One of the important problems in condensed matter is to identify Hamiltonian's whose ground states have interesting phases of matter. On the "list of interesting phases", spin liquids rank highly. In this paper, we numerically identify a Hamiltonian with a spin-liquid ground state; in particular we discover a (abelian nu=1/2) chiral spin liquid.
In what Hamiltonian do we find the chiral spin liquid? We look at the XY model on the kagome lattice at m=2/3 (i.e. the number of spin up minus spin down is 2/3). Kagome lattices are highly frustrated (they consist of corner-sharing triangles) and so are good places to look for spin-liquids. We can say with confidence that our numerical results show that if you take the XY Hamiltonian and add in a tiny (~0.04) chiral term, the ground state clearly looks like a chiral spin liquid. The reason we add the chiral term is to explicitly break the chiral symmetry. Even when the chirality term goes away, the evidence for the chiral spin-liquid is pretty strong.
How do we tell something is a chiral spin liquid? There are various measures we use to identify the spin liquid. In this case, we find the expected topological degeneracy, get a chern number per state of 1/2 and find the expected modular matrices. All the work involved in discovering (through many wrong paths) a CSL is quite involved (kudos to Hitesh and Krishna who pulled it off!) and a lot of computer time (~50,000 node-hours - thanks Blue Waters!) but now we have added one more Hamiltonian to the short-list of known spin liquids.
We've recently posted our paper, Fixed points of Wegner-Wilson flows and many-body localization. In this paper, we use an RG approach (Wegner-Wilson flows) to work out the flow diagram for a MBL system. To accomplish this we look at the flow of the probability distribution of the couplings of the l-bit Hamiltonian as the range of the coupling increases.
We find stable MBL and ergodic fixed points which are characterized by power-law and narrow distributions respectively. In addition, we find an unstable fixed point at the critical point (maybe critical phase?) which exhibits scale invariance with range.
To accomplish this, we've improved on our previous methodology for finding l-bits. In particular, instead of using bipartite matching we now use Wegner-Wilson flow.
The semester has just started and I'm teaching graduate quantum mechanics. Quantum mechanics has gotten a reputation as a subject that is conceptually difficult to understand. But in its most basic form, the 'rules' of quantum mechanics are fairly straight-forward. What people then typically mean by this is that the intepretation of these rules break our intuition for how we expect the world to work: electrons which can act like waves and particles at the same time, pairs of particles which exhibit 'spooky action at a distance', etc.
In 1958, Freeman Dyson talked about this second stage of learning quantum mechanics as confusing because the student is "trying to explain everything in terms of prequantum conceptions" but then goes on to say "Each new generation of students learns quantum mechanics more easily than their teachers learned it. [...] Ultimately [...] quantum mechanics will be accepted by students from the beginning as a simple and natural way of thinking [... and] we shall be ready for the next big jump into the unknown."
Its been over 50 years since Dyson has made this comment and I think it's certainly true as time goes on that we have shed many of the canonical difficulties of trying to learn quantum mechanics by "canonizing" classical mechanics in the correct way instead accepting the quantum mechanical rules on their own terms. At least one "big jump" this has brought us has been the perspective of using the power of quantum mechanics to accomplish tasks impossible under classical rules (i.e. quantum computing).
I look forward to my personal attempt to try to present the modern perspective on quantum mechanics to a new generation of graduate students.