Theory of defect production in nonlinear quench across a quantum critical point

Abstract

We study defect production in a quantum system subjected to a nonlinear power-law quench which takes it either through a quantum critical or multicritical point or along a quantum critical line. We elaborate on our earlier work ͓D. Sen, K. Sengupta, and S. Mondal, Phys. Rev. Lett. 101, 016806 ͑2008͔͒ and present a detailed analysis of the scaling of the defect density n with the quench rate and exponent ␣ for each of the abovementioned cases. We also compute the correlation functions for defects generated in nonlinear quenches through a quantum critical point and discuss the dependence of the amplitudes of such correlation functions on the exponent ␣. We discuss several experimental systems where these theoretical predictions can be tested.

Scaling Behavior and Beyond Equilibrium in the Hexagonal Manganites

“…Such vortexantivortex annihilation causes a leveling off of the rate at which the density of vortex cores increases with cooling rate, but it does not cause the decrease in density that we observe. The effect of nonlinearity in the quench rate on the density of defects has been calculated to yield a modified scaling law [50], which again would not cause our observed turnaround at fast cooling rates. In addition, inhomogeneous cooling, and departures from linear cooling, which are both more likely in the fast-quench regime, have been shown to result in a suppression of defect formation [51,52] but again should result in a leveling off rather than our observed pronounced downturn.…”

Kibble-Zurek scaling of the irreversible entropy production

“…and thus the constant quench rate˙ (t) is given by one over driving is straight forward and can be found, for instance, in Refs. [31][32][33][34][35].…”

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

“…A non-KZS behavior (n ∼ 1/τ 1/6 ) of the density of defects (wrongly oriented spins) for quenching across the MCP of the spin-1/2 transverse XY chain was reported for the first time in reference [8] which was later explained in reference [21] introducing an effective dynamical exponent z 2 (= 3) for Jordan-Wigner solvable spin chains [22] reducible to a collection of decoupled two-level systems in the Fourier space and applying Landau-Zener (LZ) transition formula [23]. This argument was extended to the non-linear quenching of a general Hamiltonian in refer- * Electronic address: victor@iitk.ac.in † Electronic address: dutta@iitk.ac.in ence [24]. In a recent communication, Deng et al [25], attributed this anomalous scaling behavior to the existence of quasicritical points close to a MCP where the energy gap is minimum and proposed a generic scaling for the multicritical quantum quenches in terms of the effective critical exponents associated with these quasicritical points.…”

“…Since in the limit of τ → ∞, the maximum contribution to the defect comes from the vicinity of t 0 , we linearize the Hamiltonian (6) [24] …”