The continuum limit of a tensor network: a path integral representation

Abstract

We argue that the natural way to generalise a tensor network variational class to a continuous quantum system is to use the Feynman path integral to implement a continuous tensor contraction. This approach is illustrated for the case of a recently introduced class of quantum field states known as continuous matrix-product states (cMPS). As an example of the utility of the path-integral representation we argue that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. An argument that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity is also provided.

13 pages, 1 figure

References in corpus (5)

• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Matrix Product States for dynamical simulation of infinite chains
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Holographic quantum states