Gapped quantum criticality gains long-time quantum correlations

Abstract

-We show gapped critical environment could remarkably prevent an enhanced decay of decoherence factor and quantum correlations at the critical point, which is nontrivially different from the ones in a gapless critical environment (Quan, et.al Phys. Rev. Lett. 96, 140604 (2006)). The quantum correlations display very fast decaying to their local minimum at the critical point while maximum decaying occurs away from this point. In particular, our results imply that collapse of decoherence factor is not indicator of a quantum phase transition of environment as opposed to what happens in a gapless criticallity. In the week coupling regime, the relaxation time, at which the quantum correlations touch rapidly local minima, shows a power-law singularity as a function of gap. Furthermore, quantum correlations decay exponentially with second power of relaxation time. Our results are important for a better understanding and characterisation of gap critical environment and its ability as entanglers in open quantum systems.Quantum correlations (QCs) are of primary importance in quantum information [1,2] and quantum computation [3][4][5]. They are related to the basic issue of understanding the nature of non-locality in quantum mechanics [6,7]. Quantum systems used in quantum information processing inevitably interact with the surrounding environment. These correlated surrounding systems induce quantum decoherency which plays a key role in the understanding of the quantum to the classical transition [8,9]. As a result, in the last decade a lot of efforts have been devoted to investigate QCs dynamics and decoherence factors of central systems in various environments [10,11]. The decoherence of a system coupled to a spin environment with quantum phase transition (QPT) has been investigated intensively in various studies [11][12][13][14][15][16][17][18][19][20]. Quan et al. [21] considered induction of the Ising-type correlated environment on the Loschmidt echo (LE), and found that the decaying behavior of LE is best enhanced by gapless QPT of the surrounding system. Rossini et al. [22] depicted that in the short time region the LE decays as a Gaussian. However for long time limits they found that it approaches an asymptotic value, which strongly depends on the strength of the transverse magnetic field. Further, the decoherence of a system coupled to a spin environment with QPT has been investigated [12][13][14].The quantum phase transition occurs at a level crossing point (gapless phase transition) or converged point of avoided level crossing point (gapped critical point) [23]. Because of the convergence of the energy levels at the critical point (CP), some special dynamic features may appear in the dynamic evolution of the central system in contact with an environment with QPT. It is shown that the disentanglement of the central system is greatly enhanced by the gapless quantum criticality of the environment [12]. Furthermore, the decoherence induced by the critical environment may display some universal features [13]...

Quench dynamics and zero-energy modes: The case of the Creutz model

“…In the case of a sudden quench, a very efficient approach is to employ the notion of the Loschmidt echo (LE) [7] − the modulus of the Loschmidt amplitude (LA) − which measures the overlap of the initial quantum state with its time-evolved state controlled by the post-quench Hamiltonian. In fact, the LE has been explored for a variety of problems connected directly or indirectly to quench dynamics, including quantum chaos [8][9][10], quantum speed limit time [11], quantum decoherence [12][13][14][15][16][17][18], equilibrium quantum phase transitions [13,[19][20][21][22][23][24][25][26], dynamical quantum phase transitions [22,[27][28][29][30][31][32][33][34][35][36][37][38], work statistics [26,39,40] and entropy production [23].…”

Magnetic quantum correlations in the one-dimensional transverse-field XXZ model

“…Moreover, there exist intimations that the QD is the resource responsible for the speed up in deterministic quantum computation with one quantum bit [11,12]. Entanglement and QD have been studied extensively in a number of contexts, e.g., low dimensional spin models [13][14][15][16][17][18][19], open quantum systems [20][21][22][23][24], biological [25], and relativistic [26,27] systems. Recently, pairwise QD and entanglement have been analyzed as a function of distance between spins in the transverse field XY chain for both zero and finite temperatures cases [18,[28][29][30].…”

Real Space Renormalization of Majorana Fermions in Quantum Nano-Wire Superconductors

“…Unlike traditional approaches, prior knowledge about the symmetries and order parameters of the model are not required in the fidelity notion to find out a QPT. In addition, fidelity has an interdisciplinary role, for example, it is related to the density of topological defects after a quench [38,39], decoherence rate of a test qubit interacting with a non-equilibrium environment [40,41], and orthogonality catastrophe of condensed matter systems [42]. In this section, we implement the formalism introduced in Refs.…”