Fidelity susceptibility and general quench near an anisotropic quantum critical point

Abstract

We study the scaling behavior of fidelity susceptibility density (χf) at or close to an anisotropic quantum critical point characterized by two different correlation length exponents ν|| and ν⊥ along parallel and perpendicular spatial directions, respectively. Our studies show that the response of the system due to a small change in the Hamiltonian near an anisotropic quantum critical point is different from that seen near an isotropic quantum critical point. In particular, for a finite system with linear dimension L|| (L⊥) in the parallel (perpendicular) directions, the maximum value of χf is found to increases in a power-law fashion with L|| for small L||, with an exponent depending on both ν|| and ν⊥ and eventually crosses over to a scaling with L⊥ for L1/ν||||≳L1/ν⊥⊥. We also propose scaling relations of heat density and defect density generated following a quench starting from an anisotropic quantum critical point and connect them to a generalized fidelity susceptibility. These predictions are verified exactly both analytically and numerically taking the example of a Hamiltonian showing a semi-Dirac band-crossing point.