2018/07/31 by Vincenzo Alba · 3 citations
Mathematics · Physics and Astronomy · #Anisotropy #Ansatz #Bethe ansatz #Canonical ensemble #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Model Reduction and Neural Networks #Physics #Piecewise #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Statistical physics #Tensor decomposition and applications #Upper and lower bounds #cond-mat.quant-gas #cond-mat.stat-mech #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.99.045150
published as Phys. Rev. B 99, 045150 (2019) · 18 pages, 8 figures, similar to published version
openalex created_date 2018/07/10 · openalex publication_date 2019/01/29 · arxiv created 2019/02/10 · arxiv updated 2019/02/12 · openalex updated_date 2026/08/05
We investigate the steady-state R'enyi entanglement entropies after a quench from a piecewise homogeneous initial state in integrable models. In the quench protocol, two macroscopically different chains (leads) are joined together at the initial time, and the subsequent dynamics is studied. We study the entropies of a finite subsystem at the interface between the two leads. The density of R'enyi entropies coincides with that of the entropies of the generalized Gibbs ensemble that describes the interface between the chains. By combining the generalized hydrodynamics treatment of the quench with the Bethe ansatz approach for the R'enyi entropies, we provide exact results for quenches from several initial states in the anisotropic Heisenberg chain (XXZ chain), although the approach is applicable, in principle, to any low-entangled initial state and any integrable model. An interesting protocol that we consider is the expansion quench, in which one of the two leads is prepared in the vacuum of the model excitations. An intriguing feature is that for moderately large anisotropy the transport of bound state is not allowed. Moreover, we show that there is a ``critical'' anisotropy, below which bound-state transport is permitted. This is reflected in the steady-state entropies, which for large enough anisotropy do not contain information about the bound states. Finally, we benchmark our results against time-dependent density matrix renormalization group simulations.