Reference number : GC-2017-Q1-01824, amendment number : , agreement type : G, recipient legal name : Vidal Bonafont, Guifre (University of Waterloo), recipient country : CA, recipient province : nan, recipient city : Ontario, recipient postal code : nan, program name english : Discovery Grants Program - Individual, program name french : Programme de subventions à la découverte - individuelles, program purpose english : Quantum Mechanics provides us with the basic rules of how microscopic objects behave at the atomic and subatomic scales. However, when we place many such quantum objects together, we are not capable of theoretically predicting how they will behave collectively. For instance, even though we know that the electrons in a class of high-temperature superconducting materials (called cuprates) obey the laws of Quantum Mechanics, and believe that we have an accurate microscopic model for how they interact with each other, we have not yet been able to derive the emergence of superconductivity from that microscopic model. Tensor networks are a new way of representing the collective state of quantum many-body systems, based on recent improvements in our understanding of quantum entanglement. 
This Discovery Grant will advance and further develop the tensor network formalism in three important directions. Firstly, for quantum matter on the lattice (e.g. a lattice model of quantum spins for antiferromagnetic materials). Tensor networks were originally developed for lattice models of quantum matter, which are simplified models believed to capture the essential features of a many-body system. Secondly, for quantum fields directly in the continuum. Tensor networks for continuous systems are currently under construction, and could revolutionize how we think about and compute with strongly interacting quantum fields. Thirdly, tensor networks will be investigated as a realization of the holographic principle, which relates a theory of quantum gravity with a quantum field theory. 
Thus, through a bold, multi-disciplinary research program in theoretical physics, this Discovery Grant aims to further strengthening Canada&rsquo;s leading role and international visibility in the areas of condensed matter, quantum information, computational physics, and high energy physics. The Grant will also contribute significantly to the training of highly qualified personnel, which will be exposed to fore-front research by leading experts in one of the world&rsquo;s most prestigious institutes for theoretical physics., program purpose french : Quantum Mechanics provides us with the basic rules of how microscopic objects behave at the atomic and subatomic scales. However, when we place many such quantum objects together, we are not capable of theoretically predicting how they will behave collectively. For instance, even though we know that the electrons in a class of high-temperature superconducting materials (called cuprates) obey the laws of Quantum Mechanics, and believe that we have an accurate microscopic model for how they interact with each other, we have not yet been able to derive the emergence of superconductivity from that microscopic model. Tensor networks are a new way of representing the collective state of quantum many-body systems, based on recent improvements in our understanding of quantum entanglement. 
This Discovery Grant will advance and further develop the tensor network formalism in three important directions. Firstly, for quantum matter on the lattice (e.g. a lattice model of quantum spins for antiferromagnetic materials). Tensor networks were originally developed for lattice models of quantum matter, which are simplified models believed to capture the essential features of a many-body system. Secondly, for quantum fields directly in the continuum. Tensor networks for continuous systems are currently under construction, and could revolutionize how we think about and compute with strongly interacting quantum fields. Thirdly, tensor networks will be investigated as a realization of the holographic principle, which relates a theory of quantum gravity with a quantum field theory. 
Thus, through a bold, multi-disciplinary research program in theoretical physics, this Discovery Grant aims to further strengthening Canada&rsquo;s leading role and international visibility in the areas of condensed matter, quantum information, computational physics, and high energy physics. The Grant will also contribute significantly to the training of highly qualified personnel, which will be exposed to fore-front research by leading experts in one of the world&rsquo;s most prestigious institutes for theoretical physics., agreement title english : Tensor networks for quantum matter, quantum fields, and holography, agreement title french : Tensor networks for quantum matter, quantum fields, and holography, agreement number : RGPIN, agreement value : 350000.0, agreement start date : 2017-05-10, agreement end date : nan, description english : nan, description french : nan, expected results english : nan, expected results french : nan, additional information english : Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023), additional information french : Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023), owner organization : nserc-crsng, owner organization title : Natural Sciences and Engineering Research Council of Canada | Conseil de recherches en sciences naturelles et en génie du Canada