Quantum criticality and correlations in the Ising-Gamma chain

Abstract

In this paper, we study quantum phase transitions (QPTs) and critical phenomena of the one-dimensional Ising-Gamma model, which describes the competition between the Ising interactions and the off-diagonal Gamma exchange interactions. The Hamiltonian is analytically solved in virtue of Jordan–Wigner, Fourier and Bogoliubov transformations. The phase diagram consists of three phases, including antiferromagnetic phase, paramagnetic phase and gapless spiral phase. A detailed study of information measures including the Wigner–Yanase skew information (WYSI) and quantum fidelity susceptibility (QFS) is conducted. The second-order QPTs are witnessed both by WYSI and QFS. When the QPT occurs between distinct gapped phases, a logarithmic scaling behavior of local measures and a superextensive behavior of fidelity susceptibility are identified, while they exhibit size-dependent behaviors for the gapped-to-gapless transitions. The correlation-length exponent extracted from various order parameters agrees well with each other.