Abstract
We study the two dimensional lattice Thirring model in the presence of a fermion chemical po- tential. Our model is asymptotically free, contains massive fermions that mimic a baryon and light bosons that mimic pions. Hence it is a useful toy model for QCD, especially since it too suffers from a sign problem in the auxiliary field formulation in the presence of a fermion chemical potential. In this work we formulate the model in both the world line and fermion-bag representations and show that the sign problem can be completely eliminated with open boundary conditions when the fermions are massless. Hence we are able accurately compute a variety of interesting quantities in the model, and these results could provide benchmarks for other methods that are being developed to solve the sign problem in QCD.
Highlights
Traditional lattice calculations of quantum field theories often encounter sign problems in the presence of a chemical potential
In the world line approach, we argue in this work that the sign problem is absent with open boundary conditions and zero fermion mass
In order to get a better understanding of the origin of the sign problem in our model, we look at the representation of the fermion determinant DetðW1⁄2fÞ inside free fermion bags as a sum over their world lines
Summary
Traditional lattice calculations of quantum field theories often encounter sign problems in the presence of a chemical potential. While these ideas have been able to capture some of the qualitative features of more complex field theories [10,11], in these cases, the numerical results are not always compared with benchmark calculations obtained with other methods in which the errors can be controlled An exception to this has been studies of bosonic field theories at finite densities in which a controlled Monte Carlo algorithm in the world line representation free of sign problems is available [12,13]. In the world line approach, we argue in this work that the sign problem is absent with open boundary conditions and zero fermion mass In this limit, we are able to study large lattices and can accurately compute the critical μi’s and Ni’s. These could provide a helpful benchmark to test new ideas that claim to solve sign problems in problems similar to QCD. At a large value of m, this was done recently in two space-time dimensions [25]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
