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Entanglement evolution across defects in critical anisotropic Heisenberg chains

Mario Collura, Pasquale Calabrese

Published Aug 14, 2016• 41 citations
OpenAlex

Abstract

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.

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Entanglement evolution across defects in critical anisotropic Heisenberg chains

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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 (Δ< 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 (Δ>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.

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Jie Ren, Shiqun Zhu

The quantum entanglement dynamics of a one-dimensional spin-$1/2$ anisotropic $\mathit{XXZ}$ model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.

arXiv:1006.1417•Physical Review A•Jan 21, 2010•10 citations
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.
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 (Δ< 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 (Δ>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.
The long-range entanglement dynamics of an one-dimensional spin-1/2 anisotropic XXZ model are studied using the method of the adaptive time-dependent density-matrix renormalization-group. The long-range entanglement can be generated when a local quench on one of boundary bonds is performed in the system. The anisotropic interaction has a strong influence both on the maximal value of long-range entanglement and the time of reaching the maximum long-range entanglement. The local coupling has a notable impact on the long-range entanglement, but it can be neglected in the time of reaching the maximal long-range entanglement.
Abstract We consider a quench in a free-fermion chain by joining two homogeneous half-chains via a defect. The time evolution of the entanglement negativity is studied between adjacent segments surrounding the defect. In case of equal initial fillings, the negativity grows logarithmically in time and essentially equals one-half of the Rényi mutual information with index α = 1/2 in the limit of large segments. In sharp contrast, in the biased case one finds a linear increase followed by the saturation at an extensive value for both quantities, which is due to the backscattering from the defect and can be reproduced in a quasiparticle picture. Furthermore, a closer inspection of the subleading corrections reveals that the negativity and the mutual information have a small but finite difference in the steady state. Finally, we also study a similar quench in the XXZ spin chain via density-matrix renormalization group methods and compare the results for the negativity to the fermionic case.
We study the evolution of entanglement after a global quench in a one-dimensional quantum system with a localized impurity. For systems described by a conformal field theory, the entanglement entropy between the two regions separated by the defect grows linearly in time. Introducing the notion of boundary twist fields, we show how the slope of this growth can be related to the effective central charge that emerges in the study of ground-state entropy in the presence of the defect. On the other hand, we also consider a particular lattice realization of the quench in a free-fermion chain with a conformal defect. Starting from a gapped initial state, we obtain the slope via a quasiparticle ansatz and observe small discrepancies between the field theory and lattice results, which persist even in the limit of a vanishing gap.
Using the density-matrix renormalization group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to s=9/2s=9/2s=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 ccc, the sound velocity vs{v}_{s}vs​, the anomalous dimension xbulk{x}_{bulk}xbulk​, and the surface exponent xs{x}_{s}xs​ of the anisotropic spin-sss Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entropy S(L,lA,s)S(L,{l}_{A},s)S(L,lA​,s) of the spin-sss Heisenberg chains satisfies the relation $S(L,{l}_{A},s)\ensuremath{-}S(L,{l}_{A},s\ensuremath{-}1)=1/(2s+1)$ for s>3/2s>3/2s>3/2 in the thermodynamic limit.
The quantum entanglement dynamics of a one-dimensional spin-1/21/21/2 anisotropic XXZ\mathit{XXZ}XXZ model is studied using the method of the adaptive time-dependent density-matrix renormalization group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of a staggered magnetization quench are considered. The dynamics of the pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of the entanglement.