### Abstract

We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-12 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the z direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a positive integer. For a linear quench of the strength of the magnetic field (or chemical potential) at a rate 1/τ across a quantum critical point, we find that the density of defects thereby produced scales as 1/τq ^{/(}q ^{+}1 ^{)}, deviating from the 1/√τ scaling that is ubiquitous in a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a nonlinear quench as well as by performing numerical simulations. We also show that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of τ, although it may exhibit a crossover at intermediate values of τ. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and the interaction strength.

Original language | English (US) |
---|---|

Article number | 165425 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 85 |

Issue number | 16 |

DOIs | |

State | Published - Apr 12 2012 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*85*(16), [165425]. https://doi.org/10.1103/PhysRevB.85.165425

**Quenching across quantum critical points in periodic systems : Dependence of scaling laws on periodicity.** / Thakurathi, Manisha; Degottardi, Wade; Sen, Diptiman; Vishveshwara, Smitha.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 85, no. 16, 165425. https://doi.org/10.1103/PhysRevB.85.165425

}

TY - JOUR

T1 - Quenching across quantum critical points in periodic systems

T2 - Dependence of scaling laws on periodicity

AU - Thakurathi, Manisha

AU - Degottardi, Wade

AU - Sen, Diptiman

AU - Vishveshwara, Smitha

PY - 2012/4/12

Y1 - 2012/4/12

N2 - We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-12 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the z direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a positive integer. For a linear quench of the strength of the magnetic field (or chemical potential) at a rate 1/τ across a quantum critical point, we find that the density of defects thereby produced scales as 1/τq /(q +1 ), deviating from the 1/√τ scaling that is ubiquitous in a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a nonlinear quench as well as by performing numerical simulations. We also show that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of τ, although it may exhibit a crossover at intermediate values of τ. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and the interaction strength.

AB - We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-12 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the z direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a positive integer. For a linear quench of the strength of the magnetic field (or chemical potential) at a rate 1/τ across a quantum critical point, we find that the density of defects thereby produced scales as 1/τq /(q +1 ), deviating from the 1/√τ scaling that is ubiquitous in a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a nonlinear quench as well as by performing numerical simulations. We also show that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of τ, although it may exhibit a crossover at intermediate values of τ. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and the interaction strength.

UR - http://www.scopus.com/inward/record.url?scp=84860289353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860289353&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.85.165425

DO - 10.1103/PhysRevB.85.165425

M3 - Article

AN - SCOPUS:84860289353

VL - 85

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 16

M1 - 165425

ER -