Entanglement dynamics following a sudden quench: An exact solution

Ghosh, S. K.; Gupta, Kumar S.; Srivastava, Shashi C. L.

doi:10.1209/0295-5075/120/50005

Cited by 30 publications

(36 citation statements)

References 46 publications

(82 reference statements)

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“…In order to achieve the above, we study the exact relaxation dynamics following multiple global quenches in a harmonic chain with N oscillators which is trivially integrable. For this system, the exact entanglement dynamics following a single quench has been studied earlier [42]. Under a multiple quench protocol, we show that the offdiagonal terms in the one-particle reduced density matrix [22,26] vanish exponentially fast in time in the limit of large N , while the diagonal terms saturates to a steady value.…”

Section: Introductionmentioning

confidence: 72%

“…Here the frequency ω and the nearest neighbour coupling k are explicit functions of time. A solution of the corresponding time dependent Schrödinger's equation (TDSE) [42,49,50] i…”

Section: Harmonic Chain and The Quench Protocolmentioning

confidence: 99%

“…In order to study the entanglement entropy, we bipartite the system into two parts of one oscillator versus N − 1 oscillators. The entanglement entropy of the smaller subsystem calculated using the reduced density matrix (16) has the form [42]…”

Section: Momentum Distribution and Entropymentioning

confidence: 99%

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Exact relaxation dynamics and quantum information scrambling in multiply quenched harmonic chains

2019

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The quantum dynamics of isolated systems under quench condition exhibits a variety of interesting features depending on the integrable/chaotic nature of system. We study the exact dynamics of trivially integrable system of harmonic chains under a multiple quench protocol. Out of time ordered correlator of two Hermitian operators at large time displays scrambling in the thermodynamic limit. In this limit, the entanglement entropy and the central component of momentum distribution both saturate to a steady state value. We also show that reduced density matrix assumes the diagonal form long after multiple quenches for large system size. These exact results involving infinite dimensional Hilbert space are indicative of local thermal behaviour for a trivially integrable harmonic chain.

show abstract

Section: Introductionmentioning

confidence: 72%

“…Here the frequency ω and the nearest neighbour coupling k are explicit functions of time. A solution of the corresponding time dependent Schrödinger's equation (TDSE) [42,49,50] i…”

Section: Harmonic Chain and The Quench Protocolmentioning

confidence: 99%

See 1 more Smart Citation

Exact relaxation dynamics and quantum information scrambling in multiply quenched harmonic chains

2019

Self Cite

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“…Recently, the solution (3.6) is extensively used in Ref. [31] to discuss the dynamics of entanglement for the sudden quenched states of two site Bose-Hubbard model. Since TDSE is a linear differential equation, the general solution of TDSE is Ψ(…”

Section: Solutions Of Tdsementioning

confidence: 99%

“…Recently, the entanglement is computed in the coupled harmonic oscillator system using a Schmidt decomposition [30]. The von Neumann and Rényi entropies are also explicitly computed in the similar system, called two site Bose-Hubbard model [31]. More recently, the dynamics of entanglement and uncertainty is exactly derived in the two coupled harmonic oscillator system when frequency and coupling constant parameters are arbitrary time-dependent [32].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of entanglement in three coupled harmonic oscillator system with arbitrary time-dependent frequency and coupling constants

Park

2019

Quantum Inf Process

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The dynamics of mixedness and entanglement is examined by solving the time-dependent Schrödinger equation for three coupled harmonic oscillator system with arbitrary time-dependent frequency and coupling constants parameters. We assume that part of oscillators is inaccessible and remaining oscillators accessible. We compute the dynamics of entanglement between inaccessible and accessible oscillators. In order to show the dynamics pictorially we introduce three quenched models. In the quenched models both mixedness and entanglement exhibit oscillatory behavior in time with multi-frequencies. It is shown that the mixedness for the case of one inaccessible oscillator is larger than that for the case of two inaccessible oscillators in the most time interval.Contrary to the mixedness entanglement for the case of one inaccessible oscillator is smaller than that for the case of two inaccessible oscillators in the most time interval. arXiv:1811.06256v2 [quant-ph]

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Quantum quench in c = 1 matrix model and emergent space-times

Das¹,

Hampton²,

Liu³

2020

J. High Energ. Phys.

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We consider quantum quench in large-N singlet sector quantum mechanics of a single hermitian matrix in the double scaling limit. The time dependent parameter is the self-coupling of the matrix. We find exact classical solutions of the collective field theory of eigenvalue density with abrupt smooth quench profiles which asymptote to constant couplings at early and late times, and the system is initially in its ground state. With adiabatic initial conditions we find that adiabaticity is always broken regardless of the quench speed. In a class of quench profiles the saddle point solution for the collective field diverges at a finite time, and a further time evolution becomes ambiguous. However the underlying matrix model expressed in terms of fermions predict a smooth time evolution across this point. By studying fluctuations around the saddle point solution we interpret the emergent space-times. They generically have spacelike boundaries where the couplings of the fluctuations diverge. Only for very finely tuned quench profiles, the space-time is normal.

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Entanglement dynamics following a sudden quench: An exact solution

Cited by 30 publications

References 46 publications

Exact relaxation dynamics and quantum information scrambling in multiply quenched harmonic chains

Exact relaxation dynamics and quantum information scrambling in multiply quenched harmonic chains

Dynamics of entanglement in three coupled harmonic oscillator system with arbitrary time-dependent frequency and coupling constants

Quantum quench in c = 1 matrix model and emergent space-times

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