2010/10/31 by Victor Mukherjee, Anatoli Polkovnikov, Amit Dutta · 1 citation
Physics and Astronomy · #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physrevb.83.075118
published as Phys. Rev. B 83, 075118 (2011) · 12 pages, 9 figures
arxiv created 2011/02/25 · arxiv updated 2011/02/28
We study scaling behavior of the geometric tensor χα,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 λ1∼λ2 = λ when the system size L is bounded between 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 emergence of quasi-critical points at λ∼ 1/L1/ν1, related to the proximity to the critical line of 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 step-like behavior for small quench amplitudes. Study of heat density and diagonal entropy density also show signatures of quasi-critical points.