We present a new approach to some four-fermion lattice field theories which we call the generalized fermion bag approach.The basic idea is to identify unpaired fermionic degrees of freedom that cause sign problems and collect them in a bag.Paired fermions usually act like bosons and do not lead to sign problems.A resummation of all unpaired fermion degrees of freedom inside the bag is sufficient to solve the fermion sign problem in a variety of interesting cases.Using a concept of duality we then argue that the size of the fermion bags is small both at strong and weak couplings.This allows us to construct efficient algorithms in both these limits.Using the fermion bag approach, we study the quantum phase transition of the 3D massless lattice Thirrring model which is of interest in the context of Graphene.Using our method we are able to solve the model on lattices as large as 40 3 with moderate computational resources.We obtain the precise location of the quantum critical point and the values of the critical exponents through this study.We present a new approach to some four-fermion lattice field theories which we call the generalized fermion bag approach.The basic idea is to identify unpaired fermionic degrees of freedom that cause sign problems and collect them in a bag.Paired fermions usually act like bosons and do not lead to sign problems.A resummation of all unpaired fermion degrees of freedom inside the bag is sufficient to solve the fermion sign problem in a variety of interesting cases.Using a concept of duality we then argue that the size of the fermion bags is small both at strong and weak couplings.This allows us to construct efficient algorithms in both these limits.Using the fermion bag approach, we study the quantum phase transition of the 3D massless lattice Thirrring model which is of interest in the context of Graphene.Using our method we are able to solve the model on lattices as large as 40 3 with moderate computational resources.We obtain the precise location of the quantum critical point and the values of the critical exponents through this study.

International Symposium on Lattice Field Theory (LATTICE)Jul 5, 20122 citations

Zone methods and the fermion sign problem

Dean Lee

arXiv:hep-lat/0209047Nuclear Physics B - Proceedings SupplementsMay 1, 20030 citations

Path Integrals for Fermions

World Scientific lecture notes in physicsNov 1, 19930 citations

The generalized fermion-bag approach

Shailesh Chandrasekharan A, Anyi Li

We present a new approach to some four-fermion lattice field theories which we call the generalized fermion bag approach. The basic idea is to identify unpaired fermionic degrees of freedom that cause sign problems and collect them in a bag. Paired fermions usually act like bosons and do not lead to sign problems. A resummation of all unpaired fermion degrees of freedom inside the bag is sufficient to solve the fermion sign problem in a variety of interesting cases. Using a concept of duality we then argue that the size of the fermion bags is small both at strong and weak couplings. This allows us to construct efficient algorithms in both these limits. Using the fermion bag approach, we study the quantum phase transition of the 3D massless lattice Thirrring model which is of interest in the context of Graphene. Using our method we are able to solve the model on lattices as large as $40^3$ with moderate computational resources. We obtain the precise location of the quantum critical point and the values of the critical exponents through this study.We present a new approach to some four-fermion lattice field theories which we call the generalized fermion bag approach. The basic idea is to identify unpaired fermionic degrees of freedom that cause sign problems and collect them in a bag. Paired fermions usually act like bosons and do not lead to sign problems. A resummation of all unpaired fermion degrees of freedom inside the bag is sufficient to solve the fermion sign problem in a variety of interesting cases. Using a concept of duality we then argue that the size of the fermion bags is small both at strong and weak couplings. This allows us to construct efficient algorithms in both these limits. Using the fermion bag approach, we study the quantum phase transition of the 3D massless lattice Thirrring model which is of interest in the context of Graphene. Using our method we are able to solve the model on lattices as large as $40^3$ with moderate computational resources. We obtain the precise location of the quantum critical point and the values of the critical exponents through this study.

arXiv:1111.5276Nov 22, 20114 citations

A Generic Solution of Fermion Sign Problem

J. Wang, D. Y. Sun

The fermion sign problem, the biggest obstacle in quantum Monte Carlo calculations, is completely solved in this paper. Here, we find a strategy, in which the contribution from those negative-weighted paths is thoroughly cancelled or replaced by some positive-weighted paths. The crucial point lies on the Feynman path integral formula proposed in our group, which allows us to deeply analyze the Boltzmann weight of each path. Through mathematical proof, we demonstrate that physical quantities can be exactly calculated within a specific kind of paths, which have positive the Boltzmann weight. With this finding, a new Monte Carlo method is proposed, in which the fermion sign problem is absent. As an example, the current method is applied to the two-dimensional Hubbard model, and the results do manifest the correctness.The fermion sign problem, the biggest obstacle in quantum Monte Carlo calculations, is completely solved in this paper. Here, we find a strategy, in which the contribution from those negative-weighted paths is thoroughly cancelled or replaced by some positive-weighted paths. The crucial point lies on the Feynman path integral formula proposed in our group, which allows us to deeply analyze the Boltzmann weight of each path. Through mathematical proof, we demonstrate that physical quantities can be exactly calculated within a specific kind of paths, which have positive the Boltzmann weight. With this finding, a new Monte Carlo method is proposed, in which the fermion sign problem is absent. As an example, the current method is applied to the two-dimensional Hubbard model, and the results do manifest the correctness.

arXiv:2203.04070Mar 8, 20220 citations

Path Integrals for Fermions

Michael Stone

Graduate texts in contemporary physicsJan 1, 20000 citations

40^3

with moderate computational resources. We obtain the precise location of the quantum critical point and the values of the critical exponents through this study.