Detecting Quantum Topologic Phase Transitions Through The C-Function
Abstract
Topological Quantum Field Theory or TQFT is a quantum field theory that calculates topological invariance in measurement theory and mathematical physics. In recent years, several attempts have been made 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 suggest 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: quantum topologic, phase transitions, c-function
References
[1] X.-G. Wen, Quantum field theory of many-body systems: From the origin of sound to an origin of light and electrons. Oxford University Press on Demand, 2004.
[2] Sachdev S. “Quantum phase transitions.,” In: Handbook of Magnetism and Advanced Magnetic Materials (1999). https://doi.org/10.1088/2058-7058/12/4/23.
[3] Grossman B. Hierarchy of soliton solutions to the gauged nonlinear Schrödinger equation on the plane. Phys Rev Lett. 1990 Dec;65(26):3230–2.
[4] Imada M, Fujimori A, Tokura Y. Metal-insulator transitions. Rev Mod Phys. 1998;70(4):1039–263.
[5] Laughlin RB. Anomalous quantum hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys Rev Lett. 1983;50(18):1395–8.
[6] J. Jacobsen, S. Ouvry, V. Pasquier, D. Serban, and L. Cugliandolo, Exact Methods in low-dimensional statistical physics and quantum computing: Lecture notes of the les houches summer school: Volume 89, July 2008. OUP Oxford, 2010.
[7] Casini H, Huerta M. A c-theorem for entanglement entropy. J Phys A Math Theor. 2007;40(25):7031–6.
[8] Myers RC, Sinha A. Seeing a c-theorem with holography. Phys Rev D Part Fields Gravit Cosmol. 2010;82(4):46006.
[9] Volkov B, Pankratov O. Two-dimensional massless electrons in an inverted contact. Soviet Journal of Experimental and Theoretical Physics Letters. 1985;42:178.
[10] Nielsen HB, Ninomiya M. The adler-bell-jackiw anomaly and weyl fermions in a crystal. Phys Lett B. 1983;130(6):389–96.
[11] Landsteiner K. Notes on anomaly induced transport. Acta Phys Pol B. 2016;47(12):2617.
[12] Colladay D, Kostelecký VA. Lorentz-violating extension of the standard model. Phys Rev D Part Fields. 1998;58(11):116002.