TY - UNPB

T1 - The continuum limit of a tensor network

T2 - a path integral representation

AU - Brockt, Christoph

AU - Haegeman, Jutho

AU - Jennings, David

AU - Osborne, Tobias J.

AU - Verstraete, Frank

N1 - 13 pages, 1 figure

PY - 2012/10/19

Y1 - 2012/10/19

N2 - 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.

AB - 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.

KW - quant-ph

M3 - Preprint

BT - The continuum limit of a tensor network

ER -