Sign Problems and Complex Actions
Scientific background:
The understanding of strongly interacting matter and a variety of strongly
correlated materials requires a nonperturbative analysis employing numerical
simulations. In the conventional formulations of these problems, introduction
of a chemical potential makes the action complex. Hence, the standard Monte
Carlo method to evaluate the path integral through importance sampling fails,
since there is no clear probability distribution to sample from. This problem
is commonly known as the sign problem and is an outstanding problem in field
theory and many-body physics. One prime example of a theory in particle
physics where the sign problem arises is QCD at nonzero baryon density. There
are also many condensed matter materials of interest where sign problems have
hindered progress. This includes frustrated quantum spin systems and strongly
correlated electronic systems away from half filling.
Fortunately, in recent years radical new approaches have been developed which
can handle the sign problem or even eliminate it altogether. For a class of
field and many-body theories, these methods are based on rewriting the
partition function in a dual set of variables, similar to worldline (WL)
representations. In many cases, the WL-approach suggests new solutions to the
sign problem. Promising results have also been obtained using stochastic
quantization and complex Langevin dynamics. In this case the sign problem is
potentially circumvented by complexifying all degrees of freedom, so that the
theory's phase space is explored in an inherently different fashion.
In this workshop we aim to learn about sign problems that arise in lattice
field theory, understand what has been done and explore what can be done in
the future. Although many of the researchers in the workshop will be interested
in the physics of QCD at nonzero baryon density, we wish to bring researchers
from nuclear and condensed matter physics to the workshop so that new ideas
may emerge. We have in mind a rather technical, interdisciplinary workshop
focusing on methods and techniques that have been used in different fields.
Topics will concentrate on the following set of issues:
- Nature of sign problems
- Worldline formulations
- Complex Langevin methods
- Diagrammatic Monte Carlo
- Extrapolation methods
- Reweighting methods
- Other methods ...
Practicalities:
-
The organizers can be contacted at
g.aarts @ swan.ac.uk (Aarts) and sch @ phy.duke.edu (Chandrasekharan).
- The number of participants is limited.
- Registration can be done at the
ECT* website, click on Meetings in
2009 to proceed to the registration link.
- Registration is now closed
- The workshop will start Monday March 2 at 10am. Registration will open
at 9am.
- The workshop will finish Friday March 6 at 5pm.
- There will be welcome buffet on Monday evening.
- click here for the workshop schedule
List of participants:
- Bartolome Alles
- Chris Allton
- Jacques Bloch
- Barak Bringoltz
- Philippe de Forcrand
- Massimo D'Elia
- Francesco Di Renzo
- Shinji Ejiri
- Gergely Endrodi
- Olga Goulko
- Sandor Katz
- Tamas Kovacs
- Dean Lee
- Maria-Paola Lombardo
- Joyce Myers
- Atsushi Nakamura
- Owe Philipsen
- David Reeb
- Erhard Seiler
- Denes Sexty
- Kim Splittorff
- Ion Stamatescu
- Boris Svistunov
- Urs Wenger
- Gert Aarts
- Shailesh Chandrasekharan
Presentations:
- Gert Aarts: Finite chemical potential with
complex Langevin
- Bartolome Alles: The mass gap of the 2D O(3)
Heisenberg model at theta=pi from simulations at imaginary theta
- Jacques Bloch: Random matrix theory as playground for the sign problem
- Barak Bringoltz: Baryon chemical potential in large N QCD
- Shailesh Chandrasekharan: Solution to sign problems
in the worldline approach
- Philippe de Forcrand: Finite temperature and density QCD in the
strong coupling limit
- Massimo D'Elia: Issues in analytic continuation: Spectral properties
and the critical line
- Francesco Di Renzo: Langevin equation and complex actions: Are we
missing anything? (discussion)
- Shinji Ejiri: A method to avoid the sign problem in finite density
lattice QCD
- Gergely Endrodi: The curvature of the QCD phase transition line
- Dean Lee: Symmetries, signs, and complex actions in lattice effective
field theory
- Maria-Paola Lombardo: Imaginary chemical potential and Taylor
expansion: Mix & match
- Atsushi Nakamura: Searching paths to understand systems with a
complex action
- Owe Philipsen: Lattice QCD at finite chemical potential (discussion)
- David Reeb: The severity of the sign problem in different regions of
the dense-QCD phase diagram
- Erhard Seiler: Complex Langevin: Mathematical results and problems
- Denes Sexty: Real time simulations using stochastic quantisation
- Kim Splittorff: QCD with fixed complex fermion determinant
- Ion Stamatescu: What can we do with the complex action?
- Boris Svistunov: Diagrammatic Monte Carlo
- Urs Wenger: Solution of a sign problem by explicit bosonisation in
two and three dimensions