Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

• Published in: Chinese physics B Vol. 31; no. 7; pp. 70502 - 191
• Main Authors: Dai, Yan-Wei, Li, Sheng-Hao, Chen, Xi-Hao
• Format: Journal Article
• Language: English
• Published: Chinese Physical Society and IOP Publishing Ltd 01.06.2022; Chongqing Vocational Institute of Engineering,Chongqing 402260,China%Centre for Modern Physics and Department of Physics,Chongqing University,Chongqing 400044,China; Research Institute for New Materials and Technology,Chongqing University of Arts and Sciences,Chongqing 400000,China; Centre for Modern Physics and Department of Physics,Chongqing University,Chongqing 400044,China%Centre for Modern Physics and Department of Physics,Chongqing University,Chongqing 400044,China
• Subjects: fidelity; quantum phase transitions; universal order parameter; universal order parameter; quantum phase transitions; fidelity
• ISSN: 1674-1056; 2058-3834
• DOI: 10.1088/1674-1056/ac4bd1

We investigate quantum phase transitions for q -state quantum Potts models ( q = 2,3,4) on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme. We extend the universal order parameter to a two-dimensional lattice system, which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G . The universal order parameter is zero in the symmetric phase, and it ranges from zero to unity in the symmetry-broken phase. The ground-state fidelity per lattice site is computed, and a pinch point is identified on the fidelity surface near the critical point. The results offer another example highlighting the connection between (i) critical points for a quantum many-body system undergoing a quantum phase-transition and (ii) pinch points on a fidelity surface. In addition, we discuss three quantum coherence measures: the quantum Jensen–Shannon divergence, the relative entropy of coherence, and the l 1 norm of coherence, which are singular at the critical point, thereby identifying quantum phase transitions.