Tuesday, July 25, 2006

Lattice 2006 -- Day One

Hello from Tucson, Arizona, where I am at the Lattice 2006 conference.

Unfortunately, I am facing a similar technical problem to that Matt experience last year in Dublin: the wireless age is not quite upon us yet (at least not unless one is willing to pay outrageous internet fees to the hotel), so I will have to report after the event, rather than blog live.

This year the lattice conference takes place here in the middle of the very picturesque Arizona desert (sorry, I forgot my camera at home -- I'm already kicking myself for it, so you don't need to) at the extremely luxurious Starr Pass resort. Getting here from Regina was more than a little tedious, but I won't bore you with tales of endless lineups at US customs or long-delayed flights. Instead I'll jump medias in res:

After a welcome message from the President of the University of Arizona and a number of announcements (such as that we should remember to drink plenty of water), the first plenary session (chaired by Junko Shigemitsu) started with a talk by Weonjong Lee about recent progress in Kaon physics on the lattice. The main point of his talk was to emphasize how essential improvement is in order to reduce the impact of lattice artifacts, and to advertize HYP smearing over ASQTAD. The results presented included demonstrations of how taste-breaking effects in the pion spectrum with staggered fermions get supressed by improvement, determinations of fπ and fK in full QCD, of BK in quenched QCD with an outlook towards full QCD results that should become available next year, and of K->ππ and Kl3 decays. He closed by suggesting that the MILC collaboration should create a set of Fat7bar configurations in addition to their ASQTAD configurations to allow people to investigate the better suppression of lattice spacing artifacts expected there.

Next was a talk by Stefan Schaefer about algorithms for dynamical simulations with overlap fermions. While overlap fermions have the advantages of preserving chiral symmetry exactly, possess automatic O(a) improvement and their spectrum has an exact relation to gauge field topology via the index theorem, they are extremely expensive to simulate, due to the appearance of the operator sign function in the overlap Dirac operator. One cause of this is that the exact link with topology implies that the overlap operator is discontinuous at the surfaces in the space of gauge connections that separate different topological sectors. Three possibilities to treat this have been proposed: the first is to modify the time evolution algorithm that generates the configurations by taking the existence of these surface into account and to properly reflect or refract a trajectory that would cross them; this has the advantage of being exact, but is very expensive because it requires a full inversion of the overlap operator each time a sector boundary is crossed. The second possibility is to approximate the sign function by some smooth function; this is much easier to implement, but has to deal with large forces near sector boundaries where the approximation becomes steep, and also needs a good approximation of the determinant function to work. The third alternative are topology-preserving gauge actions, which are set up so as to disallow transitions between topological sectors. In summary, while a lot of progress has been made, large volumes are still unattainable with overlap fermions at this time.

After a tea break there was a second plenary session, chaired by Mike Peardon. The first talk, by Kim Splittorf, was about the sign problem in the epsilon regima of QCD at finite chemical potential. The problem there is that at finite chemical potential, the discontinuity of the chiral condensate at zero quark mass cannot be understood in the same terms (via the Banks-Casher relation) as at zero chemical potential, because the eigenvalues can now be complex. Instead, the spectral density also becomes complex and develops oscillations that lead to the discontinuity.

The next speaker was Carlos Pena, who talked about determinations of weak matrix elements using twisted mass lattice QCD, especially about results that the ALPHA collaboration has obtained for BK, and results for BB that are expected next year.

The session was rounded off by Karl Jansen presenting the status of the ILDG. For those not active in the field, the International Lattice Data Grid is a grid framework that allows lattice theorists to share and access their configurations between countries and collaborations by linking the different national grids into a global grid. This requires agreeing on some common data format, a way to describe metadata (such as lattice size, actions used etc.) by means of an XML schema defining a language known as QCDml, and various layers of software linking it all together. The people working on this have done a lot of hard work for the benefit of the lattice community, and by giving people outside the large collaborations access to unquenched configurations on large lattices using their action of choice, this should help a lot to advance the state of the field.

In the afternoon there were two parallel session with a break for refreshments and informal conversations in between. I see little point in recounting which talks I went to, since that would at most reflect my biases rather than anything about the work being done by others in general.

In the evening there was an excursion dinner to Old Tucson, which is a movie set outside Tucson, where Westerns have been produced since the 1930s. The excursion featured some nice food, almost unbearable heat, a staged shootout between Western actors, some fairly bizarre and allegedly funny goings-on on the stage of the local Saloon, and a bit of stargazing. If that sounds odd, it doesn't half reflect how odd it really was (or at least how odd I thought it to be, which again may simply reflect my cultural biases). I might try and obtain some pictures from those who managed to bring their cameras, and if I succeed, some pictures may be posted on this blog.

3 comments:

Anonymous said...

Re: Schaefer's talk. I wanted to ask this during the plenary, but obviously didn't: how do you figure out what part of the HMC canonical momentum is perpendicular to the topological barrier? How do you even figure out which way a topological barrier points?

Xerxes

Georg said...

I don't know how this is done in practice, but maybe somebody who works on these kinds of things is reading this and can give an informed response?

Anonymous said...

The topological sector boundary is defined by lambda=0 surface in the gauge field space (lambda is the smallest eigenvalue of the overlap kernel - usually the hermitian Wilsom matrix). The direction is just the normal vector of this surface in that point where the HMC trajectory hits the surface.

KAlman