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We show that for a d-dimensional model in which a quench with a rate tau^{-1} takes the system across a d-m dimensional critical surface, the defect density scales as n sim 1/tau^{m u/(z u +1)}, where u and z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d=2 and m= u=z=1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model which can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.
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We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n sim 1/sqrt{tau} where 1/tau is the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent non-zero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d dimensional quantum model, where the quench takes the system through a d-m dimensional gapless (critical) surface characterized by correlation length exponent u and dynamical critical exponent z, the defect density n sim 1/tau^{m u /(z u +1)}. We also discuss the variation of the shape and the spatial extent of the defect correlation function with the change of both the rate of quench and the model parameters and compute the entropy generated during such a quench process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.
We consider the defect production of a quantum system, initially prepared in a current-carrying non-equilibrium state, during its unitary driving through a quantum critical point. At low values of the initial current, the quantum Kibble-Zurek scaling for the production of defects is recovered. However, at large values of the initial current, i.e., very far from an initial equilibrium situation, a universal scaling of the defect production is obtained which shows an algebraic dependence with respect to the initial current value. These scaling predictions are demonstrated by the exactly solvable Ising quantum chain where the current-carrying state is selected through the imposition of a Dzyaloshinskii-Moriya interaction term.
Quantum entanglement and its main quantitative measures, the entanglement entropy and entanglement negativity, play a central role in many body physics. An interesting twist arises when the system considered has symmetries leading to conserved quantities: Recent studies introduced a way to define, represent in field theory, calculate for 1+1D conformal systems, and measure, the contribution of individual charge sectors to the entanglement measures between different parts of a system in its ground state. In this paper, we apply these ideas to the time evolution of the charge-resolved contributions to the entanglement entropy and negativity after a local quantum quench. We employ conformal field theory techniques and find that the known dependence of the total entanglement on time after a quench, $S_A sim log(t)$, results from $simsqrt{log(t)}$ significant charge sectors, each of which contributes $simsqrt{log(t)}$ to the entropy. We compare our calculation to numerical results obtained by the time-dependent density matrix renormalization group algorithm and exact solution in the noninteracting limit, finding good agreement between all these methods.
We discuss the exact solution for the properties of the recently introduced ``necklace model for reptation. The solution gives the drift velocity, diffusion constant and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.
The study of the entanglement dynamics plays a fundamental role in understanding the behaviour of many-body quantum systems out of equilibrium. In the presence of a globally conserved charge, further insights are provided by the knowledge of the resolution of entanglement in the various symmetry sectors. Here, we carry on the program we initiated in Phys. Rev. B 103, L041104 (2021), for the study of the time evolution of the symmetry resolved entanglement in free fermion systems. We complete and extend our derivations also by defining and quantifying a symmetry resolved mutual information. The entanglement entropies display a time delay that depends on the charge sector that we characterise exactly. Both entanglement entropies and mutual information show effective equipartition in the scaling limit of large time and subsystem size. Furthermore, we argue that the behaviour of the charged entropies can be quantitatively understood in the framework of the quasiparticle picture for the spreading of entanglement, and hence we expect that a proper adaptation of our results should apply to a large class of integrable systems. We also find that the number entropy grows logarithmically with time before saturating to a value proportional to the logarithm of the subsystem size.
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