Dynamical critical scaling and effective thermalization in quantum quenches: Role of the initial state

Abstract

We explore the robustness of universal dynamical scaling behavior in a quantum system near criticality with respect to initialization in a large class of states with finite energy. By focusing on a homogeneous XY quantum spin chain in a transverse field, we characterize the non-equilibrium response under adiabatic and sudden quench processes originating from a pure as well as a mixed excited initial state, and involving either a regular quantum critical or a multicritical point. We find that the critical exponents of the ground-state quantum phase transition can be encoded in the dynamical scaling exponents despite the finite energy of the initial state. In particular, we identify conditions on the initial distribution of quasi-particle excitation which ensure Kibble-Zurek scaling to persist. The emergence of effective thermal equilibrium behavior following a sudden quench towards criticality is also investigated, with focus on the long-time expectation value of the quasi-particle number operator. Despite the integrability of the XY model, this observable is found to behave thermally in quenches to a regular quantum critical point, provided that the system is initially prepared at sufficiently high temperature. However, a similar thermalization behavior fails to occur in quenches towards a multi-critical point. We argue that the observed lack of thermalization originates in this case in the asymmetry of the impulse region that is also responsible for anomalous multicritical dynamical scaling.

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

“…where p ex k is the probability of excitation of the k-th momentum mode during the quench [16,43], f k is related to fidelity (75) through (9)(10)(11)(12)(13), and again we assume |δ|, |ǫ| ≪ 1 and c = ǫ/|δ|. The scaling function B(c) -presented in Fig.…”

“…We estimated numerically the error between the exact integral (15) and the approximated one (43), what is presented in the Appendix. Note that (44) quantifies decay rate of fidelity with system size even when the oscillations are present (Fig.…”

Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems

“…In the case of an integrable system, it was shown that the quasi-particle number operator behaves thermally for a thermal (mixed) initial state at sufficiently high temperature [20]. Subsequently, it was argued that this would hold only for infinite temperature [21].…”

“…Cases have been presented of chaotic Hamiltonians where thermalization was not observed for certain initial states [12][13][14][15][16] and of integrable systems where thermalization appeared to be reached [17][18][19][20][21][22].…”

Effects Induced by the Initial Condition in the Quantum Kibble–Zurek Scaling for Changing the Symmetry-Breaking Field

“…As a result, the initial condition will affect the driven dynamics. This inspires many studies on how to generalize the Kibble-Zurek mechanism to take the effects induced by the initial conditions into account in both classical and quantum phase transitions [33][34][35][36][37][38].…”