Tensor network analysis of critical coupling in two dimensional ϕ4 theory

• Published in: The journal of high energy physics Vol. 2019; no. 5
• Main Authors: Kadoh, Daisuke, Kuramashi, Yoshinobu, Nakamura, Yoshifumi, Sakai, Ryo, Takeda, Shinji, Yoshimura, Yusuke
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2019
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Discrete Symmetries; Field Theories in Lower Dimensions; Lattice Quantum Field Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2019)184

A bstract We make a detailed analysis of the spontaneous Z 2 -symmetry breaking in the two dimensional real ϕ 4 theory with the tensor renormalization group approach, which allows us to take the thermodynamic limit easily and determine the physical observables without statistical uncertainties. We determine the critical coupling in the continuum limit employing the tensor network formulation for scalar field theories proposed in our previous paper. We obtain [ λ / μ c 2 ] cont.  = 10.913(56) with the quartic coupling λ and the renormalized critical mass μ c . The result is compared with previous results obtained by different approaches.