Topological Characterization of Extended Quantum Ising Models

Zhang, G.; Song, Z.

doi:10.1103/physrevlett.115.177204

Cited by 100 publications

(85 citation statements)

References 39 publications

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“…The three-site interactions include again either (XZX+YZY) [18][19][20][21][22][23][24] or (XZY−YZX) forms [24][25][26][27][28]. Differently from the situation on the XX chains, two kinds of three-site interactions on the XY chains are not unitary equivalent.…”

Section: Introductionmentioning

confidence: 99%

Emergent phases in a compass chain with multisite interactions

You

Zhang

et al. 2017

Phys. Rev. B

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We study a dimerised spin chain with biaxial magnetic interacting ions in the presence of an externally induced three-site interactions out of equilibrium. In the general case, the three-site interactions play a role in renormalizing the effective uniform magnetic field. We find that the existence of zero-energy Majorana modes is intricately related to the sign of Pfaffian of the Bogoliubov-de Gennes Hamiltonian and the relevant Z2 topological invariant. In contrast, we show that an exotic spin liquid phase can emerge in the compass limit through a Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition. Such a BKT transition is characterized by a large dynamic exponent z = 4, and the spin-liquid phase is robust under a uniform magnetic field. We find the relative entropy and the quantum discord can signal the BKT transitions. We also uncover a few differences in deriving the correlation functions for the systems with broken reflection symmetry.

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Section: Introductionmentioning

confidence: 99%

Emergent phases in a compass chain with multisite interactions

You

Zhang

et al. 2017

Phys. Rev. B

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“…This model is related to the extended quantum Ising model with additional three-body interaction by JordanWigner transformation 23,24 . When ∆ 1,2 take real numbers, the Hamiltonian preserves the TRS for the spinless system, and belongs to the BDI class (Z type) characterized by the winding number.…”

Section: D Classmentioning

confidence: 99%

Topological invariants for phase transition points of one-dimensional Z2 topological systems

Yang

Chen

2016

Eur. Phys. J. B

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We study topological properties of phase transition points of two topologically non-trivial Z 2 classes (D and DIII) in one dimension by assigning a Berry phase defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter. While the topological property of the Z 2 system is generally characterized by a Z 2 topological invariant, we identify that it has a correspondence to the quantized Berry phase protected by the particle-hole symmetry, and then give a proper definition of Berry phase to the phase transition point. By applying our scheme to some specific models of class D and DIII, we demonstrate that the topological phase transition can be well characterized by the Berry phase of the transition point, which reflects the change of Berry phases of topologically different phases across the phase transition point.

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“…Recently, Zhang et al 25. propose a class of exactly solvable Ising models including short-range anisotropic interaction.…”

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confidence: 99%

Quantum correlation dynamics subjected to critical spin environment with short-range anisotropic interaction

Guo

Zhang

2016

Sci Rep

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Short-range interaction among the spins can not only results in the rich phase diagram but also brings about fascinating phenomenon both in the contexts of quantum computing and information. In this paper, we investigate the quantum correlation of the system coupled to a surrounding environment with short-range anisotropic interaction. It is shown that the decay of quantum correlation of the central spins measured by pairwise entanglement and quantum discord can serve as a signature of quantum phase transition. In addition, we study the decoherence factor of the system when the environment is in the vicinity of the phase transition point. In the strong coupling regime, the decay of the decoherence factor exhibits Gaussian envelop in the time domain. However, in weak coupling limit, the quantum correlation of the system is robust against the disturbance of the magnetic field through optimal control of the anisotropic short-range interaction strength. Based on this, the effects of the short-range anisotropic interaction on the sudden transition from classical to quantum decoherence are also presented.The quantum aspects of correlations in composite systems are a key issue in quantum information theory 1 . Quantum entanglement, which determines the given state is separable or not, has been regarded as a valuable resource for quantum information processing 2 . Even many people take it granted that quantum entanglement is quantum correlation. However, some separate states also contains quantum correlation and there exist quantum tasks that display the quantum advantage without entanglement 3 , so entanglement is not the only type of quantum correlation. Quantum discord (QD) defined as the difference between quantum mutual information and classical correlation 4 , is supposed to characterize all of nonclassical correlations including entanglement. Such states with non-zero QD but not entanglement may be responsible for the efficiency of a quantum computer 5,6 . Consequently, QD is believed a new resource for quantum computation.Meanwhile, study of quantum phase transition (QPT) 7 purely driven by quantum fluctuations can help us understand the physical properties of various matters from the perspective of quantum mechanics. During the past decade, the central spin model served as a paradimatic model characterizing the interaction between the quantum system and surrounding environment has received a lot of attentions [8][9][10] . On the one hand, it can provide a platform to investigate the underlying mechanism of the decoherence 11,12 due to the exact solvability of the model, which can pave the way to develop new methods that enhance the coherence time in the context of quantum computation and information 1,13 . On the other hand, one can identify the quantum phase transition through the quantum-classical transition of the system described by a reduction from a pure state to a mixture 14 . This stimulates a series of works regarding the disentanglement of central spins subjected to critical surrounding environment 10...

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Topological Characterization of Extended Quantum Ising Models

Cited by 100 publications

References 39 publications

Emergent phases in a compass chain with multisite interactions

Emergent phases in a compass chain with multisite interactions

Topological invariants for phase transition points of one-dimensional Z2 topological systems

Quantum correlation dynamics subjected to critical spin environment with short-range anisotropic interaction

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