Symmetry-Resolved Entanglement Entropy for Local and Non-local QFTs

In this paper, we study symmetry-resolved entanglement entropy in free bosonic quantum many-body systems. Precisely, by making use of the lattice regularization scheme, we compute symmetry-resolved R\'enyi entropies for free complex scalar fields as well as for a simple class of non-local field theories in which entanglement entropy exhibits volume-law scaling. We present effective and approximate eigenvalues for the correlation matrix used to compute the symmetry-resolved entanglement entropy and show that they are consistent with the numerical results. Furthermore, we explore the equipartition of entanglement entropy and verify an effective equipartition in the massless limit. Finally, we make a comment on the entanglement entropy in the non-local quantum field theories and write down an explicit expression for the symmetry-resolved R\'enyi entropies.Comment: 27 pages, 15 figs, References added, typo fixe

An Upper Bound on Computation for the Anharmonic Oscillator

For a quantum system with energy E, there is a limitation in quantum computation which is identified by the minimum time needed for the state to evolve to an orthogonal state. In this paper, we will compute the minimum time of orthogonalization (i.e. quantum speed limit) for a simple anharmonic oscillator and find an upper bound on the rate of computations. We will also investigate the growth rate of complexity for the anharmonic oscillator by treating the anharmonic terms perturbatively. More precisely, we will compute the maximum rate of change of complexity and show that for even order perturbations, the rate of complexity increases while for the odd order terms it has a decreasing behavior.Comment: 9 pages, 5 figure

Complexity Growth Following Multiple Shocks

In this paper by making use of the "Complexity=Action" proposal, we study the complexity growth after shock waves in holographic field theories. We consider both double black hole-Vaidya and AdS-Vaidya with multiple shocks geometries. We find that the Lloyd's bound is respected during the thermalization process in each of these geometries and at the late time, the complexity growth saturates to the value which is proportional to the energy of the final state. We conclude that the saturation value of complexity growth rate is independent of the initial temperature and in the case of thermal initial state, the rate of complexity is always less than the value for the vacuum initial state such that considering multiple shocks it gets more smaller. Our results indicate that by increasing the temperature of the initial state, the corresponding rate of complexity growth starts far from final saturation rate value.Comment: 19 pages, 3 figs, Ref.s adde

Observable Quantities in Weyl Gravity

In this paper, the cosmological "constant" and the Hubble parameter are considered in the Weyl theory of gravity, by taking them as functions of $r$ and $t$, respectively. Based on this theory and in the linear approximation, we obtain the values of $H_0$ and $\Lambda_0$ which are in good agreement with the known values of the parameters for the current state of the universe.Comment: to be appear in MPL