Quenching across quantum critical points in periodic systems: Dependence of scaling laws on periodicity

Manisha Thakurathi, Wade Degottardi, Diptiman Sen, Smitha Vishveshwara

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number165425
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume85
Issue number16
DOIs
StatePublished - Apr 12 2012

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Scaling laws
Time varying systems
scaling laws
periodic variations
Quenching
critical point
Chemical potential
quenching
Magnetic fields
magnetic fields
Hamiltonians
Fermions
integers
crossovers
Momentum
Physics
fermions
interactions
momentum
scaling

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 85, No. 16, 165425, 12.04.2012.

Research output: Contribution to journalArticle

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