### Abstract

By means of free fermionic techniques combined with multiple precision arithmetic we study the time evolution of the averagemagnetization, m(t), of the randomtransverse-field Ising chain after global quenches.Weobserve different relaxation behaviors for quenches starting from different initial states to the critical point. Starting from a fully ordered initial state, the relaxation is logarithmically slow described by, m(t) ∼ ln^{a} t , and in a finite sample of length L the averagemagnetization saturates at a size-dependent plateau m_{p} (L)∼ L^{-b} here the two exponents satisfy the relation b/a = ψ = 1 2. Starting from a fully disordered initial state, the magnetization stays at zero for a period of time until t = t_{d} with ln t_{d} ∼L ψ and then starts to increase until it saturates to an asymptotic value m_{p} (L)∼ L^{-b}'with b'≈1.5. For both quenching protocols, finite-size scaling is satisfied in terms of the scaled variable ln t L^{ψ}. Furthermore, the distribution of long-time limiting values of the magnetization shows that the typical and the average values scale differently and the average is governed by rare events. The non-equilibrium dynamical behavior of the magnetization is explained through semi-classical theory.

Original language | English |
---|---|

Article number | 023055 |

Journal | New Journal of Physics |

Volume | 19 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1 2017 |

### Fingerprint

### Keywords

- disorder effects
- quantum ising chains
- quantum quench dynamics

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Critical quench dynamics of random quantum spin chains : Ultra-slow relaxation from initial order and delayed ordering from initial disorder.** / Roósz, Gergö; Lin, Yu Cheng; Iglói, F.

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 19, no. 2, 023055. https://doi.org/10.1088/1367-2630/aa60e6

}

TY - JOUR

T1 - Critical quench dynamics of random quantum spin chains

T2 - Ultra-slow relaxation from initial order and delayed ordering from initial disorder

AU - Roósz, Gergö

AU - Lin, Yu Cheng

AU - Iglói, F.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - By means of free fermionic techniques combined with multiple precision arithmetic we study the time evolution of the averagemagnetization, m(t), of the randomtransverse-field Ising chain after global quenches.Weobserve different relaxation behaviors for quenches starting from different initial states to the critical point. Starting from a fully ordered initial state, the relaxation is logarithmically slow described by, m(t) ∼ lna t , and in a finite sample of length L the averagemagnetization saturates at a size-dependent plateau mp (L)∼ L-b here the two exponents satisfy the relation b/a = ψ = 1 2. Starting from a fully disordered initial state, the magnetization stays at zero for a period of time until t = td with ln td ∼L ψ and then starts to increase until it saturates to an asymptotic value mp (L)∼ L-b'with b'≈1.5. For both quenching protocols, finite-size scaling is satisfied in terms of the scaled variable ln t Lψ. Furthermore, the distribution of long-time limiting values of the magnetization shows that the typical and the average values scale differently and the average is governed by rare events. The non-equilibrium dynamical behavior of the magnetization is explained through semi-classical theory.

AB - By means of free fermionic techniques combined with multiple precision arithmetic we study the time evolution of the averagemagnetization, m(t), of the randomtransverse-field Ising chain after global quenches.Weobserve different relaxation behaviors for quenches starting from different initial states to the critical point. Starting from a fully ordered initial state, the relaxation is logarithmically slow described by, m(t) ∼ lna t , and in a finite sample of length L the averagemagnetization saturates at a size-dependent plateau mp (L)∼ L-b here the two exponents satisfy the relation b/a = ψ = 1 2. Starting from a fully disordered initial state, the magnetization stays at zero for a period of time until t = td with ln td ∼L ψ and then starts to increase until it saturates to an asymptotic value mp (L)∼ L-b'with b'≈1.5. For both quenching protocols, finite-size scaling is satisfied in terms of the scaled variable ln t Lψ. Furthermore, the distribution of long-time limiting values of the magnetization shows that the typical and the average values scale differently and the average is governed by rare events. The non-equilibrium dynamical behavior of the magnetization is explained through semi-classical theory.

KW - disorder effects

KW - quantum ising chains

KW - quantum quench dynamics

UR - http://www.scopus.com/inward/record.url?scp=85014311347&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014311347&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/aa60e6

DO - 10.1088/1367-2630/aa60e6

M3 - Article

VL - 19

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 2

M1 - 023055

ER -