Finite-Size Scaling Theory at a Self-Dual Quantum Critical Point
Long Zhang1* and Chengxiang Ding2
1Kavli Institute for Theoretical Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China 2School of Microelectronics & Data Science, Anhui University of Technology, Maanshan 243002, China
Abstract：The nondivergence of the generalized Grüneisen ratio (GR) at a quantum critical point (QCP) has been proposed to be a universal thermodynamic signature of self-duality. We study how the Kramers–Wannier-type self-duality manifests itself in the finite-size scaling behavior of thermodynamic quantities in the quantum critical regime. While the self-duality cannot be realized as a unitary transformation in the total Hilbert space for the Hamiltonian with the periodic boundary condition, it can be implemented in certain symmetry sectors with proper boundary conditions. Therefore, the GR and the transverse magnetization of the one-dimensional transverse-field Ising model exhibit different finite-size scaling behaviors in different sectors. This implies that the numerical diagnosis of self-dual QCP requires identification of the proper symmetry sectors.
Wang Z, Lorenz T, Gorbunov D I, Cong P T, Kohama Y, Niesen S, Breunig O, Engelmayer J, Herman A, Wu J, Kindo K, Wosnitza J, Zherlitsyn S, and Loidl A 2018 Phys. Rev. Lett.120 207205
2023, Vol. 40 
