Critical behavior of geometric measure of quantum discord when approaching the critical points via different paths |
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| Institution: | 1. Department of Applied Physics, Xi’an Jiaotong University, Xi’an 710049, China;2. Department of Physics, Weinan Normal University, Weinan 714099, China;1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 221005, India;2. Department of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong, China;1. Graduate Institute of Applied Physics, National Chengchi University, Taipei 11605, Taiwan;2. Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan;1. College of Physics and Engineering, Chengdu Normal University, Chengdu 611130, China;2. Department of Transportation, Southeast University, Nanjing 210096, China;3. School of Mechanical and Vehicular Engineering, Beijing Institute of Technology, Beijing 100081, China;4. Research Institute of Internet of Mobility, Southeast University, China and UW-Madison, Nanjing 210096, China;1. LAMIS Laboratory, Department of Mathematics and Computer Science, University of Tebessa, Algeria;2. School of Basic Sciences and Humanities, German Jordanian University, Amman 11180, Jordan;3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;4. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;1. Department of Physics, Bahauddin Zakariya University, Multan 60800, Pakistan;2. Department of Physics, Government of College University Faisalabad, Layyah Campus, Layyah 31200, Pakistan;3. Department of Civil Engineering, Bahauddin Zakariya University, Multan 60800, Pakistan;1. Department of Physics, Faculty of Science, Kaduna State University, P.M.B. 2339, Kaduna State, Nigeria;2. School of Physics, Universiti Sains Malaysia, 11800 Penang, Malaysia |
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| Abstract: | We investigate the critical behavior of geometric measure of quantum discord (GMQD) in a one-dimensional transverse XY spin chain. The critical and the scaling behavior of the ground state GMQD are investigated both at the multi-critical and Ising critical points. Our results show that the behavior of GMQD at muti-critical point (MCP) has close relation with the path, which is determined by the parameter α, that approaching the MCP. For α < 2, the GMQD and its first derivation show oscillation behavior. For α ≥ 2, no oscillation behavior is observed. This indicates that the GMQD can not describe exactly the multi-critical point of the XY model. However, at the Ising critical point, the path parameter has no influence on the critical behavior. The GMQD (first derivation of GMQD) shows peaks (dips) and indicates exactly the position of Ising critical point. The results also show that the path parameter influences much to the scaling behavior near the MCP, but less to that of Ising critical point. Our results may provide reference to the exploration of relationships between GMQD and quantum phase transitions. |
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