A measure of quantum correlation defined from an information-theoretic perspective, namely, quantum discord, is applied to study the time-evolved nonequilibrium state of the infinite anisotropic quantum XY spin chain in a transverse time-dependent field. In particular, we probe whether the collapse and revival of nearest-neighbor entanglement of the state seen with a varying initial applied field strength, at a fixed evolution time, may be predicted from the behavior of the quantum correlation measure. For this quantum many-body system, realizable with currently available technology, we find that the revival of entanglement of the evolved state occurs if there is an increase in quantum discord in the vicinity of entanglement collapse. © 2012 Europhysics Letters Association.

Rupamanjari Ghosh

SNU Management

H. Shekhar Dhar

A. Sen

U. Sen

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Shiv Nadar University

We investigate the static and dynamical patterns of entanglement in an anisotropic XY model with an alternating transverse magnetic field, which is equivalent to a two-component one-dimensional Fermi gas on a lattice, a system realizable with current technology. Apart from the antiferromagnetic and paramagnetic phases, the model possesses a dimer phase which is not present in the transverse XY model. At zero temperature, we find that the first derivative of bipartite entanglement can detect all the three phases. We analytically show that the model has a "factorization line" on the plane of system parameters, in which the zero-temperature state is separable. Along with investigating the effect of temperature on entanglement in a phase plane, we also report a nonmonotonic behavior of entanglement with respect to temperature in the antiferromagnetic and paramagnetic phases, which is surprisingly absent in the dimer phase. Since the time dynamics of entanglement in a realizable physical system plays an important role in quantum information processing tasks, the evolutions of entanglement at small as well as large time are examined. Consideration of large-time behavior of entanglement helps us to prove that in this model, entanglement is always ergodic. We observe that other quantum correlation measures can qualitatively show similar features in zero and finite temperatures. However, unlike nearest-neighbor entanglement, the nearest-neighbor information-theoretic measures can be both ergodic as well as nonergodic, depending on the system parameters. © 2016 American Physical Society.

Physical Review A

Static and dynamical quantum correlations in phases of an alternating-field XY model

We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures or belong to the information-theoretic paradigm, exhibit a universal behavior. In particular, for Haar uniformly simulated arbitrary two-qubit states, we find that the first-digit distributions corresponding to a collection of chosen computable quantum correlation quantifiers tend to follow the first-digit law, known as Benford's law, when the rank of the states increases. Considering a two-qubit state which is obtained from a system governed by paradigmatic spin Hamiltonians, namely, the XY model in a transverse field, and the XXZ model, we show that entanglement as well as information-theoretic measures violate Benford's law. We quantitatively discuss the violation of Benford's law by using a violation parameter, and demonstrate that the violation parameter can signal quantum phase transitions occurring in these models. We also comment on the universality of the statistics of the first significant digits corresponding to appropriate measures of quantum correlations in the case of multipartite systems as well as systems in higher dimensions. © CopyrightEPLA, 2016.