Entanglement entropy dynamics of Heisenberg chains

By Gabriele De Chiara, Simone Montangero, Pasquale Calabrese, Rosario Fazio. 2005

243 citations recorded by the source corpus.

By means of the time dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyse the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare our results, wherever possible, with those obtained by means of conformal field theory. In the disordered case we find a slower (logarithmic) evolution which may signal the onset of entanglement localization.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/17a36d3a24e9a486478d0bd4646f4e6a7ae8c9d3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. E. Tonni
2. Pasquale Calabrese
3. A. Nahum
4. M. Fagotti
5. J. Cardy
6. J. Ruhman
7. S. Shenker
8. A. Allais

In Atomic and Molecular Physics, and Optics

1. Pasquale Calabrese
2. J. Cardy
3. E. Tonni
4. A. Nahum
5. M. Fagotti
6. A. Allais
7. F. Essler
8. D. Stanford

In Statistical and Nonlinear Physics

1. Pasquale Calabrese
2. D. Stanford
3. E. Tonni
4. S. Shenker
5. J. Cardy
6. A. Nahum
7. M. Fagotti
8. A. Allais

Citations in the corpus

• Black holes and the butterfly effect (2013, methodology): “Mutual information and entanglement entropy have been used to diagnose thermalization after a quantum quench, in both conventional [17, 18] and holographic setups [10, 19–26].”
• Quantum quenches in 1  +  1 dimensional conformal field theories (2016, background): “Quantum quenches in the presence of boundaries were also studied in the framework of boundary CFT [32, 63], but the results are very similar to those in the bulk and we do not discuss them here.”
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose–Hubbard model (2008, result): “ic boundary conditions, while t OBC = l=vfor blocks aligned with an open boundary. These characteristics of the entanglement evolution are similar to the results obtained for dierent models in Refs. [16,42,43,17,1,44]. A linear growth of the entropy has been seen up to times t= l=2v, where vis the m”
• Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos (2018, unknown): “Known exceptions to this empirical fact are systems exhibiting realspace localization [16,46], confinement [47], and quenched disorder creating weak links [48].”
• Quench dynamics and relaxation in isolated integrable quantum spin chains (2016, background): “This behaviour has been observed in a variety of lattice and continuum models [31, 48, 89, 109, 127, 182, 183, 206, 209], including non-integrable cases [183], in which the quasi-particle picture does not apply by virtue of the finite quasi-particle life time.”
• Local integrals of motion in many‐body localized systems (2016, background): “Numerical simulations performed on disordered spin chains initialized in a low-entangled/product state [13, 28, 106] display a transient fast growth of S(t) (dominated by the direct nearest-neighbor interactions across the cut and extending to times of the order of the inverse interaction coupling),”
• Holographic evolution of the mutual information (2011, methodology): “es through the translationally invariant Hamiltonian (local quench). These situations have been studied for two dimensional systems by employing conformal eld theory techniques and spin chains models [25, 26, 27, 28, 29]. Thermalization processes have been also widely considered from the holographic”