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Untangling the mysteries of time evolution

Mathematical descriptions of particle interactions provide insight into condensed matter physics, quantum computing and the origins of the Universe. Two new theories overcoming previous limitations should spur discovery.
Untangling the mysteries of time evolution
Lattice gauge theories (LGTs) are field theories explaining the dynamics of elementary particles formulated on a space–time lattice where space–time has been quantised into discrete units. They have played an important role in descriptions spanning many areas of particle physics with relevance to both basic understanding and applied knowledge. Quantum chromodynamics (QCD) is an LGT describing the physics of strong interactions among quarks mediated by gluons. LGTs are also important to quantum ferromagnetism, superconductivity and quantum computation.

Most implementations of LGTs rely on Monte Carlo simulations that are associated with several important limitations, including difficulty in describing quantum entanglement (essentially an interdependence of the quantum states of two or more objects) and in performing time evolutions. The EU-funded project 'Entanglement renormalization and gauge symmetry' (ENGAGES) overcame these limitations by applying entanglement renormalisation (ER) to the LGT formulation. ER is an approach to reduce the amount of entanglement of a block of lattice sites to simplify the connectivity of the lattice.

Two new LGTs developed within the context of the project lay the groundwork for experimental and numerical studies of both ground-state properties and short-time out-of-equilibrium dynamics that were previously inaccessible with Monte Carlo simulations. Results have been published in 11 scientific papers within 2 years and will be included in a numerical LGT toolbox currently being developed.

ENGAGES has extended the available mathematical techniques for describing and investigating elementary particle dynamics with two new LGTs exploiting ER. Better descriptions of quantum entanglement and real-time evolutions have direct impact on quantum computing, spintronics and even the astrophysics of compact stars. Application of the techniques promises a flurry of innovation in both the experimental and theoretical realms.

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