCAS days at University of Leeds. The lecture is entitled "Entangled quantum matter" and introduces my research to the lay audience. This was done about 10 times during academic years 2016/17 and 2017/18 involving total audience of about 400 prospective undergraduate students and their parents.
Year(s) Of Engagement Activity 2016,2017,2018