arXiv:1210.7328 · New Journal of Physics

Non-equilibrium quench dynamics in quantum quasicrystals

Ferenc Iglói, Gergő Roósz, Yu‐Cheng Lin

Published Feb 25, 2013• 23 citations

Abstract

We study the non-equilibrium dynamics of a quasiperiodic quantum Ising chain after a sudden change in the strength of the transverse field at zero temperature. In particular, we consider the dynamics of the entanglement entropy and the relaxation of the magnetization. The entanglement entropy increases with time as a power law, and the magnetization is found to exhibit stretched-exponential relaxation. These behaviors are explained in terms of anomalously diffusing quasiparticles, which are studied in a wave packet approach. The non-equilibrium magnetization is shown to have a dynamical phase transition.

DOI: 10.1088/1367-2630/15/2/023036

Related papers

Density of kinks after a sudden quench in the quantum Ising spin chain

Sei Suzuki, Davide Rossini, Giuseppe E. Santoro

arXiv:0910.4055Oct 21, 20090 citations

Quantum quenches from excited states in the Ising chain

Leda Bucciantini, Márton Kormos, Pasquale Calabrese

arXiv:1401.7250Journal of Physics A Mathematical and TheoreticalApr 11, 201477 citations

Nonequilibrium quantum relaxation across a localization-delocalization transition

Gergő Roósz, Uma Divakaran, Heiko Rieger +1 more

arXiv:1407.7829Physical Review BNov 7, 201440 citations

Entanglement entropy dynamics of disordered quantum spin chains

Ferenc Iglói, Zsolt Szatmári, Yu‐Cheng Lin

arXiv:1201.3695Physical Review BMar 12, 201288 citations

Entanglement entropy in a periodically driven quantum Ising ring

Tony J. G. Apollaro, G. Massimo Palma, Jamir Marino

arXiv:1603.03579Physical review. B./Physical review. BOct 12, 201618 citations

Quantum quenches from excited states in the Ising chain

Leda Bucciantini, Márton Kormos, Pasquale Calabrese

Jan 1, 201486 citations

arXiv:1210.7328 · New Journal of Physics

Non-equilibrium quench dynamics in quantum quasicrystals

Ferenc Iglói, Gergő Roósz, Yu‐Cheng Lin

Published Feb 25, 2013• 23 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1367-2630/15/2/023036

Related papers

Density of kinks after a sudden quench in the quantum Ising spin chain

Sei Suzuki, Davide Rossini, Giuseppe E. Santoro

We investigate the time evolution of the density of kinks in the spin-1/2 quantum Ising spin chain after a sudden quench in the transverse field strength, and find that it relaxes to a value which depends on the initial and the final values of the transverse field, with an oscillating power-law decay. We provide analytical estimates of the long-time behavior and of the asymptotic value reached after complete relaxation, and discuss the role of quantum criticality in the quench dynamics. We show that, for a dynamics at the critical point, the residual density of kinks after the quench can be described by equilibrium statistical mechanics at a finite temperature dictated by the energy of the state after the quench. On the other hand, outside of criticality it does not exhibit thermalization.We investigate the time evolution of the density of kinks in the spin-1/2 quantum Ising spin chain after a sudden quench in the transverse field strength, and find that it relaxes to a value which depends on the initial and the final values of the transverse field, with an oscillating power-law decay. We provide analytical estimates of the long-time behavior and of the asymptotic value reached after complete relaxation, and discuss the role of quantum criticality in the quench dynamics. We show that, for a dynamics at the critical point, the residual density of kinks after the quench can be described by equilibrium statistical mechanics at a finite temperature dictated by the energy of the state after the quench. On the other hand, outside of criticality it does not exhibit thermalization.

arXiv:0910.4055Oct 21, 20090 citations

Quantum quenches from excited states in the Ising chain

Leda Bucciantini, Márton Kormos, Pasquale Calabrese

We consider the non-equilibrium dynamics after a sudden quench of the magnetic field in the transverse field Ising chain starting from excited states of the pre-quench Hamiltonian. We prove that stationary values of local correlation functions can be described by the generalized Gibbs ensemble. Then we study the full time evolution of the transverse magnetization by means of stationary phase methods. The equal-time two-point longitudinal correlation function is analytically derived for a particular class of excited states for quenches within the ferromagnetic phase, and studied numerically in general. The full time dependence of the entanglement entropy of a block of spins is also obtained analytically for the same class of states and for arbitrary quenches.We consider the non-equilibrium dynamics after a sudden quench of the magnetic field in the transverse field Ising chain starting from excited states of the pre-quench Hamiltonian. We prove that stationary values of local correlation functions can be described by the generalized Gibbs ensemble. Then we study the full time evolution of the transverse magnetization by means of stationary phase methods. The equal-time two-point longitudinal correlation function is analytically derived for a particular class of excited states for quenches within the ferromagnetic phase, and studied numerically in general. The full time dependence of the entanglement entropy of a block of spins is also obtained analytically for the same class of states and for arbitrary quenches.

arXiv:1401.7250Journal of Physics A Mathematical and TheoreticalApr 11, 201477 citations

Nonequilibrium quantum relaxation across a localization-delocalization transition

Gergő Roósz, Uma Divakaran, Heiko Rieger +1 more

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), $h<{h}_{c}$ , the excitations (fermions) are delocalized, but become localized for $h>{h}_{c}$ . 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.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), $h<{h}_{c}$, the excitations (fermions) are delocalized, but become localized for $h>{h}_{c}$. 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.

arXiv:1407.7829Physical Review BNov 7, 201440 citations

Entanglement entropy dynamics of disordered quantum spin chains

Ferenc Iglói, Zsolt Szatmári, Yu‐Cheng Lin

By means of free fermionic techniques we study the time evolution of the entanglement entropy $\mathcal{S}(t)$ of a block of spins in the random transverse-field Ising chain after a sudden change of the parameters of the Hamiltonian. We consider global quenches, when the parameters are modified uniformly in space, as well as local quenches, when two disconnected blocks are suddenly joined together. For a noncritical final state, the dynamical entanglement entropy is found to approach a finite limiting value for both types of quenches. If the quench is performed to the critical state, the entropy grows for an infinite block as $\mathcal{S}(t)\ensuremath{\sim}\mathrm{ln}\mathrm{ln}t$. This type of ultraslow increase is explained through the strong disorder renormalization group method.By means of free fermionic techniques we study the time evolution of the entanglement entropy $\mathcal{S}(t)$ of a block of spins in the random transverse-field Ising chain after a sudden change of the parameters of the Hamiltonian. We consider global quenches, when the parameters are modified uniformly in space, as well as local quenches, when two disconnected blocks are suddenly joined together. For a noncritical final state, the dynamical entanglement entropy is found to approach a finite limiting value for both types of quenches. If the quench is performed to the critical state, the entropy grows for an infinite block as $\mathcal{S}(t)\ensuremath{\sim}\mathrm{ln}\mathrm{ln}t$. This type of ultraslow increase is explained through the strong disorder renormalization group method.

arXiv:1201.3695Physical Review BMar 12, 201288 citations

Entanglement entropy in a periodically driven quantum Ising ring

Tony J. G. Apollaro, G. Massimo Palma, Jamir Marino

We numerically study the dynamics of entanglement entropy, induced by an oscillating time periodic driving of the transverse field, $h(t)$ , of a one-dimensional quantum Ising ring. We consider several realizations of $h(t)$ , and we find a number of results in analogy with entanglement entropy dynamics induced by a sudden quantum quench. After a short-time relaxation, the dynamics of entanglement entropy synchronizes with $h(t)$ , displaying an oscillatory behavior at the frequency of the driving. Synchronization in the dynamics of entanglement entropy is spoiled by the appearance of quasirevivals which fade out in the thermodynamic limit, and which we interpret using a quasiparticle picture adapted to periodic drivings. We show that the time-averaged entanglement entropy in the synchronized regime obeys a volume law scaling with the subsystem's size. Such result is reminiscent of a thermal state or a generalized Gibbs ensemble, although the system does not heat up towards infinite temperature as a consequence of the integrability of the model.We numerically study the dynamics of entanglement entropy, induced by an oscillating time periodic driving of the transverse field, $h(t)$, of a one-dimensional quantum Ising ring. We consider several realizations of $h(t)$, and we find a number of results in analogy with entanglement entropy dynamics induced by a sudden quantum quench. After a short-time relaxation, the dynamics of entanglement entropy synchronizes with $h(t)$, displaying an oscillatory behavior at the frequency of the driving. Synchronization in the dynamics of entanglement entropy is spoiled by the appearance of quasirevivals which fade out in the thermodynamic limit, and which we interpret using a quasiparticle picture adapted to periodic drivings. We show that the time-averaged entanglement entropy in the synchronized regime obeys a volume law scaling with the subsystem's size. Such result is reminiscent of a thermal state or a generalized Gibbs ensemble, although the system does not heat up towards infinite temperature as a consequence of the integrability of the model.

arXiv:1603.03579Physical review. B./Physical review. BOct 12, 201618 citations

Quantum quenches from excited states in the Ising chain

Leda Bucciantini, Márton Kormos, Pasquale Calabrese

We consider the non-equilibrium dynamics after a sudden quench of the magnetic field in the transverse field Ising chain starting from excited states of the pre-quench Hamiltonian. We prove that stationary values of local correlation functions can be described by the generalised Gibbs ensemble (GGE). Then we study the full time evo-lution of the transverse magnetisation by means of stationary phase methods. The equal time two-point longitudinal correlation function is analytically derived for a par-ticular class of excited states for quenches within the ferromagnetic phase, and studied numerically in general. The full time dependence of the entanglement entropy of a block of spins is also obtained analytically for the same class of states and for arbitrary quenches. arWe consider the non-equilibrium dynamics after a sudden quench of the magnetic field in the transverse field Ising chain starting from excited states of the pre-quench Hamiltonian. We prove that stationary values of local correlation functions can be described by the generalised Gibbs ensemble (GGE). Then we study the full time evo-lution of the transverse magnetisation by means of stationary phase methods. The equal time two-point longitudinal correlation function is analytically derived for a par-ticular class of excited states for quenches within the ferromagnetic phase, and studied numerically in general. The full time dependence of the entanglement entropy of a block of spins is also obtained analytically for the same class of states and for arbitrary quenches. ar

Jan 1, 201486 citations

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),

h<{h}_{c}

, the excitations (fermions) are delocalized, but become localized for

h>{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.

By means of free fermionic techniques we study the time evolution of the entanglement entropy

\mathcal{S}(t)

of a block of spins in the random transverse-field Ising chain after a sudden change of the parameters of the Hamiltonian. We consider global quenches, when the parameters are modified uniformly in space, as well as local quenches, when two disconnected blocks are suddenly joined together. For a noncritical final state, the dynamical entanglement entropy is found to approach a finite limiting value for both types of quenches. If the quench is performed to the critical state, the entropy grows for an infinite block as $\mathcal{S}(t)\ensuremath{\sim}\mathrm{ln}\mathrm{ln}t$. This type of ultraslow increase is explained through the strong disorder renormalization group method.

We numerically study the dynamics of entanglement entropy, induced by an oscillating time periodic driving of the transverse field,

h(t)

, of a one-dimensional quantum Ising ring. We consider several realizations of

h(t)

, and we find a number of results in analogy with entanglement entropy dynamics induced by a sudden quantum quench. After a short-time relaxation, the dynamics of entanglement entropy synchronizes with

h(t)

, displaying an oscillatory behavior at the frequency of the driving. Synchronization in the dynamics of entanglement entropy is spoiled by the appearance of quasirevivals which fade out in the thermodynamic limit, and which we interpret using a quasiparticle picture adapted to periodic drivings. We show that the time-averaged entanglement entropy in the synchronized regime obeys a volume law scaling with the subsystem's size. Such result is reminiscent of a thermal state or a generalized Gibbs ensemble, although the system does not heat up towards infinite temperature as a consequence of the integrability of the model.