Tensor Network Theory for strongly correlated quantum systems
Lead Research Organisation:
University of Oxford
Department Name: Oxford Physics
Abstract
Physical systems that display strong correlations as a result of interactions between their constituents are present everywhere around us in our daily lives. For example traffic jams form on our roads every day in the morning due to strong interactions between cars that do not allow two of them to occupy the same piece of road. However, ants marching in a line never form such traffic jams despite facing very similar restrictions of not being allowed to sit on top of each other. These two examples demonstrate how subtle differences in the precise microscopic nature of interactions may lead to qualitatively different macroscopically observed properties and this poses major challenges for their theoretical study. In the quantum case strong interactions lead to some of the least well understood phenomena of condensed matter like high-Tc superconductivity, frustration, and topological phases such fractional quantum Hall physics which only appear in materials with a dominant two dimensional character.
An amazing feature of these systems is that one can readily write down simple looking models which are believed to capture the main physics on a macroscopic level. However, because of the strong interactions even these simple models turn out to be very hard to solve. Despite almost four decades of research in this area a detailed theoretical understanding of macroscopic properties in thermodynamic equilibrium emerging from strong interactions is still lacking for many of these seemingly simple models. In addition recent experimental progress now allows for the dynamical study of driven strongly correlated quantum systems far away from equilibrium and this poses new opportunities for applications in quantum enhanced devices as well as new challenges for theoretical physics research.
In this project we will develop high performance software which will enable tackling basic questions about models for strongly correlated systems in the quantum and also in the classical case. The underlying so-called tensor network algorithms have been developed over the past two decades but it is only now that a unified framework for these algorithms is known. This justifies the development of high performance computer software which will encompass existing and well-tested algorithms but is also sufficiently versatile to form the basis for future developments in this field of research. Indeed, the software developed in this project will be available to researchers throughout the UK and form the backbone of numerical studies based on tensor network algorithms for the next decade and possibly beyond.
Developing this powerful new tool for enhancing simulation methods will enable such things as the optimisation of quantum enhanced effects in promising new generations of technology. Improved numerical algorithms will enable sensors as well as energy transfer and storage devices to utilise physically enhanced processes at the scale where dynamical quantum effects are crucial. In particular the software will be required to study strongly correlated models without being hindered by boundary effects or minus-sign problems inherent in some other methods. The insights gained from this research could lead to novel superconducting materials or the exploitation of dynamical non-equilibrium properties in applications of nano-materials. Furthermore these may also be applicable to everyday classical strongly interacting systems like e.g. the formation of traffic jams or the dynamics of queues forming at box offices or in order books at the stock exchange.
An amazing feature of these systems is that one can readily write down simple looking models which are believed to capture the main physics on a macroscopic level. However, because of the strong interactions even these simple models turn out to be very hard to solve. Despite almost four decades of research in this area a detailed theoretical understanding of macroscopic properties in thermodynamic equilibrium emerging from strong interactions is still lacking for many of these seemingly simple models. In addition recent experimental progress now allows for the dynamical study of driven strongly correlated quantum systems far away from equilibrium and this poses new opportunities for applications in quantum enhanced devices as well as new challenges for theoretical physics research.
In this project we will develop high performance software which will enable tackling basic questions about models for strongly correlated systems in the quantum and also in the classical case. The underlying so-called tensor network algorithms have been developed over the past two decades but it is only now that a unified framework for these algorithms is known. This justifies the development of high performance computer software which will encompass existing and well-tested algorithms but is also sufficiently versatile to form the basis for future developments in this field of research. Indeed, the software developed in this project will be available to researchers throughout the UK and form the backbone of numerical studies based on tensor network algorithms for the next decade and possibly beyond.
Developing this powerful new tool for enhancing simulation methods will enable such things as the optimisation of quantum enhanced effects in promising new generations of technology. Improved numerical algorithms will enable sensors as well as energy transfer and storage devices to utilise physically enhanced processes at the scale where dynamical quantum effects are crucial. In particular the software will be required to study strongly correlated models without being hindered by boundary effects or minus-sign problems inherent in some other methods. The insights gained from this research could lead to novel superconducting materials or the exploitation of dynamical non-equilibrium properties in applications of nano-materials. Furthermore these may also be applicable to everyday classical strongly interacting systems like e.g. the formation of traffic jams or the dynamics of queues forming at box offices or in order books at the stock exchange.
Planned Impact
The proposed work will change the accessibility and applicability of many well established algorithms for studying strongly correlated physical systems and open the way to the development and application of novel tensor network algorithms. This will benefit not only researchers in the fields of condensed matter physics and cold atom physics, but also those who have no previous experience with TNT. Additionally, it will benefit researchers in the field of numerical analysis by providing optimised general functionality for manipulating tensors.
The impact to these different groups of beneficiaries will be achieved through access to the three tiers of the software library:
(1) The tier I software library will provide basic routines for tensor manipulation that can be used by developers of tensor network algorithms and researchers, which we would usually expect to be theorists, who require non-standard usage of well-known tensor network algorithms. These routines will also be useful for commercial and academic users who wish to work with tensor manipulation in any general context.
(2) The tier II software library will provide the building blocks for tensor network algorithms using the most common network types. It will allow customised, yet highly optimised, algorithms to be written by the user with the minimum of effort, allowing simplified testing of new tensor network algorithms by researchers.
(3) The tier III software library will contain ready-to-use implementations of the most common and already widely used tensor network algorithms. It will make these algorithms accessible to a large group of users, and they will be able to use software of unprecedented power which will significantly enlarge the class of physical models that can be studied with them. This tier will contain algorithms that can be directly applied to standard strongly correlated quantum models and also routines for application to classical stochastic systems.
The impact to these different groups of beneficiaries will be achieved through access to the three tiers of the software library:
(1) The tier I software library will provide basic routines for tensor manipulation that can be used by developers of tensor network algorithms and researchers, which we would usually expect to be theorists, who require non-standard usage of well-known tensor network algorithms. These routines will also be useful for commercial and academic users who wish to work with tensor manipulation in any general context.
(2) The tier II software library will provide the building blocks for tensor network algorithms using the most common network types. It will allow customised, yet highly optimised, algorithms to be written by the user with the minimum of effort, allowing simplified testing of new tensor network algorithms by researchers.
(3) The tier III software library will contain ready-to-use implementations of the most common and already widely used tensor network algorithms. It will make these algorithms accessible to a large group of users, and they will be able to use software of unprecedented power which will significantly enlarge the class of physical models that can be studied with them. This tier will contain algorithms that can be directly applied to standard strongly correlated quantum models and also routines for application to classical stochastic systems.
People |
ORCID iD |
Dieter Jaksch (Principal Investigator) |
Publications
Giscard P
(2015)
An exact formulation of the time-ordered exponential using path-sums
in Journal of Mathematical Physics
Giscard P. -L.
(2014)
An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System
in arXiv e-prints
Guichard R
(2015)
Decoherence of nuclear spins in the frozen core of an electron spin
in Physical Review B
Johnson T
(2016)
Thermometry of ultracold atoms via nonequilibrium work distributions
in Physical Review A
Johnson T
(2015)
Capturing Exponential Variance Using Polynomial Resources: Applying Tensor Networks to Nonequilibrium Stochastic Processes
in Physical Review Letters
Johnson TH
(2013)
Solving search problems by strongly simulating quantum circuits.
in Scientific reports
Johnson TH
(2016)
Hubbard Model for Atomic Impurities Bound by the Vortex Lattice of a Rotating Bose-Einstein Condensate.
in Physical review letters
Kiffner M
(2017)
Topological spin models in Rydberg lattices
in Applied Physics B
Lang J. E.
(2015)
Decoherence of electron spins in isotopically enriched silicon near Clock Transitions
in arXiv e-prints
Lubasch M
(2019)
Variational quantum algorithms for nonlinear problems
Description | We have developed key insights into how entanglement and strong quantum correlations can be encoded in tensor networks. These results enable us to study equilibrium and non-equilibrium properties of strongly correlated quantum systems. We also utilize them for emulating quantum computing algorithms on classical computers. |
Exploitation Route | The software resulting from this project is available for others to use. We currently have joint projects with industry to develop industrially relevant applications of our research findings. |
Sectors | Aerospace, Defence and Marine,Chemicals,Digital/Communication/Information Technologies (including Software),Other |
Description | The PI has moved his main affiliation to Germany and was recently awarded an EU funded project for developing a framework for Quantum Computational Fluid Dynamics leading towards industrial applications. This project contains a work package that develops tensor network based algorithms (based partly on results obtained in EP/K038311/1) for studying fluid flows and benchmarking corresponding quantum algorithms. In this project, tensor networks also provide important tools for identifying potential quantum advantages and developing the quantum software underlying the overall framework.s. |
First Year Of Impact | 2022 |
Sector | Aerospace, Defence and Marine |
Impact Types | Economic |
Description | Designing Out-of-Equilibrium Many-Body Quantum Systems |
Amount | £5,834,555 (GBP) |
Funding ID | EP/P009565/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 02/2017 |
End | 02/2022 |
Description | ERC synergy grant |
Amount | € 9,966,878 (EUR) |
Organisation | European Research Council (ERC) |
Sector | Public |
Country | Belgium |
Start | 10/2013 |
End | 09/2019 |
Description | FETPROACT-3-2014 - Quantum simulation |
Amount | € 2,268,746 (EUR) |
Funding ID | 641277 |
Organisation | European Commission |
Department | Horizon 2020 |
Sector | Public |
Country | European Union (EU) |
Start | 04/2015 |
End | 03/2018 |
Description | Quantum device verification and benchmarking: Tensor Network Theory "tntgo.org" web tool |
Amount | £10,458 (GBP) |
Funding ID | EPSRC Institutional Sponsorship for Quantum Technologies Award EP/M506977/1- project D4D00130 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 11/2014 |
End | 03/2015 |
Description | Tensor Network Theory for strongly correlated quantum systems |
Amount | £720,431 (GBP) |
Funding ID | EP/K038311/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 08/2013 |
End | 07/2018 |
Title | TNT Core Library |
Description | The TNT (tensor network theory) core library provides a functions for manipulating tensors, which are represented as nodes in a network. The manipulations are carried out using highly efficient routines, that do not depend on the network geometry, and that can be used to build tensor network theory algorithms e.g. for simulation of strongly correlated quantum systems. |
Type Of Technology | Software |
Year Produced | 2014 |
Open Source License? | Yes |
Impact | This software library has been used widely in our group for tensor network simulations, as well as being downloaded by users in other groups/institutions for use in their own calculations. |
URL | http://ccpforge.cse.rl.ac.uk/gf/project/tntlibrary/ |
Title | TNT Go |
Description | This provides a web interface for running simulations using the TNT library. It allows ground states and dynamical evolution to be calculated for 1D quantum many body systems (spin and boson systems are currently supported), in a very easy-to-use way. Results can be saved, with the output data available for download for further manipulation if necessary. |
Type Of Technology | Webtool/Application |
Year Produced | 2014 |
Impact | TNT Go was demonstrated at various summer schools as a way of generating interest in the TNT library project and providing an easy to use introduction to performing simulations using the TNT algorithms. This is the first web tool we are aware of that allows TNT simulations to be carried out without the need for any software to be installed by the user. |
URL | http://www.tntgo.org |
Title | TNT MPS library |
Description | The TNT (tensor network theory) MPS (matrix product state) library uses the TNT core library functions to provide building block functions that act on MPS and MPO (matrix product operator) networks. They can be used to easily build complete MPS algorithms for time evolution and ground state calculation of many body quantum systems. |
Type Of Technology | Software |
Year Produced | 2014 |
Open Source License? | Yes |
Impact | This software library has been used widely in our group for tensor network simulations, as well as being downloaded by users in other groups/institutions for use in their own calculations. |
URL | http://ccpforge.cse.rl.ac.uk/gf/project/tntlibrary/ |