Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1711.01892 · EPJ Web of Conferences

Application of tensor network method to two dimensional lattice N = 1 Wess–Zumino model

Ryo Sakai, Daisuke Kadoh, Yoshinobu Kuramashi, Yoshifumi Nakamura, Shinji Takeda, Yusuke Yoshimura

Published Jan 1, 2018• 2 citations
arXivHTMLPDF

Abstract

We study a tensor network formulation of the two dimensional lattice N = 1 Wess–Zumino model with Wilson derivatives for both fermions and bosons. The tensor renormalization group allows us to compute the partition function without the sign problem, and basic ideas to obtain a tensor network for both fermion and scalar boson systems were already given in previous works. In addition to improving the methods, we have constructed a tensor network representation of the model including the Yukawatype interaction of Majorana fermions and real scalar bosons. We present some numerical results.

DOI
10.1051/epjconf/201817511019

Related papers

Tensor network formulation for two-dimensional lattice $$ \mathcal{N} $$ = 1 Wess-Zumino model

Daisuke Kadoh, Yoshinobu Kuramashi, Y. Nakamura +3 more

Abstract Supersymmetric models with spontaneous supersymmetry breaking suffer from the notorious sign problem in stochastic approaches. By contrast, the tensor network approaches do not have such a problem since they are based on deterministic procedures. In this work, we present a tensor network formulation of the two-dimensional lattice $$ \mathcal{N} $$ N = 1 Wess-Zumino model while showing that numerical results agree with the exact solutions for the free case.

arXiv:1801.04183•Journal of High Energy Physics•Mar 1, 2018•52 citations

Tensor renormalization group for fermions

Shinichiro Akiyama, Yannick Meurice, Ryo Sakai

We review the basic ideas of the tensor renormalization group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson-Majorana fermions and multi-flavor Gross-Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

arXiv:2401.08542•Journal of Physics Condensed Matter•May 3, 2024•9 citations

More about the Grassmann tensor renormalization group

Shinichiro Akiyama, Daisuke Kadoh

Abstract We derive a general formula of the tensor network representation for d-dimensional lattice fermions with ultra-local interactions, including Wilson fermions, staggered fermions, and domain-wall fermions. The Grassmann tensor is concretely defined with auxiliary Grassmann variables that play a role in bond degrees of freedom. Compared to previous works, our formula does not refer to the details of lattice fermions and is derived by using the singular value decomposition for the given Dirac matrix without any ad-hoc treatment for each fermion. We numerically test our formula for free Wilson and staggered fermions and find that it properly works for them. We also find that Wilson fermions show better performance than staggered fermions in the tensor renormalization group approach, unlike the Monte Carlo method.

arXiv:2005.07570•Journal of High Energy Physics•Oct 1, 2021•30 citations

Improved coarse-graining methods for two dimensional tensor networks including fermions

Muhammad Asaduzzaman, Simon M. Catterall, Yannick Meurice +2 more

Abstract We show how to apply renormalization group algorithms incorporating entanglement filtering methods and a loop optimization to a tensor network which includes Grassmann variables which represent fermions in an underlying lattice field theory. As a numerical test a variety of quantities are calculated for two dimensional Wilson-Majorana fermions and for the two flavor Gross-Neveu model. The improved algorithms show much better accuracy for quantities such as the free energy and the determination of Fisher’s zeros.

arXiv:2210.03834•Journal of High Energy Physics•Jan 9, 2023•7 citations

Two-color lattice QCD in $(1+1)$ dimensions with Grassmann tensor renormalization group

Kwok Ho Pai, Akiyama, Shinichiro, Synge Todo

The $(1+1)$-dimensional two-color lattice QCD is studied with the Grassmann tensor renormalization group. We construct tensor network representations of theories with the staggered fermion and the Wilson fermion and show that Grassmann tensor networks can describe both cases with the same bond dimension. We also propose an efficient initial tensor compression scheme to gauge degrees of freedom. We compute the number density, chiral condensate, and diquark condensate at finite density, employing the staggered fermions. For the theory with Wilson fermion, a critical point in the negative mass region is identified by inspecting the pseudoscalar condensate and the conformal field theory data.

arXiv:2501.18918•Jan 31, 2025•0 citations

Two-color lattice QCD in (1 + 1) dimensions with Grassmann tensor renormalization group

Kwok Ho Pai, Shinichiro Akiyama, Synge Todo

The $(1+1)$-dimensional two-color lattice QCD is studied with the Grassmann tensor renormalization group. We construct tensor network representations of theories with the staggered fermion and the Wilson fermion and show that Grassmann tensor networks can describe both cases with the same bond dimension. We also propose an efficient initial tensor compression scheme to gauge degrees of freedom. We compute the number density, chiral condensate, and diquark condensate at finite density, employing the staggered fermions. For the theory with Wilson fermion, a critical point in the negative mass region is identified by inspecting the pseudoscalar condensate and the conformal field theory data.

International Symposium on Lattice Field Theory (LATTICE)•Jan 27, 2025•2 citations
We study a tensor network formulation of the two dimensional lattice N = 1 Wess–Zumino model with Wilson derivatives for both fermions and bosons. The tensor renormalization group allows us to compute the partition function without the sign problem, and basic ideas to obtain a tensor network for both fermion and scalar boson systems were already given in previous works. In addition to improving the methods, we have constructed a tensor network representation of the model including the Yukawatype interaction of Majorana fermions and real scalar bosons. We present some numerical results.
Tensor network formulation for two-dimensional lattice N \mathcal{N} N = 1 Wess-Zumino model
Abstract Supersymmetric models with spontaneous supersymmetry breaking suffer from the notorious sign problem in stochastic approaches. By contrast, the tensor network approaches do not have such a problem since they are based on deterministic procedures. In this work, we present a tensor network formulation of the two-dimensional lattice N \mathcal{N} N N = 1 Wess-Zumino model while showing that numerical results agree with the exact solutions for the free case.
We review the basic ideas of the tensor renormalization group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson-Majorana fermions and multi-flavor Gross-Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.
Abstract We derive a general formula of the tensor network representation for d-dimensional lattice fermions with ultra-local interactions, including Wilson fermions, staggered fermions, and domain-wall fermions. The Grassmann tensor is concretely defined with auxiliary Grassmann variables that play a role in bond degrees of freedom. Compared to previous works, our formula does not refer to the details of lattice fermions and is derived by using the singular value decomposition for the given Dirac matrix without any ad-hoc treatment for each fermion. We numerically test our formula for free Wilson and staggered fermions and find that it properly works for them. We also find that Wilson fermions show better performance than staggered fermions in the tensor renormalization group approach, unlike the Monte Carlo method.
Abstract We show how to apply renormalization group algorithms incorporating entanglement filtering methods and a loop optimization to a tensor network which includes Grassmann variables which represent fermions in an underlying lattice field theory. As a numerical test a variety of quantities are calculated for two dimensional Wilson-Majorana fermions and for the two flavor Gross-Neveu model. The improved algorithms show much better accuracy for quantities such as the free energy and the determination of Fisher’s zeros.
Two-color lattice QCD in (1+1)(1+1)(1+1) dimensions with Grassmann tensor renormalization group
The (1+1)(1+1)(1+1)-dimensional two-color lattice QCD is studied with the Grassmann tensor renormalization group. We construct tensor network representations of theories with the staggered fermion and the Wilson fermion and show that Grassmann tensor networks can describe both cases with the same bond dimension. We also propose an efficient initial tensor compression scheme to gauge degrees of freedom. We compute the number density, chiral condensate, and diquark condensate at finite density, employing the staggered fermions. For the theory with Wilson fermion, a critical point in the negative mass region is identified by inspecting the pseudoscalar condensate and the conformal field theory data.
The (1+1)(1+1)(1+1)-dimensional two-color lattice QCD is studied with the Grassmann tensor renormalization group. We construct tensor network representations of theories with the staggered fermion and the Wilson fermion and show that Grassmann tensor networks can describe both cases with the same bond dimension. We also propose an efficient initial tensor compression scheme to gauge degrees of freedom. We compute the number density, chiral condensate, and diquark condensate at finite density, employing the staggered fermions. For the theory with Wilson fermion, a critical point in the negative mass region is identified by inspecting the pseudoscalar condensate and the conformal field theory data.