Quench dynamics near a quantum critical point

Abstract

We study the dynamical response of a system to a sudden change of the tuning parameter starting ͑or ending͒ at the quantum critical point. In particular, we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude, and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning parameter, showing a close connection between the scaling behavior of these quantities with the singularities of the adiabatic susceptibilities of order m at the quantum critical point, where m is related to the power of the quench. Precisely for sudden quenches, the relevant susceptibility of the second order coincides with the fidelity susceptibility. We discuss the generalization of the scaling laws to the finite-temperature quenches and show that the statistics of the low-energy excitations becomes important. We illustrate the relevance of those results for cold-atom experiments.PACS number͑s͒: 64.70. Tg, 64.70.qj, 67.85.Ϫd Understanding the dynamics of quantum interacting systems is one of the key challenges of the modern physics. The theoretical research in this area has been stimulated by the fast developments in the field of cold-atom experiments 1 and the emerging possibility of manipulating quantum systems. 2 In particular, the idea of suddenly changing a parameter of the Hamiltonian, i.e., performing a quench, has been widely addressed within different approaches.3-6 Furthermore, recently the interest in studying quenches has been motivated by the questions on the thermalization of quantum systems. 7 Quenches near quantum critical points are especially interesting because of the expected universality of the response of the system and thus the possibility of using the quench dynamics as a nonequilibrium probe of phase transitions. This universality is well established in equilibrium systems. 8 It has been shown that a universal scaling arises as well in the case of slow adiabatic perturbations that drive the system through a quantum critical point. 9,10 The predicted scaling for the number of created quasiparticles with the quench rate was verified for various specific models. [11][12][13][14][15][16] This analysis was also generalized to nonlinear quenches. 17,18 In this work we consider a d-dimensional system described by a Hamiltonian H͑͒ = H 0 + V, where H 0 is the Hamiltonian corresponding to a quantum critical point ͑QCP͒ and V is a relevant ͑or marginal͒ perturbation, which drives the system to a particular phase. The quench process is implemented through the parameter that changes in time, according to some protocol, between the initial value =0 at time t = 0, corresponding to the critical point, and the final value f at final time t f . 29 We expect two qualitatively different scenarios: ͑i͒ for fast quenches, the response of the system only depends on the quench amplitude f , but not on the details of the protocol used to change -we refer to this regime as sudden quench; ͑ii͒ for slow quenches, i...

Pinning quantum phase transition in a Tonks-Girardeau gas: Diagnostics by ground-state fidelity and the Loschmidt echo

“…[6] and Eq. (20). Adding more particles, i.e., N > N pinn , leads to ρ 0 (N,0) > n c , but now in some regions left and right from x = 0, the density becomes commensurate with lattice, i.e., ρ 0 (N,−d) ≈ n c and ρ 0 (N,d) ≈ n c , for some d > 0, and pinning still occurs, i.e., additional gaps in SP spectrum are present and GSF still lowers.…”

“…which yields N pinn ≈ k 2h 2mω 0 (20) for the number of particles where pinning occurs. Equation (20) is obtained for n 1; in experiments, one usually has N > 30.…”

“…If the system is in the ground state | 0 and we suddenly turn on optical lattice V l (x), the probability that we will excite the system away from the initial ground state is conveniently related to the ground-state fidelity [20] …”

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