Quantum phase transitions and scaling behaviors of extended 1D compass spin-chain model
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Quantum phase transitions and scaling behaviors of extended 1D compass spin-chain model Qi Chen1 · Guo-Qing Zhang2 · Jing-Bo Xu1 Received: 10 April 2020 / Accepted: 17 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We use multipartite entanglement and trace distance to detect the quantum phase transitions of the extended one-dimensional compass spin-chain model by applying the density matrix renormalization group method which is represented by the matrix product state. It is shown that singular behaviors of the first-order derivative of the multipartite entanglement and trace distance occur at the critical point of the system. The scaling behaviors of trace distance and multipartite entanglement are also discussed, and we show that the universal finite-size scaling law is valid for the multipartite entanglement and trace distance around the critical point. Moreover, we explore the quantum coherence for this model and find that the first-order derivative of the quantum coherence also displays discontinuity and exhibits singular critical behaviors that are the same as the trace distance and multipartite entanglement. Keywords Quantum phase transitions · Multipartite entanglement · Quantum coherence · Trace distance
1 Introduction In recent years, quantum phase transitions (QTPs) have been an increasingly important topic within condensed matter physics. It is known that quantum fluctuations are the driver of QPTs in many-body systems under absolute zero temperature conditions, where classical fluctuations become inactive [1,2]. When the external parameter of a system reaches a particular value, the properties of the ground state of that system will
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Jing-Bo Xu [email protected]
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Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, People’s Republic of China
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Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, Frontier Research Institute for Physics and SPTE, South China Normal University, Guangzhou 510006, People’s Republic of China 0123456789().: V,-vol
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undergo a qualitative change. This particular value is actually the critical point of the QPT and is generated by the overlapping of the energy level of the ground state and the elimination of gaps within the energy spectrum. Traditionally, the task of obtaining the critical point of a QPT requires knowledge of order parameters and symmetry breaking [3]. Inspired by quantum information theory, a new alternative method to analyze the QTPs of a system has recently been developed. This new method uses some physical concepts from quantum information, including quantum entanglement [4], quantum coherence [5], trace distance [6] and fidelity [7], to investigate the QPTs of many-body systems. The benefit of this new method is that it enables researchers to study QPTs without an advanced understanding of symmetry breaking or order parameters. Quantum entangleme
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