Homework 2: Algorithmic Perspective

Although I've tried to make things correct/clear there are occassionally typos/confusing wording/etc. When there is a discrepancy between the problem I clearly mean to be asking and the one I've asked, please solve the former. The piazza website is a good place to help us clarify the problem statements.

When answering questions please write out in a complete and explanatory way what you're doing. Someone who doesn't know what's going on should be able to read it and understand (so in addition to equations, use words!).

Problem 1: Uniform RVB

In class we've seen that you can represent the uniform RVB state as a

Explicitly write out the uniform RVB states in these three different forms (you may choose which boundary conditions you want for each representation). For the bosonic and fermionic RVB wave-function you need to establish the values of $f_{ij}.$ (For the fermionic case, it is a nice exercise to figure out how to do this in general for planar states). For the PEPS, you need to explicitly write out a set of tensors whose contraction gives the amplitude for the uniform RVB state.

Problem 2: Write a variational Monte Carlo code

Follow the tutorial at [https://dl.dropboxusercontent.com/u/90045/site/Tutorials/VMCIntroTutorial/index.html] to write a variational Monte Carlo code translating appropriately from python to Julia where necessary.

Problem 3: Matrix Product States

This problem is designed to get you to think about conceptual questions with MPS.