Showing papers by "Uma Divakaran published in 2014"

Nonequilibrium quantum relaxation across a localization-delocalization transition

Abstract: We consider the one-dimensional $XX$ model in a quasiperiodic transverse field described by the Harper potential, which is equivalent to a tight-binding model of spinless fermions with a quasiperiodic chemical potential. For weak transverse field (chemical potential), $hl{h}_{c}$, the excitations (fermions) are delocalized, but become localized for $hg{h}_{c}$. We study the nonequilibrium relaxation of the system by applying two protocols: a sudden change of $h$ (quench dynamics) and a slow change of $h$ in time (adiabatic dynamics). For a quench into the delocalized (localized) phase, the entanglement entropy grows linearly (saturates) and the order parameter decreases exponentially (has a finite limiting value). For a critical quench the entropy increases algebraically with time, whereas the order parameter decreases with a stretched exponential. The density of defects after an adiabatic field change through the critical point is shown to scale with a power of the rate of field change and a scaling relation for the exponent is derived.

Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model

Abstract: We study the dynamics of a tilted one-dimensional Bose-Hubbard model for two distinct protocols using numerical diagonalization for a finite sized system ($N\ensuremath{\le}18$). The first protocol involves periodic variation of the effective electric field $E$ seen by the bosons which takes the system twice (per drive cycle) through the intermediate quantum critical point. We show that such a drive leads to nonmonotonic variation of the excitation density $D$ and the wave function overlap $F$ at the end of a drive cycle as a function of the drive frequency ${\ensuremath{\omega}}_{1}$, relate this effect to a generalized version of St\"uckelberg interference phenomenon, and identify special frequencies for which $D$ and $1\ensuremath{-}F$ approach zero leading to near-perfect dynamic freezing phenomenon. The second protocol involves a simultaneous linear ramp of both the electric field $E$ (with a rate ${\ensuremath{\omega}}_{1}$) and the boson hopping parameter $J$ (with a rate ${\ensuremath{\omega}}_{2}$) starting from the ground state for a low effective electric field up to the quantum critical point. We find that both $D$ and the residual energy $Q$ decrease with increasing ${\ensuremath{\omega}}_{2}$; our results thus demonstrate a method of achieving near-adiabatic protocol in an experimentally realizable quantum critical system. We suggest experiments to test our theory.

Fidelity susceptibility and Loschmidt echo for generic paths in a three-spin interacting transverse Ising model

Abstract: We study the effect of the presence of different types of critical points, such as ordinary critical points, multicritical points and quasicritical points, along different paths on the fidelity susceptibility and Loschmidt echo of a three-spin interacting transverse Ising chain using a method that does not involve the language of tensors. We find that the scaling of the fidelity susceptibility and Loschmidt echo with the system size at these special critical points of the model studied is in agreement with the known results, thus supporting our method.