We study the transition of a quantum system S from a pure state to a mixed one, which is induced by the quantum criticality of the surrounding system E coupled to it. To characterize this transition quantitatively, we carefully examine the behavior of the Loschmidt echo (LE) of E modelled as an Ising model in a transverse field, which behaves as a measuring apparatus in quantum measurement. It is found that the quantum critical behavior of E strongly affects its capability of enhancing the decay of LE: near the critical value of the transverse field entailing the happening of quantum phase transition, the off-diagonal elements of the reduced density matrix describing S vanish sharply. Introduction: Nowadays quantum -classical transitions described by a reduction from a pure state to a mixture [1, 2] renew interests in many areas of physics, mainly due to the importance of quantum measurement and decoherence problem in quantum computing. To study this transition, some exactly-solvable models were proposed for a system coupled to the macroscopic [3,4,5] or classical [6,7] surrounding systems. Relevantly, in association with the quantum -classical transition in quantum chaos, the concept of Loschmidt echo (LE) from NMR experiments was introduced to describe the hypersensitivity of the time evolution to the perturbations experienced by the surrounding system [8,9]. In this letter, by a concrete example, we will show how quantum phase transition (QPT) [10] of the surrounding system can also sensitively affect the decay of its own LE, which means a dynamic reduction of its coupled system from pure state to a mixed one. Here, we note that a QPT effect has been explored for the Dicke model at the transition from quasi-integrable to quantum chaotic phases [11].

We show that a perfect quantum state transmission can be realized through a spin chain possessing a commensurate structure of energy spectrum, which is matched with the corresponding parity. As an exposition of the mirror inversion symmetry discovered by Albanese et. al (quant-ph/0405029), the parity matched the commensurability of energy spectra help us to present the novel pre-engineered spin systems for quantum information transmission. Based on the these theoretical analysis, we propose a protocol of near-perfect quantum state transfer by using a ferromagnetic Heisenberg chain with uniform coupling constant, but an external parabolic magnetic field. The numerical results shows that the initial Gaussian wave packet in this system with optimal field distribution can be reshaped near-perfectly over a longer distance.

We study the Non-Hermitian quantum mechanics for the discrete system. This paper gives an exact analytic single-particle solution for an N -site tight-binding chain with two conjugated imaginary potentials ±iγ at two end sites, which Hamiltonian has parity-time symmetry (PT symmetry). Based on the Bethe ansatz results, it is found that, in single-particle subspace, this model is comprised of two phases, an unbroken symmetry phase with a purely real energy spectrum in the region γ ≺ γc and a spontaneously-broken symmetry phase with N − 2 real and 2 imaginary eigenvalues in the region γ ≻ γc. The behaviors of eigenfunctions and eigenvalues in the vicinity of γc are investigated. It is shown that the boundary of two phases possesses the characteristics of exceptional point. We also construct the equivalent Hermitian Hamiltonian of the present model in the framework of metric-operator theory. We find out that the equivalent Hermitian Hamiltonian can be written as another bipartite lattice model with real long-range hoppings.

Asymmetric coupling amplitudes effectively create an imaginary gauge field, which induces a non-Hermitian Aharonov-Bohm (AB) effect. Nonzero imaginary magnetic flux invalidates the bulk-boundary correspondence and leads to a topological phase transition. However, the way of non-Hermiticity appearance may alter the system topology. By alternatively introducing the non-Hermiticity under symmetry to prevent nonzero imaginary magnetic flux, the bulk-boundary correspondence recovers and every bulk state becomes extended; the bulk topology of Bloch Hamiltonian predicts the (non)existence of edge states and topological phase transition. These are elucidated in a non-Hermitian Su-Schrieffer-Heeger model, where chiral-inversion symmetry ensures the vanishing of imaginary magnetic flux. The average value of Pauli matrices under the eigenstate of chiralinversion symmetric Bloch Hamiltonian defines a vector field, the vorticity of topological defects in the vector field is a topological invariant. Our findings are applicable in other non-Hermitian systems. We first uncover the roles played by non-Hermitian AB effect and chiral-inversion symmetry for the breakdown and recovery of bulk-boundary correspondence, and develop new insights for understanding non-Hermitian topological phases of matter. arXiv:1809.03139v3 [cond-mat.mes-hall]

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