07 November 2014 New toolbox for Gauge Symmetries

Tensor Network encoding of the Hamiltonian of a lattice gauge theory

Tensor networks for lattice gauge theories with continuous groups in Physical Review X. There is evidence that three out of the four fundamental interactions (electromagnetic, strong, weak) are a manifestation of gauge symmetries. These interactions are described by gauge theories that, despite their elegance, still have not been fully solved. As a consequence, we do not understand the role of gauge symmetry in hot and dense nuclear matter, nor do we understand which phases of matter gauge theories can ultimately describe. For instance, it is unknown if gauge theories can explain the onset of high-temperature superconductivity in cuprates. Likewise, we do not fully understand the role of local symmetries in the heavy ion collisions produced in particle accelerators.

In a work titled ‘Tensor networks for lattice gauge theories with continuous groups’ which has been published in the APS journal, Physical Review X by ICFO researchers Drs. Luca Tagliacozzo and Alessio Celi in the Quantum Optics Theory group led by ICREA Professor at ICFO Maciej Lewenstein ,researchers extend the formulation of gauge theories to tensor network, the LEGO of many body quantum systems, where quantum states and operators (the equivalent of LEGO figurines) are obtained by contracting “small” constituent tensors (the equivalent of LEGO bricks).

In the paper the authors used tensor networks to uncover new classes of gauge theories designed for quantum simulators whose physics is still not well understood.

Their numerical results show that the tensor network approach makes it possible to distinguish two topological phases that cannot be detected by local order parameters. Researchers thus anticipate that their approach will foster new insights on gauge symmetries from table-top experiments with quantum simulators, including quantum magnets in cold-atom experiments, and/or numerical simulations based on tensor networks.