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Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching

We study adiabatic quantum quenches across a quantum multicritical point (MCP) using a quenching scheme that enables the system to hit the MCP along different paths. We show that the power-law scaling of the defect density with the rate of driving depends non-trivially on the path, i.e., the exponent varies continuously with the parameter $α$ that defines the path, up to a critical value $α= α_c$; on the other hand for $α\geq α_c$, the scaling exponent saturates to a constant value. We show that dynamically generated and {\it path($α$)-dependent} effective critical exponents associated with the quasicritical points lying close to the MCP (on the ferromagnetic side), where the energy-gap is minimum, lead to this continuously varying exponent. The scaling relations are established using the integrable transverse XY spin chain and generalized to a MCP associated with a $d$-dimensional quantum many-body systems (not reducible to two-level systems) using adiabatic perturbation theory. We also calculate the effective {\it path-dependent} dimensional shift $d_0(α)$ (or the shift in center of the impulse region) that appears in the scaling relation for special paths lying entirely in the paramagnetic phase. Numerically obtained results are in good agreement with analytical predictions.