Fermion bag approach to lattice field theories
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhaba Road, Mumbai 400005 (India)
We propose a new approach to the fermion sign problem in systems where there is a coupling U such that when it is infinite the fermions are paired into bosons, and there is no fermion permutation sign to worry about. We argue that as U becomes finite, fermions are liberated but are naturally confined to regions which we refer to as fermion bags. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the ''silver blaze problem'' also emerges. Using the three-dimensional massless lattice Thirring model as an example, we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find {nu}=0.87(2) and {eta}=0.62(2).
- OSTI ID:
- 21410151
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevD.82.025007; (c) 2010 The American Physical Society; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ALGORITHMS
BOSONS
COUPLING
EFFICIENCY
FERMIONS
LATTICE FIELD THEORY
MATHEMATICAL SOLUTIONS
MONTE CARLO METHOD
PHASE TRANSFORMATIONS
THIRRING MODEL
THREE-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
CONSTRUCTIVE FIELD THEORY
FIELD THEORIES
MATHEMATICAL LOGIC
QUANTUM FIELD THEORY