Sign Problems and Complex Actions

workshop at ECT* Trento

Monday March 2 - Friday March 6 2009

organizers: Gert Aarts (Swansea University) & Shailesh Chandrasekharan (Duke University)

click here for the workshop schedule and pdf's of the talks

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:


List of participants:

  1. Bartolome Alles
  2. Chris Allton
  3. Jacques Bloch
  4. Barak Bringoltz
  5. Philippe de Forcrand
  6. Massimo D'Elia
  7. Francesco Di Renzo
  8. Shinji Ejiri
  9. Gergely Endrodi
  10. Olga Goulko
  11. Sandor Katz
  12. Tamas Kovacs
  13. Dean Lee
  14. Maria-Paola Lombardo
  15. Joyce Myers
  16. Atsushi Nakamura
  17. Owe Philipsen
  18. David Reeb
  19. Erhard Seiler
  20. Denes Sexty
  21. Kim Splittorff
  22. Ion Stamatescu
  23. Boris Svistunov
  24. Urs Wenger
  25. Gert Aarts
  26. Shailesh Chandrasekharan


  1. Gert Aarts: Finite chemical potential with complex Langevin
  2. Bartolome Alles: The mass gap of the 2D O(3) Heisenberg model at theta=pi from simulations at imaginary theta
  3. Jacques Bloch: Random matrix theory as playground for the sign problem
  4. Barak Bringoltz: Baryon chemical potential in large N QCD
  5. Shailesh Chandrasekharan: Solution to sign problems in the worldline approach
  6. Philippe de Forcrand: Finite temperature and density QCD in the strong coupling limit
  7. Massimo D'Elia: Issues in analytic continuation: Spectral properties and the critical line
  8. Francesco Di Renzo: Langevin equation and complex actions: Are we missing anything? (discussion)
  9. Shinji Ejiri: A method to avoid the sign problem in finite density lattice QCD
  10. Gergely Endrodi: The curvature of the QCD phase transition line
  11. Dean Lee: Symmetries, signs, and complex actions in lattice effective field theory
  12. Maria-Paola Lombardo: Imaginary chemical potential and Taylor expansion: Mix & match
  13. Atsushi Nakamura: Searching paths to understand systems with a complex action
  14. Owe Philipsen: Lattice QCD at finite chemical potential (discussion)
  15. David Reeb: The severity of the sign problem in different regions of the dense-QCD phase diagram
  16. Erhard Seiler: Complex Langevin: Mathematical results and problems
  17. Denes Sexty: Real time simulations using stochastic quantisation
  18. Kim Splittorff: QCD with fixed complex fermion determinant
  19. Ion Stamatescu: What can we do with the complex action?
  20. Boris Svistunov: Diagrammatic Monte Carlo
  21. Urs Wenger: Solution of a sign problem by explicit bosonisation in two and three dimensions