The Diary of A Space Traveller (Coding up functions to calculate entanglement in lattice models)

Why did I start writing a blog all of a sudden? Very simple. I had an epiphany! It materialized in the form of being asked to do so by my employers. This is for Google Summer of Code 2019. I shall be developing programs for Qutip and NumFOCUS for lattice models calculations(yay!).  https://summerofcode.withgoogle.com/projects/#5960123627864064  I am very excited about this. I have always loved Qutip( http://qutip.org/ ) for the clarity of their codes. I have to develop codes that can deal with lattice models. I already like my mentors. It should be fun being part of this great team. I am very tired of people who do not disclose their codes citing excuses of 'intellectual property'. Getting paid to write open source codes is indeed the dream job!

I decided exact diagonalizing would be the smartest thing to do for a start. In concept, calculating the entanglement entropy from the ground state of a exact diagonalization procedure is fairly straightforward. Conceptualizing and writing the algorithm for diagonalizing a one diimensional Fermionic Hubbard chain has been fun. I shall only mention the trick that makes the whole process really elegant and fun. Any site has four possibilities namely no fermions, only spin-up, only spin-down and both spins. The four possibilities are very neatly cataloged with binary 00,01,10 and 11. So we take a binary string twice as long as the number of sites and every two bits of it represents the occupation of a site. Then we only have to count through the numbers from all 0's to all 1's and all the possible bases of the Hamiltonian are enumerated. I wish that was all the challenge there was. Unfortunately, it looks like I am looking at a long list of woes which starts with limited computer...

A highlight of my childhood is the adventures of Professor Shonku, a timeless creation of Satyajit Ray. The first short story that tells the tale of the discovery of the diary of Professor Shonku is titled "Byom Yatrir Diary" that translates into the title of my blog. If you are reading this blog out of curiosity for how some fascinating functions for quantum entanglement and topological quantization were developed, then sit tight, you are in for a journey of a lifetime.