50 research outputs found

    Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary

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    We investigate the effect of a time-reversal breaking impurity term on both the equilibrium and non-equilibrium critical properties of entanglement entropy (EE) in a three-spin interacting transverse Ising model which can be mapped to a one-dimensional p-wave superconductor with next-nearest-neighbor hopping. Due to the presence of next-nearest-neighbor hopping, a new topological phase with two zero-energy Majorana modes at each end of an open chain appears in the phase diagram. We show that the derivative of EE with respect to one of the parameters of the Hamiltonian can detect the quantum phase transitions by exhibiting cusp like structure at those points; impurity strength (\la_d) can substantially modify the peak/dip height associated with the cusp. Importantly, we find that the logarithmic scaling of the EE with block size remains unaffected by the application of the impurity term, although, the coefficient (i.e., central charge) varies logarithmically with the impurity strength for a lower range of \la_d and eventually saturates with an exponential damping factor (\sim \exp(-\la_d)) for the phase boundaries shared with the phase containing two Majorana edge modes. On the other hand, it receives a linear correction in term of \la_d for an another phase boundary. Finally, we focus to study the effect of the impurity in the time evolution of the EE for the critical quenching case where impurity term is applied only to the final Hamiltonian. Interestingly, it has been shown that for all the phase boundaries in contrary to the equilibrium case, the saturation value of the EE increases logarithmically with the strength of impurity in a certain region of \la_d and finally, for higher values of \la_d, it increases very slowly which is dictated by an exponential damping factor.Comment: 10 pages, 10 figure

    Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

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    We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low frequency limit we use adiabatic theory, while in the high frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an "engineered" initial state where the particles (taken to be hard core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light cone like spreading of the particles in real space.Comment: 8 pages, 5 figures; this is the final published versio

    Fidelity, Rosen-Zener Dynamics, Entropy and Decoherence in one dimensional hard-core bosonic systems

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    We study the non-equilibrium dynamics of a one-dimensional system of hard core bosons (HCBs) in the presence of an onsite potential (with an alternating sign between the odd and even sites) which shows a quantum phase transition (QPT) from the superfluid (SF) phase to the so-called "Mott Insulator" (MI) phase. The ground state quantum fidelity shows a sharp dip at the quantum critical point (QCP) while the fidelity susceptibility shows a divergence right there with its scaling given in terms of the correlation length exponent of the QPT. We then study the evolution of this bosonic system following a quench in which the magnitude of the alternating potential is changed starting from zero (the SF phase) to a non-zero value (the MI phase) according to a half Rosen Zener (HRZ) scheme or brought back to the initial value following a full Rosen Zener (FRZ) scheme. The local von Neumann entropy density is calculated in the final MI phase (following the HRZ quench) and is found to be less than the equilibrium value (log2\log 2) due to the defects generated in the final state as a result of the quenching starting from the QCP of the system. We also briefly dwell on the FRZ quenching scheme in which the system is finally in the SF phase through the intermediate MI phase and calculate the reduction in the supercurrent and the non-zero value of the residual local entropy density in the final state. Finally, the loss of coherence of a qubit (globally and weekly coupled to the HCB system) which is initially in a pure state is investigated by calculating the time-dependence of the decoherence factor when the HCB chain evolves under a HRZ scheme starting from the SF phase. This result is compared with that of the sudden quench limit of the half Rosen-Zener scheme where an exact analytical form of the decoherence factor can be derived.Comment: To appear in European Physical Journal