Quenching through Dirac and semi-Dirac points in optical lattices: Kibble-Zurek scaling for anisotropic quantum critical systems

Dutta, Amit ; Singh, R. R. P. ; Divakaran, Uma (2010) Quenching through Dirac and semi-Dirac points in optical lattices: Kibble-Zurek scaling for anisotropic quantum critical systems EPL (Europhysics Letters), 89 (6). p. 67001. ISSN 0295-5075

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Official URL: http://doi.org/10.1209/0295-5075/89/67001

Related URL: http://dx.doi.org/10.1209/0295-5075/89/67001

Abstract

We propose that Kibble-Zurek scaling can be studied in optical lattices by creating geometries that support Dirac, semi-Dirac and quadratic band crossings. On a honeycomb lattice with fermions, as a staggered on-site potential is varied through zero, the system crosses the gapless Dirac points, and we show that the density of defects created scales as 1/τ, where τ is the inverse rate of change of the potential, in agreement with the Kibble-Zurek relation. We generalize the result for a passage through a semi-Dirac point in d dimensions, in which spectrum is linear in m parallel directions and quadratic in the rest of the perpendicular (d-m) directions. We find that the defect density is given by 1/τmν||z||+(d-m)ν⊥z⊥ where ν||, z|| and ν⊥, z⊥ are the dynamical exponents and the correlation length exponents along the parallel and perpendicular directions, respectively. The scaling relations are also generalized to the case of non-linear quenching.

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Deposited On:16 Apr 2021 04:47
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