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We consider the dynamics of the quantum XY chain with disorder under thegeneral assumption that the expectation of the eigenfunction correlator of theassociated one-particle Hamiltonian satisfies a decay estimate typical ofAnderson localization. We show that, starting from a broad class of productinitial states, entanglement remains bounded for all times. For the XX chain,we also derive bounds on the particle transport which, in particular, show thatthe density profile of initial states that consist of fully occupied and emptyintervals, only have significant dynamics near the edges of those intervals,uniformly for all times.

Deep neural networks (DNN) can be applied at the post-processing stage for the improvement of the results of quantum computations on noisy intermediate-scale quantum (NISQ) processors. Here, we propose a method based on this idea, which is most suitable for digital quantum simulation characterized by the periodic structure of quantum circuits consisting of Trotter steps. A key ingredient of our approach is that it does not require any data from a classical simulator at the training stage. The network is trained to transform data obtained from quantum hardware with artificially increased Trotter steps number (noise level) toward the data obtained without such an increase. The additional Trotter steps are fictitious, i.e., they contain negligibly small rotations and, in the absence of hardware imperfections, reduce essentially to the identity gates. This preserves, at the training stage, information about relevant quantum circuit features. Two particular examples are considered that are the dynamics of the transverse-field Ising chain and XY spin chain, which were implemented on two real five-qubit IBM Q processors. A significant error reduction is demonstrated as a result of the DNN application that allows us to effectively increase quantum circuit depth in terms of Trotter steps. [ABSTRACT FROM AUTHOR]

In this review, we discuss the zero and finite temperature behavior of various bipartite quantum and total correlation measures, the skew information-based quantum coherence and the local quantum uncertainty in the thermal ground state of the one-dimensional anisotropic XY model in a transverse magnetic field. We compare the ability of the considered measures to correctly detect or estimate the quantum critical point and the non-trivial factorization point possessed by the spin chain.

Quantum many-body systems have been extensively studied from the perspective of quantum technology, and conversely, critical phenomena in such systems have been characterized by operationally relevant resources like entanglement. In this paper, we investigate robustness of magic (RoM), the resource in magic state injection based quantum computation schemes, in the context of the transverse field anisotropic XY model. We show that the the factorizable ground state in the symmetry broken configuration is composed of an enormous number of highly magical H states. We find the existence of a point very near the quantum critical point where magic contained explicitly in the correlation between two distant qubits attains a sharp maxima. Unlike bipartite entanglement, this persists over very long distances, capturing the presence of long range correlation near the phase transition. We derive scaling laws and extract corresponding exponents around criticality. Finally, we study the effect of temperature on two-qubit RoM and show that it reveals a crossover between dominance of quantum and thermal fluctuations.

In this review, we discuss the zero and finite temperature behavior of various bipartite quantum and total correlation measures, the skew information-based quantum coherence and the local quantum uncertainty in the thermal ground state of the one-dimensional anisotropic XY model in a transverse magnetic field. We compare the ability of the considered measures to correctly detect or estimate the quantum critical point and the non-trivial factorization point possessed by the spin chain. [ABSTRACT FROM AUTHOR]

We investigate the quantum discord dynamics of a two-qubit system coupled to an XY spin-chain environment with energy current. We compared dynamical behaviors of quantum discord under different system-environment couplings, the size of the degrees of freedom of the environment, the anisotropy parameter, and the energy current. The results indicate that the energy current can strongly suppress the quantum discord in the weak-coupling region, while it has no obvious effect on the quantum discord in the strong-coupling regime. [ABSTRACT FROM AUTHOR]

We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky-Moriya (DM) interaction in the presence of a transverse magnetic field. An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit. We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the thermal quantum and total correlations in the anisotropic XY spin chain in transverse field. While we adopt concurrence and geometric quantum discord to measure quantum correlations, we use measurement-induced non-locality and an alternative quantity defined in terms of Wigner–Yanase information to quantify total correlations. We show that the ability of these measures to estimate the critical point at finite temperature strongly depend on the anisotropy parameter of the Hamiltonian. We also identify a correlation measure which detects the factorized ground state in this model. Furthermore, we study the effect of temperature on long-range correlations. [Copyright &y& Elsevier]

By calculating the Berry Phase (BP) of a central spin, the quantum criticality of the surrounding environment described by an XY spin chain with the three-site interaction in a transverse magnetic field is explored. The BP presents anomalous behavior along the critical region. The finite-size scaling behaviors suggest that the BP of the central spin can well capture the critical properties of the XY spin chain with the three-site interaction. [ABSTRACT FROM AUTHOR]

Abstract: By means of the Loschmidt Echo (LE) and Berry Phase (BP) calculations, quantum phase transition (QPT) of an XY spin chain with three-site interaction (α) in a transverse magnetic field (λ) is studied. Both the LE and BPʼs λ derivative present anomaly behaviors at the critical regions and . The model is in the Ferromagnetic phase as and in the Spin Liquid I phase as . and are independent on the anisotropy parameter γ. But, the anisotropy interaction can shift the critical line between the Spin Liquid II phase and the Ferromagnetic phase. The present work suggests that QPT of the XY spin chain with three-site interaction can be characterized by exploring the dynamical behaviors of the LE and BP. [Copyright &y& Elsevier]

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities. [ABSTRACT FROM AUTHOR]

We study an asymptotic behavior of the probability of formation of a ferromagnetic string (referred to as EFP) of length n in the ground state of the one-dimensional anisotropic XY model in a transversal magnetic field as n→∞. We find that it is exponential everywhere in the phase diagram of the XY model except at the critical lines where the spectrum is gapless. One of those lines corresponds to the isotropic XY model where EFP decays in a Gaussian way, as was shown in [J. Phys. Soc. Jpn. 70 (2001) 3535]. The other lines are at the critical value of the magnetic field. There, we show that EFP is still exponential but acquires a non-trivial power-law prefactor with a universal exponent. [Copyright &y& Elsevier]

• Investigation of the single- and two-spin coherence in the extended XY chain. • Relation between the coherence and topological phase transitions is established. • Finite temperatures affect the accuracy of detection for phase transition points. • Critical properties of the coherence for long-distance spin-pairs are analyzed. We study the quantum criticality of single- and two-spin coherence, based on the quantum skew information, in the extended XY model, and analyze the impact of different driving parameters, finite temperatures and site distances of spin-pair on their critical behaviors. We find that the first-order derivative of quantum coherence can correctly detect the topological quantum phase transitions (TQPTs), but the finite temperatures strongly affect the accuracy of detection for critical points. For the case of long-distance spin-pairs, we find that the quantum coherence is a long-range correlation and its first-order derivative can also correctly detect the TQPTs at the absolute zero temperature. Moreover, the quantum coherence itself under absolute zero temperature can also signal the partial TQPTs by a local extrema in several certain situations. [ABSTRACT FROM AUTHOR]