Oscillating fidelity susceptibility near a quantum multicritical point

Abstract

We study scaling behavior of the geometric tensor χα,β(λ1,λ2) and the fidelity susceptibility χF in the vicinity of a quantum multicritical point (MCP) using the example of a transverse XY model. We show that the behavior of the geometric tensor (and thus of χF) is drastically different from that seen near a critical point. In particular, we find that it is a highly nonmonotonic function of λ along the generic direction λ1~λ2=λ when the system size L is bounded by the shorter and longer correlation lengths characterizing the MCP: 1/|λ|ν1≪L≪1/|λ|ν2, where ν1<ν2 are the two correlation-length exponents characterizing the system. We find that the scaling of the maxima of the components of χαβ is associated with the emergence of quasicritical points at λ~1/L1/ν1, related to the proximity to the critical line of the finite-momentum anisotropic transition. This scaling is different from that in the thermodynamic limit L≫1/|λ|ν2, which is determined by the conventional critical exponents. We use our results to calculate the defect density following a rapid quench starting from the MCP and show that it exerts a steplike behavior for small quench amplitudes. A study of heat density and diagonal entropy density also shows signatures of quasicritical points.