By means of free fermionic techniques we study the time evolution of the entanglement entropy
S(t) of a block of spins in the random transverse-field Ising chain after a sudden change of the parameters of the Hamiltonian. We consider global quenches, when the parameters are modified uniformly in space, as well as local quenches, when two disconnected blocks are suddenly joined together. For a noncritical final state, the dynamical entanglement entropy is found to approach a finite limiting value for both types of quenches. If the quench is performed to the critical state, the entropy grows for an infinite block as $\mathcal{S}(t)\ensuremath{\sim}\mathrm{ln}\mathrm{ln}t$. This type of ultraslow increase is explained through the strong disorder renormalization group method.
Abstract. We study the out-of-equilibrium time evolution after a local quench connecting two anisotropic spin-1/2 XXZ Heisenberg open chains via an impurity bond. The dynamics is obtained by means of the adaptive time-dependent density-matrix renormalization group. We show that the entanglement entropies (Von Neumann and Rényi), in the presence of a weakened bond depend on the sign of the bulk interaction. For attractive interaction ( ∆ < 0), the defect turns out to be irrelevant and the evolution is asymptotically equivalent to the one without defect obtained by conformal field theory. For repulsive interaction ( ∆> 0), the defect is relevant and the entanglement saturates to a finite value. This out-of-equilibrium behavior generalizes the well known results for the ground-state entanglement entropy of the model. 1.
Using the density-matrix renormalization group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to
s=9/2. We show that through the relations arising from the conformal invariance and the DMRG technique it is possible to obtain accurate finite-size estimates of the conformal anomaly
c, the sound velocity
vs, the anomalous dimension
xbulk, and the surface exponent
xs of the anisotropic spin-
s Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entropy
S(L,lA,s) of the spin-
s Heisenberg chains satisfies the relation $S(L,{l}_{A},s)\ensuremath{-}S(L,{l}_{A},s\ensuremath{-}1)=1/(2s+1)$ for
s>3/2 in the thermodynamic limit.
In this article, we study the quench dynamics of the binary bond disordered Heisenberg spin chain. First, we develop a new algorithm, the ancilla TEBD method, which combines the purification technique and the time-evolving block decimation (TEBD) algorithm to study the entanglement dynamics of binary bonded disordered spin chains. With the support of exact diagonalization (ED), we calculate the multifaractal dimension of the binary bond disordered Heisenberg spin model and study its dependence on the strength of the disorder potential; we find that the multifaractal dimension shows no critical behavior which rules out the existence of the many body localization transition. Then, we reproduce the long time scaling of the von Neumann entropy at the time scale that is beyond the reach of typical TEBD and time dependent density matrix renormalization group (tDMRG) algorithms. Based on the numerical analysis, we propose that such a long time scaling is due to the competition of the spin interaction and the disorder which can be seen as a new mechanism for the generating of long time scale entropy dynamics. At last, we numerically proved the existence of the transient Mpemba effect in the bond disordered Heisenberg chain.
We numerically investigate the growth of the entanglement entropy
Sent(t) in time
t, after a global quench from a product state, in quantum chains with various kinds of disorder. The main focus is, in particular, on fermionic chains with bond disorder. In the noninteracting case at criticality we numerically test recent predictions by the real-space renormalization group for the entanglement growth in time, the maximal entanglement as a function of block size, and the decay of a density-wave order parameter. We show that multiprecision calculations are required to reach the scaling regime and perform such calculations for specific cases. For interacting models with binary bond disorder we present data based on infinite-size density matrix renormalization group calculations and exact diagonalizations. We obtain numerical evidence of a many-body localized phase in bond-disordered systems where ${S}_{\mathrm{ent}}(t)\ensuremath{\sim}lnt$ seems to hold. Our results for bond disorder are contrasted with the well-studied case of potential disorder.
We investigate the entanglement spreading in the anisotropic spin-
1/2 Heisenberg
(XXZ) chain after a geometric quench. This corresponds to a sudden change of the geometry of the chain or, in the equivalent language of interacting fermions confined in a box trap, to a sudden increase of the trap size. The entanglement dynamics after the quench is associated with the ballistic propagation of a magnetization wave front. At the free fermion point (
XX chain), the von Neumann entropy
SA exhibits several intriguing dynamical regimes. Specifically, at short times a logarithmic increase is observed, similar to local quenches. This is accurately described by an analytic formula that we derive from heuristic arguments. At intermediate times partial revivals of the short-time dynamics are superposed with a power-law increase ${S}_{A}\ensuremath{\sim}{t}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}<1$. Finally, at very long times a steady state develops with constant entanglement entropy, apart from oscillations. As expected, since the model is integrable, we find that the steady state is nonthermal, although it exhibits extensive entanglement entropy. We also investigate the entanglement dynamics after the quench from a finite to the infinite chain (sudden expansion). While at long times the entanglement vanishes, we demonstrate that its relaxation dynamics exhibits a number of scaling properties. Finally, we discuss the short-time entanglement dynamics in the
XXZ chain in the gapless phase. The same formula that describes the time dependence for the
XX chain remains valid in the whole gapless phase.