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

TL;DR

This paper investigates how the scaling of defect density during adiabatic quantum quenches across a multicritical point varies continuously with the quench path, revealing path-dependent critical exponents and their theoretical foundations.

Contribution

It introduces a path-dependent scaling framework for quantum quenches at multicritical points, extending the understanding of non-equilibrium dynamics in quantum many-body systems.

Findings

Scaling exponent varies with path parameter α up to a critical value α_c.

Effective critical exponents depend on the quench path and proximity to the MCP.

Analytical predictions match numerical results in the transverse XY model.

Abstract

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 $\alpha$ that defines the path, up to a critical value $\alpha= \alpha_c$; on the other hand for $\alpha \geq \alpha_c$, the scaling exponent saturates to a constant value. We show that dynamically generated and {\it path($\alpha$)-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 $d_0(\alpha)$ (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.