DETECTING QUANTUM TOPOLOGIC PHASE TRANSITIONS THROUGH THE C-FUNCTION
Samuel Juliardi Sinaga1*, Jessie Manopo2, Ruben Cornelius Siagian3, Kevin William Andri Siahaan4

1 Mathematical Education Study Program, Faculty of Teacher Training and Education, Universitas HKBP Nommensen Medan, Jl. Sutomo, No. 4A, Medan 20235, Indonesian
2 Department of Physics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Gedung Ahmad Bakrie, Labtek VIII Lantai 1, Jalan Ganesha No. 10, Bandung 40132, Indonesian.
3 Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Medan, Jl. William Iskandar Ps. V, No.104, Medan 20371, Indonesian
4 Chemistry Education Study Program, Faculty of Teacher Training and Education, University of HKBP Nommensen Pematangsiantar Jl. Sangnawaluh, No. 4, Pematangsiantar 21136, Indonesian

Abstract

In measurement theory and mathematical physics, Topological Quantum Field Theory or TQFT is a quantum field theory that calculates topological invariance. In recent years, there have been several attempts to find efficient observations to determine the TQFT of quasiparticle properties. In this paper, we propose a different and very effective way to detect the critical points of TQFT by considering the system functions. We propose the C-Function as a novel probe that is accurate for detecting the location of critical points on topological quantum. The C-function uses a holographic model to show a topological quantum phase transition between a simple topological isolation phase and a gapless Weyl semimetal. The quantum tipping point displays a strong Lifshitz-like anisotropy in the spatial direction, and a quantum phase transition that does not follow the standard Landau paradigm. The C-function precisely shows the global features of quantum criticality and distinguishes very accurately between two separate zero-temperature phases. Considering the C-function relationship with entanglement entropy can detect quantum phase transitions and can be applied outside the holographic framework.

Keywords: TQFT, Phase Transition, C-Function

Topic: Physics