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

Every Quantum-problem-solver person is a repeat-offender of a simple crime! Diagonalizing! I am writing about the philosophy of diagonalizing in a bid to elucidate the underlying motive of the QuTiP functions I am writing. I am writing about a humble problem of calculating the dispersion relationship. Although, algorithmically or computationally it is not intimidating, it exemplifies one of the most effective diagonalization technique at our disposal-- translational symmetry! In exact diagonalization of an interacting model translational symmetry technique can become the difference between an in and out-of-reach problem. If a 1d lattice can be resolved into a unit cell repeating N times, the translational symmetry can help reduce the length of the matrix to be diagonalized by a factor of N. For interacting models which scale as 2(or 4) to the power N, this little reduction in size can make a problem solvable with a given computational resource. Using other symmetries can help

At first, I did not think it necessary to add the "subject-to-change" clause at the end of the title, but now I know better! The process of first getting the correct functionality to actually convince the developers of QuTiP of the 'mergabilty'/readiness of the code is painstaking. Long before I managed to convince my mentors of the readiness of the code, I was able to get the codes to work and Writing codes for a popular simulation tool is much more demanding than writing codes for your research. My codes have already undergone a complete overhaul, almost everyday change, so as to make the code compatible with the spirit and soul of QuTiP. The science problem is only a fraction of the challenge. Finding the most convenient data structure and optimization philosophy is the . The code capability is crucially dependent on data structures and memory usage. I have had to spend a massive amount of time restructuring the code and developing documentation. Please ch