Tensor Networks

from entangled quantum matter to emergent space time

Tensor networks have in recent years emerged as a powerful tool to describe strongly entangled quantum many-body systems. Applications range from the study of collective phenomena in condensed matter to providing a discrete realization of the holographic principle in quantum gravity.

Tensor networks – such as the matrix product state (MPS), the multi-scale entanglement renormalization ansatz (MERA), and the projected entangled-pair states (PEPS) – were originally proposed as novel numerical approaches to study strongly entangled quantum many-body systems, including quantum criticality and topological order. However, the range of applicability of the tensor network formalism has quickly extended well beyond the computational domain.

Tensor networks are currently also investigated as a natural framework to classify exotic phases of quantum matter, as the basis for new non-perturbative formulations of the renormalization group and interacting quantum field theories, as a lattice realization of the AdS/CFT correspondence in quantum gravity, and in machine learning.

Topics that the tensor network initiative at Perimeter Institute explores include:

  • Strongly entangled quantum matter: characterization of exotic phases and critical phenomena
  • Novel non-perturbative approaches to quantum field theories, including their dynamics
  • Tensor network realization of the AdS/CFT correspondence
  • New theoretical and computational frameworks for quantum gravity
  • Machine learning

We are recruiting postdoctoral fellows with interests in tensor networks. Interested candidates should apply online to the Perimeter Institute.

Juan Maldacena, who first proposed the AdS/CFT correspondence in 1997, talks to Perimeter Faculty member Guifre Vidal about tensor networks as a realization of the AdS/CFT correspondence at Mathematica Summer School 2015.




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tensor network is a collection of tensors with indices connected according to a network pattern. It can be used to efficiently represent a many-body wave-function in an otherwise exponentially large Hilbert space.