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arXiv:2002.00230 · Physical Review A

Dynamics of quantum coherence and quantum Fisher information after a sudden quench

Rouhollah Jafari, Alireza Akbari

Published Jun 8, 2020• 44 citations
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Abstract

The dynamics of relative entropy and ${l}_{1}$ norm of coherence, as well as, the Wigner-Yanase skew and quantum Fisher information are studied in the one-dimensional $XY$ spin chain in the presence of a time-dependent transverse magnetic field. We show that, independent of the initial state of the system and while the relative entropy of coherence, the ${l}_{1}$ norm of coherence, and quantum Fisher information are incapable, surprisingly, the Wigner-Yanase skew information dynamic can truly spotlight the equilibrium critical point. We also observe that, when the system is quenched to the critical point, these quantities show suppressions and revivals. Moreover, the first suppression (revival) time scales linearly with the system size and its scaling ratio is unique for all quenches independent of the initial phase of the system. This is the promised universality of the first suppression (revival) time.

DOI
10.1103/physreva.101.062105

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The dynamics of relative entropy and l1{l}_{1}l1​ norm of coherence, as well as, the Wigner-Yanase skew and quantum Fisher information are studied in the one-dimensional XYXYXY spin chain in the presence of a time-dependent transverse magnetic field. We show that, independent of the initial state of the system and while the relative entropy of coherence, the l1{l}_{1}l1​ norm of coherence, and quantum Fisher information are incapable, surprisingly, the Wigner-Yanase skew information dynamic can truly spotlight the equilibrium critical point. We also observe that, when the system is quenched to the critical point, these quantities show suppressions and revivals. Moreover, the first suppression (revival) time scales linearly with the system size and its scaling ratio is unique for all quenches independent of the initial phase of the system. This is the promised universality of the first suppression (revival) time.
We study the effect of noise on the dynamics of the transverse-field Ising model quenched across a quantum critical point. To quantify two-spin correlations, we employ the quantum Fisher information (QFI) and the Wigner-Yanase skew information (WYSI) as measures of quantum coherence. In the noiseless case, in contrast to the dynamics of entanglement in anisotropic XY chains, both QFI and WYSI increase monotonically with the ramp quench time, approaching their adiabatic limits without exhibiting any Kibble-Zurek-type scaling with quench duration. In contrast, when noise is added to the quench protocol, the coherence dynamics change qualitatively: QFI and WYSI both decay exponentially with the timescale of a ramp quench, with an exponent determined by the noise intensity. Furthermore, the maximum ramp time, at which either of these measures reaches its maximum, scales linearly with the noise variance, featuring the same exponent that determines the optimal annealing time for minimizing defect production in noisy quantum annealing.
We consider the dynamics of maximal quantum Fisher information (MQFI) after sudden quenches for the one-dimensional transverse-field Ising model. Our results show, the same as Loschmidt echo, that there is a universality for the revival times, i.e., they do not depend on the initial state and the size of the quench and are given by integer multiples of ${T}_{\text{rev}}\ensuremath{\simeq}\frac{N}{2{v}_{\text{max}}}$, where NNN is the system size and vmax{v}_{\text{max}}vmax​ is the maximal group velocity of quasiparticles. Critically enhanced and decreased at revival and decay times as ${T}_{\text{rev}}\ensuremath{\equiv}{T}_{\text{dec}}$ are characterized by quenching from the order and disorder phases into the quantum phase transition, respectively, that can be utilized to detect the quantum critical point (QCP). In some quenches crossed from the QCP, nonanalytic behaviors appear at some times due to the turning of the local observable from one direction to another because of identifying the maximum value. We name this phenomenon the dynamical MQFI transitions, occurring at the critical times tc{t}_{c}tc​. Interestingly, although no Fisher zero exists in the dynamics of MQFI, the first critical time emerged from the dynamical quantum phase transition is equal to the first time when the logarithm of MQFI is minimum. In addition, we unveil the long-time run of MQFI indicates a signature of a nonequilibrium quantum phase transition at the QCP. We also discuss the probability of the arising of macroscopic superpositions in the nonequilibrium dynamics of the system.
We investigate the behaviors of Wigner–Yanase skew information and the l1 norm, as two different measures of quantum coherence, in a tripartite ground state of the anisotropic spin-1/2 XY model. Following the renormalization-group method, we analytically link the two measures with each other and with the ground state energy of the system. We demonstrate that both the quantities show distinctive behaviors at the critical point of the system. The analysis of the first derivatives of the quantities reveals nonanalyticity in their behaviors, capturing quantum phase transition. The scaling behavior of the system is analyzed and it is shown that the minimum of the first derivative of Wigner–Yanase skew information converges to zero and the maximum of the first derivative of l1 norm diverges and both approach to the critical point with increasing size of the system.
We study the quantum dynamics resulting from preparing a one-dimensional quantum system in the ground state of initially two decoupled parts which are then joined together (local quench). Specifically we focus on the transverse Ising chain and compute the time-dependence of the magnetization profile, m_l(t), and correlation functions at the critical point, in the ferromagnetically ordered phase and in the paramagnetic phase. At the critical point we find finite size scaling forms for the nonequilibrium magnetization and compare predictions of conformal field theory with our numerical results. In the ferromagnetic phase the magnetization profiles are well matched by our predictions from a quasi-classical calculation.
Based on the obtained exact results we systematically study the quench dynamics of a one-dimensional spin-1/2 transverse field Ising model with zero- and finite-temperature initial states. We focus on the magnetization of the system after a sudden change of the external field and a coherent time-evolution process. With a zero-temperature initial state, the quench magnetic susceptibility as a function of the initial field strength exhibits strongly similar scaling behaviors to those of the static magnetic susceptibility, and the quench magnetic susceptibility as a function of the final field strength shows a discontinuity at the quantum critical point. This discontinuity remains robust and always occurs at the quantum critical point even for the case of finite-temperature initial systems, which indicates a great advantage of employing quench dynamics to study quantum phase transitions.
We study the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems, arising from sudden quenches of the Hamiltonian parameter ggg driving quantum transitions between disordered and ordered phases. In particular, we consider quenches to values of ggg around the critical value gc{g}_{c}gc​, and mainly address the question whether, and how, the quantum transition leaves traces in the evolution of the transverse and longitudinal magnetizations during such a deep out-of-equilibrium dynamics. We shed light on the emergence of singularities in the thermodynamic infinite-size limit, likely related to the integrability of the model. Finite systems in periodic and open boundary conditions develop peculiar power-law finite-size scaling laws related to revival phenomena, but apparently unrelated to the quantum transition, because their main features are generally observed in quenches to generic values of ggg. We also investigate the effects of dissipative interactions with an environment, modeled by a Lindblad equation with local decay and pumping dissipation operators within the quadratic fermionic model obtainable by a Jordan-Wigner mapping. Dissipation tends to suppress the main features of the unitary dynamics of closed systems. We finally address the effects of integrability breaking, due to further lattice interactions, such as in anisotropic next-to-nearest-neighbor Ising (ANNNI) models. We show that some qualitative features of the post-quench dynamics persist, in particular, the different behaviors when quenching to quantum ferromagnetic and paramagnetic phases, and the revival phenomena due to the finite size of the system.