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

Thakurathi, Manisha and DeGottardi, Wade and Sen, Diptiman and Vishveshwara, Smitha (2012) Quenching across quantum critical points in periodic systems: Dependence of scaling laws on periodicity. In: Phys Rev B, 85 (16).

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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-1/2 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the (z) over cap 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/tau across a quantum critical point, we find that the density of defects thereby produced scales as 1/tau(q/(q+1)), deviating from the 1/root tau 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 tau, although it may exhibit a crossover at intermediate values of tau. 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.

Item Type: Journal Article
Additional Information: Copyright of this article is belongs to The American Physical Society.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: review EPrints Reviewer
Date Deposited: 22 Aug 2012 05:01
Last Modified: 22 Aug 2012 05:01
URI: http://eprints.iisc.ac.in/id/eprint/44465

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