Accurate Computations Near a Fermionic Quantum Critical Point
Understanding quantum critical behavior in strongly correlated fermion systems is an exciting contemporary topic of research, that arises in condensed matter, nuclear and particle physics. Although Monte Carlo calculations offer a first-principles approach to the problem, accurate computations near a fermionic quantum critical point has been missing so far due to difficulties in fermionic Monte Carlo methods. In a recent article that was accepted for publication in Physical Review Letters, Prof. Shailesh Chandrasekharanand a former Duke post doc Anyi Li (currently at the Institute for Nuclear Theory, in Seattle) propose a new idea in which fermionic physics is collected inside "fermion bags'' and the Monte Carlo calculations are performed using these extended objects as degrees of freedom. Interestingly, the size of the bags determines the computational cost and not the thermodynamic volume as earlier methods suggest. Using a new concept of duality one can also define bags such that their size is small at both small and large couplings. In the two figures shown here we show an artists rendition of a fermion bag and a dual fermion bag on a space-time lattice.
The solid bonds represent interactions. Difficulties that conventional methods encounter close to fermionic critical points are completed eliminated in the fermion bag approach. For the first time, Chandrasekharan and Li are able to accurately compute some important critical properties of an interesting fermionic quantum critical point in a strongly correlated fermion system using the new approach. Their research paper can be found here. It will appear in PRL shortly.