scholarly journals Entanglement-based tensor-network strong-disorder renormalization group

2021 ◽  
Vol 104 (13) ◽  
Author(s):  
Kouichi Seki ◽  
Toshiya Hikihara ◽  
Kouichi Okunishi
Keyword(s):  
Renormalization Group ◽  
Strong Disorder ◽  
Tensor Network

scholarly journals Loop-TNR analysis of CP(1) model with theta term

2018 ◽  
Vol 175 ◽  
pp. 11015
Author(s):  
Hikaru Kawauchi ◽  
Shinji Takeda
Keyword(s):  
Renormalization Group ◽  
Phase Structure ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Tensor Networks ◽  
Tensor Network ◽  
Network Methods ◽  
Renormalization Method ◽  
Future Work

The phase structure of the two dimensional lattice CP(1) model in the presence of the θ term is analyzed by tensor network methods. The tensor renormalization group, which is a standard renormalization method of tensor networks, is used for the regions θ = 0 and θ ≠ 0. Loop-TNR, which is more suitable for the analysis of near criticality, is also implemented for the region θ = 0. The application of Loop-TNR for the region θ ≠ 0 is left for future work.

scholarly journals Tensor Renormalization Group for interacting quantum fields

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 586
Author(s):  
Manuel Campos ◽  
German Sierra ◽  
Esperanza Lopez
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Real Space ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Excellent Performance ◽  
Tensor Network ◽  
Feynman Graphs

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.

scholarly journals Strong-disorder renormalization group for periodically driven systems

2018 ◽  
Vol 98 (17) ◽  
Author(s):  
William Berdanier ◽  
Michael Kolodrubetz ◽  
S. A. Parameswaran ◽  
Romain Vasseur
Keyword(s):  
Renormalization Group ◽  
Driven Systems ◽  
Strong Disorder ◽  
Periodically Driven

scholarly journals Tensor renormalization group approach to four-dimensional complex ϕ4 theory at finite density

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Shinichiro Akiyama ◽  
Daisuke Kadoh ◽  
Yoshinobu Kuramashi ◽  
Takumi Yamashita ◽  
Yusuke Yoshimura
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Large Volume ◽  
Numerical Algorithms ◽  
Two Dimensions ◽  
Test Bed ◽  
Finite Density ◽  
Sign Problem ◽  
Tensor Network ◽  
Volume Limit

Abstract Tensor network is an attractive approach to the field theory with negative sign problem. The complex ϕ4 theory at finite density is a test bed for numerical algorithms to verify their effectiveness. The model shows a characteristic feature called the Silver Blaze phenomenon associated with the sign problem in the large volume limit at low temperature. We analyze the four-dimensional model employing the anisotropic tensor renormalization group algorithm with a parallel computation. We find a clear signal of the Silver Blaze phenomenon on a large volume of V = 10244, which implies that the tensor network approach is effective even for four-dimensional field theory beyond two dimensions.

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