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

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

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.

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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 -