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Title: Fermion bag approach to lattice field theories

Abstract

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 themore » critical exponents at the quantum phase transition and find {nu}=0.87(2) and {eta}=0.62(2).« less

Authors:
 [1]
  1. Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhaba Road, Mumbai 400005 (India)
Publication Date:
OSTI Identifier:
21410151
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 82; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.82.025007; (c) 2010 The American Physical Society; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 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

Citation Formats

Chandrasekharan, Shailesh. Fermion bag approach to lattice field theories. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.82.025007.
Chandrasekharan, Shailesh. Fermion bag approach to lattice field theories. United States. doi:10.1103/PHYSREVD.82.025007.
Chandrasekharan, Shailesh. Thu . "Fermion bag approach to lattice field theories". United States. doi:10.1103/PHYSREVD.82.025007.
@article{osti_21410151,
title = {Fermion bag approach to lattice field theories},
author = {Chandrasekharan, Shailesh},
abstractNote = {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).},
doi = {10.1103/PHYSREVD.82.025007},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 2,
volume = 82,
place = {United States},
year = {2010},
month = {7}
}