Repository logo

Data and code to generate figures for "Generating Symmetry-Protected Long-Range Entanglement (Dutta, Kuhr, Cooper)"

No Thumbnail Available



Change log


Dutta, Shovan 
Kuhr, Stefan 


Graphs for all figures are provided along with codes that implement the results described in the paper. We simulate how a spin chain subject to timed local pulses develops long-range entanglement and how timed pulses can also drive a Hubbard chain to a maximally-correlated η-pairing state. All simulations are performed using exact diagonalization in Mathematica. In Figure 2 we obtain how the central-spin magnetization and the bipartite entanglement in an XY spin-1/2 chain evolves in time. We also obtain the distribution among symmetry sectors with different levels of entanglement and concurrence matrices that show the build-up of long-range Bell pairs. In Figure 3 we show how the result generalizes to larger systems and how the entanglement and preparation time scale with the system size. We also show how the protocol is not sensitive to random timing error of the pulses. In Figure 4 we calculate how the fidelity is affected by several types of imperfections, showing it is relatively robust. In Figure 7 we compute experimentally measurable spin-spin correlations at different stages of the protocol. In Figure 8 we calculate level statistics in the presence of integrability breaking and show that the scaling of entanglement and preparation time are largely unaffected. In Figure 5 we illustrate the protocol for η-pairing by simulating the evolution of a strongly-interacting, finite Hubbard chain. In Figure 6 we compute signatures of eta pairing, including the average number of η pairs, their momentum distribution, and the overlap with the maximally-correlated state as a function of system size.


Software / Usage instructions

Graphs for all Figures are provided in a Mathematica notebook. The notebook also contains codes that implement the formulas. The records can be conveniently viewed by the (free) Wolfram Player, and documentation and labelling is provided.


Entanglement, Quantum many-body systems, Symmetry


Simons Foundation (511029)
Engineering and Physical Sciences Research Council (EP/P009565/1)