Free-particle descriptions of topological quantum matter and many-body localisation
Lead Research Organisation:
University of Leeds
Department Name: Physics and Astronomy
Abstract
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.
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.
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.
Publications
Salgado-Rebolledo P
(2023)
Emerging (2+1) D massive graviton in graphene-like systems
in New Journal of Physics
Desaules J
(2023)
Weak ergodicity breaking in the Schwinger model
in Physical Review B
Anand A
(2023)
Torus geometry eigenfunctions of an interacting multi-Landau-level Hamiltonian
in Physical Review B
Deger A
(2023)
AdS/CFT correspondence with a three-dimensional black hole simulator
in Physical Review B
Horner MD
(2023)
Chiral Spin-Chain Interfaces Exhibiting Event-Horizon Physics.
in Physical review letters
Benhemou A
(2023)
Universality of Z 3 parafermions via edge-mode interaction and quantum simulation of topological space evolution with Rydberg atoms
in Physical Review Research
Matos G
(2023)
Characterization of variational quantum algorithms using free fermions
in Quantum
Desaules J
(2023)
Prominent quantum many-body scars in a truncated Schwinger model
in Physical Review B
Pachos J
(2022)
Quantifying fermionic interactions from the violation of Wick's theorem
in Quantum
Benhemou A
(2022)
Non-Abelian statistics with mixed-boundary punctures on the toric code
in Physical Review A
Pu S
(2022)
Local density of states and particle entanglement in topological quantum fluids
in Physical Review B
Bull K
(2022)
Tuning between Continuous Time Crystals and Many-Body Scars in Long-Range XYZ Spin Chains.
in Physical review letters
Kirmani A
(2022)
Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers.
in Physical review letters
Balram A
(2022)
Very-High-Energy Collective States of Partons in Fractional Quantum Hall Liquids
in Physical Review X
Turner C
(2021)
Correspondence Principle for Many-Body Scars in Ultracold Rydberg Atoms
in Physical Review X
Liu Z
(2021)
Topological Contextuality and Anyonic Statistics of Photonic-Encoded Parafermions
in PRX Quantum
Matos G
(2021)
Emergence of gaussianity in the thermodynamic limit of interacting fermions
in Physical Review B
Matos G
(2021)
Quantifying the Efficiency of State Preparation via Quantum Variational Eigensolvers
in PRX Quantum
Sonner M
(2021)
Thouless energy across the many-body localization transition in Floquet systems
in Physical Review B
Horner M
(2021)
Edge density of bulk states due to relativity
in Physical Review B
Liu Z
(2021)
Quench Dynamics of Collective Modes in Fractional Quantum Hall Bilayers.
in Physical review letters
Desaules JY
(2021)
Proposal for Realizing Quantum Scars in the Tilted 1D Fermi-Hubbard Model.
in Physical review letters
Shi Q
(2020)
Odd- and even-denominator fractional quantum Hall states in monolayer WSe2.
in Nature nanotechnology
Salgado-Rebolledo P
(2020)
Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation.
in Scientific reports
Michailidis A
(2020)
Stabilizing two-dimensional quantum scars by deformation and synchronization
in Physical Review Research
Michailidis A
(2020)
Slow Quantum Thermalization and Many-Body Revivals from Mixed Phase Space
in Physical Review X
Horner M
(2020)
Equivalence between vortices, twists, and chiral gauge fields in the Kitaev honeycomb lattice model
in Physical Review B
Farjami A
(2020)
Geometric description of the Kitaev honeycomb lattice model
in Physical Review B
Rubio-García A
(2020)
Seeing topological edge and bulk currents in time-of-flight images
in Physical Review B
Self C
(2020)
Topological bulk states and their currents
in Physical Review B
Bull K
(2020)
Quantum scars as embeddings of weakly broken Lie algebra representations
in Physical Review B
Patrick K
(2019)
Efficiency of free auxiliary models in describing interacting fermions: From the Kohn-Sham model to the optimal entanglement model
in Physical Review B
Choi S
(2019)
Emergent SU(2) Dynamics and Perfect Quantum Many-Body Scars.
in Physical review letters
Bull K
(2019)
Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models.
in Physical review letters
Yang B
(2019)
Effective Abelian theory from a non-Abelian topological order in the ? = 2 / 5 fractional quantum Hall effect
in Physical Review B
Patrick K
(2019)
Interaction distance in the extended XXZ model
in Physical Review B
Matty M
(2019)
Multifaceted machine learning of competing orders in disordered interacting systems
in Physical Review B
Self C
(2019)
Thermally induced metallic phase in a gapped quantum spin liquid: Monte Carlo study of the Kitaev model with parity projection
in Physical Review B
Xu JS
(2018)
Photonic implementation of Majorana-based Berry phases.
in Science advances
Turner C
(2018)
Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations
in Physical Review B
Lee CH
(2018)
Floquet Mechanism for Non-Abelian Fractional Quantum Hall States.
in Physical review letters
Pachos J
(2018)
Quantifying the effect of interactions in quantum many-body systems
in SciPost Physics Lecture Notes
Liu Z
(2018)
Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
in Physical Review B
| 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 |
| URL | https://archive.researchdata.leeds.ac.uk/660/ |
| Title | Supporting data for "Many-body Hilbert space scarring on a superconducting processor" |
| Description | |
| Type Of Material | Database/Collection of data |
| Year Produced | 2022 |
| Provided To Others? | Yes |
| URL | https://archive.researchdata.leeds.ac.uk/1021/ |