Oscillating fidelity susceptibility near a quantum multicritical point

We study scaling behavior of the geometric tensor χ_α,β\(λ₁,λ₂\) and the fidelity susceptibility \(χ_{rm F}\) 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 $χ_{rm F}$ is drastically different from that seen near a critical point. In particular, we find that is highly non-monotonic function of λ along the generic direction λ_1simλ₂ = λ when the system size L is bounded between the shorter and longer correlation lengths characterizing the MCP: 1/|λ|^ν₁ll Lll 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 χ_αβ is associated with emergence of quasi-critical points at λsim 1/L^1/ν₁, related to the proximity to the critical line of finite momentum anisotropic transition. This scaling is different from that in the thermodynamic limit Lgg 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 step-like behavior for small quench amplitudes. Study of heat density and diagonal entropy density also show signatures of quasi-critical points.