Spin-spin decoherence

This code simulates the dynamics of a closed spin chain using the Bethe ansatz for an XXX chain model. There is a figure of merit comparing the simulations for different implementations of the algorithms. The times are ordered like the legend of the figure final_plot.png. Two of the Python files are named as the algorithm they implement, and the final_plot.py one combines the implementation of both to obtain the figure of merit.

Experiment

The simulated experiment is the spin echo experiment. The observable is the $x$ component of the magnetization of the rotated spin.

Algorithms

The simulation has been run using two algorithms:

1. Using the analytical solution, which required exponential resources as the amount of particles in the chain increases.
2. Using a polinomially expensive algorithm in a truncated Hilbert space where the available excitations are considered to be limited given an external magnetic field that is strong enough. You can find more details about this algorithm in the paper by A. Lunghi and S. Sanvito, Electronic Spin-Spin Decoherence Contribution in Molecular Qubits by Quantum Unitary Dynamics, Journal of magnetism and Magnetic materials 487 (2019)

Variables and results

After running the codes there are some clear results:

1. Increase of the decoherence due to:
   • More spins in the chain
   • Longer distance interaction (which strength decay can be tuned)
   • Stronger spin-spin interaction
2. The implemented algorithm improves significantly the performance when the analytical solution begins to compile too slowly. Considering 2 excitations is usually enough to have almost no numerical error in the simulation, and compiles around 10 times faster.

Future work

The algorithm can be personalized even further:

• Considering an even more truncated hilbert space, with excitations only close to the rotated spin in the spin chain
• Comparing how the distance and magnitude of the interaction constant affects the decoherence in a quantitative way
• Instead of using the parameters for an isotropic material and an XXX spin chain, the g-factor and dipolar interaction matrices can be tuned to simulate real molecules or lattices.