2021
Campos, Manuel; Sierra, German; Lopez, Esperanza
Tensor Renormalization Group for interacting quantum fields Journal Article
In: Quantum, vol. 5, pp. 586, 2021.
@article{Campos_2021,
title = {Tensor Renormalization Group for interacting quantum fields},
author = {Manuel Campos and German Sierra and Esperanza Lopez},
url = {https://arxiv.org/abs/2105.00010},
doi = {10.22331/q-2021-11-23-586},
year = {2021},
date = {2021-11-01},
urldate = {2021-11-01},
journal = {Quantum},
volume = {5},
pages = {586},
publisher = {Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften},
abstract = {We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level of fields. This strategy was applied in Ref.[1] to the much simpler case of a free boson, obtaining an excellent performance. Here we include an arbitrary self-interaction and treat it in the context of perturbation theory. A real space analogue of the Wilsonian effective action and its expansion in Feynman graphs is proposed. Using a λϕ4 theory for benchmark, we evaluate the order λ correction to the free energy. The results show a fast convergence with the bond dimension, implying that our algorithm captures well the effect of interaction on entanglement.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level of fields. This strategy was applied in Ref.[1] to the much simpler case of a free boson, obtaining an excellent performance. Here we include an arbitrary self-interaction and treat it in the context of perturbation theory. A real space analogue of the Wilsonian effective action and its expansion in Feynman graphs is proposed. Using a λϕ4 theory for benchmark, we evaluate the order λ correction to the free energy. The results show a fast convergence with the bond dimension, implying that our algorithm captures well the effect of interaction on entanglement.
Nielsen, Anne E. B.; Herwerth, Benedikt; Cirac, J. Ignacio; Sierra, Germán
Field tensor network states Journal Article
In: Physical Review B, vol. 103, no. 15, 2021.
@article{Nielsen_2021,
title = {Field tensor network states},
author = {Anne E. B. Nielsen and Benedikt Herwerth and J. Ignacio Cirac and Germán Sierra},
url = {https://arxiv.org/abs/2001.07723},
doi = {10.1103/physrevb.103.155130},
year = {2021},
date = {2021-04-01},
urldate = {2021-04-01},
journal = {Physical Review B},
volume = {103},
number = {15},
publisher = {American Physical Society (APS)},
abstract = {We define a class of tensor network states for spin systems where the individual tensors are functionals of fields. The construction is based on the path integral representation of correlators of operators in quantum field theory. These tensor network states are infinite dimensional versions of matrix product states and projected entangled pair states. We find the field-tensor that generates the Haldane-Shastry wave function and extend it to two dimensions. We give evidence that the latter underlies the topological chiral state described by the Kalmeyer-Laughlin wave function.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We define a class of tensor network states for spin systems where the individual tensors are functionals of fields. The construction is based on the path integral representation of correlators of operators in quantum field theory. These tensor network states are infinite dimensional versions of matrix product states and projected entangled pair states. We find the field-tensor that generates the Haldane-Shastry wave function and extend it to two dimensions. We give evidence that the latter underlies the topological chiral state described by the Kalmeyer-Laughlin wave function.