An extension of tensor networks—mathematical tools that simplify the study of complex quantum systems—could allow their application to a broad range of quantum field theory problems.
Not long after the birth of quantum mechanics, Paul Dirac and others postulated that, in principle, quantum mechanics could predict any desired property of matter [1]. That is, provided one can solve the relevant quantum equations. Often, however, these equations are fiendishly difficult or impossible to solve, as is the case, for instance, for strongly correlated electron systems and other systems in which many-body interactions play an important role. Solving such many-body problems could help us find new high-temperature superconductors, design quantum computing architectures, or describe exotic phase transitions. So-called tensor networks, mathematical tools introduced decades ago, have been widely successful in simplifying the treatment of complex quantum systems. So far, however, these tools could only tackle quantum systems in spatial dimensions higher than 1 by discretizing them—representing them in the form of a discrete lattice. Such a representation can be inadequate for numerous many-body problems. Now, Antoine Tilloy and Ignacio Cirac at the Max Planck Institute for Quantum Optics in Germany have extended tensor networks so that they can represent continuous systems in any spatial dimension (including 2D and 3D) [2]. This result may allow researchers to apply tensor networks to a wide class of problems in quantum field theory.
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