Tensor network formulation for two-dimensional lattice N $$ \mathcal{N} $$ = 1 Wess-Zumino model
- PDF / 1,491,571 Bytes
- 33 Pages / 595 x 842 pts (A4) Page_size
- 60 Downloads / 144 Views
Springer
Received: January 15, Revised: March 9, Accepted: March 12, Published: March 23,
2018 2018 2018 2018
Daisuke Kadoh,a Yoshinobu Kuramashi,b,c Yoshifumi Nakamura,c Ryo Sakai,d Shinji Takedad and Yusuke Yoshimurab a
Research and Educational Center for Natural Sciences, Keio University, Yokohama 223-8521, Japan b Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Japan c RIKEN Advanced Institute for Computational Science, Kobe 650-0047, Japan d Institute for Theoretical Physics, Kanazawa University, Kanazawa 920-1192, Japan
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] 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 = 1 Wess-Zumino model while showing that numerical results agree with the exact solutions for the free case. Keywords: Field Theories in Lower Dimensions, Lattice Quantum Field Theory, Supersymmetry Breaking ArXiv ePrint: 1801.04183
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP03(2018)141
JHEP03(2018)141
Tensor network formulation for two-dimensional lattice N = 1 Wess-Zumino model
Contents 1 Introduction
1
2 Two-dimensional N = 1 Wess-Zumino model 2.1 Continuum theory 2.2 Lattice theory
3 3 3 6 6 8 9 10 10 12 13 14
4 Numerical test in free theory 4.1 Some details 4.2 Free Majorana-Wilson fermion 4.3 Free Wilson boson 4.4 Witten index of the free N = 1 Wess-Zumino model
14 15 17 17 23
5 Summary and outlook
26
A Coarse-graining step in Grassmann TRG
27
1
Introduction
Supersymmetric field theories have attracted great attention because they provide a deep insight about the non-perturbative physics [1–3] and have a close relation with the gravitational theory [4]. The lattice simulations are promising approaches to obtain a further understanding of them. However, it is generally difficult to use the standard Monte Carlo techniques for the lattice supersymmetric theories on account of the sign problem, and the theories with the supersymmetry breaking may be the most difficult cases as suggested from the vanishing Witten index [5]. In this paper, we apply the tensor network approach, which is free of the sign problem, to the two-dimensional lattice N = 1 Wess-Zumino model in order to make a breakthrough on the issue. The two-dimensional N = 1 Wess-Zumino model is a supersymmetric theory in which a real scalar interacts with a Majorana fermion via the Yukawa term originate from the
–1–
JHEP03(2018)141
3 Tensor network representation of partition function 3.1 Fermion Pfaffian 3.2 Boson partition function 3.2.1 Introduction of auxiliary fields 3.2.2 Symmetric property of local Boltzmann weight 3.2.3 Discretization o
Data Loading...
