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Entanglement renormalization of the class of continuous matrix product states

Niloofar Vardian
(
- SISSA, Trieste and
- INFN, Trieste
)

Aug 31, 2022

6 pages

Published in:

Phys.Rev.D 108 (2023) 9, 094029

Published: Nov 1, 2023

e-Print:

2208.14827 [hep-th]

DOI:

10.1103/PhysRevD.108.094029 (publication)

View in:

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Abstract: (APS)

Continuous tensor networks give a variational ansatz for the ground state of the quantum field theories (QFTs). Notable examples are the continuous matrix product state (cMPS) and the continuous multiscale entanglement renormalization ansatz (cMERA). While cMPS is just adapted to the nonrelativistic QFTs, only the Gaussian cMERA is well understood, which we cannot use to approximate the ground state of the interacting relativistic QFTs. But, instead, cMERA also corresponds to a real-space renormalization group flow in the context of the wave functions. In this paper, we investigate the backward Gaussian cMERA renormalization group flow of the class of cMPS by putting the standard cMPS at the IR scale. At the UV scale, for the bosonic systems in the thermodynamic limit, we achieve the variational class of states that has been proposed recently, as the relativistic cMPS (RCMPS) is adapted to the relativistic QFTs without requiring one to introduce of any additional IR or UV cutoff. We also extend the RCMPS to fermionic systems and theories on a finite circle.

Note:

6 pages, 1 figure

renormalization group: flow
field theory: relativistic
field theory: nonrelativistic
network: tensor
renormalization
ground state
entanglement
variational
thermodynamical
circle

References(77)

Figures(0)

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