Simulating Wilson fermions without critical slowing down

We present a simulation algorithm for Wilson fermions based on the exact hopping expansion of the fermion action. The algorithm essentially eliminates critical slowing down by sampling the fermionic two-point correlation function and it allows simulations directly in the massless limit. As illustrative examples, the algorithm is applied to the Gross-Neveu and the Schwinger model, the latter in the strong coupling limit.Comment: 7 pages, 3 figures. Presented at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, Chin

Loop formulation of the supersymmetric nonlinear O(N) sigma model

We derive the fermion loop formulation for the supersymmetric nonlinear O$(N)$ sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over all possible closed non-oriented fermion loop configurations. The interaction between the bosonic and fermionic degrees of freedom is encoded in the constraints arising from the supersymmetry and induces flavour changing fermion loops. For $N \ge 3$ this leads to fermion loops which are no longer self-avoiding and hence to a potential sign problem. Since we use Wilson fermions the bare mass needs to be tuned to the chiral point. For $N=2$ we determine the critical point and present boson and fermion masses in the critical regime.Comment: 7 pages, 4 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Exact results for supersymmetric quantum mechanics on the lattice

We discuss N=2 supersymmetric quantum mechanics on the lattice using the fermion loop formulation. In this approach the system naturally decomposes into a bosonic and fermionic sector. This allows us to deal with the sign problem arising in the context of broken supersymmetry due to the vanishing of the Witten index. Employing transfer matrix techniques we obtain exact results at finite lattice spacing and are hence able to study how the continuum limit is approached. In particular, we determine how supersymmetry is restored and how, in the case of broken supersymmetry, the goldstino mode emerges.Comment: 7 pages, 2 figures, proceedings of the XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, Californi

Loop formulation of supersymmetric Yang-Mills quantum mechanics

We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.Comment: 20 pages, 3 figure

Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms

In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a fluctuating open fermion string. It guarantees sufficient tunnelling between the topological sectors, and hence provides a solution to the fermion sign problem affecting systems with broken supersymmetry. Moreover, the algorithm shows no critical slowing down even in the massless limit and can hence handle the massless Goldstino mode emerging in the supersymmetry broken phase. In this paper -- the third in a series of three -- we present the details of the simulation algorithm and demonstrate its efficiency by means of a few examples.Comment: 21 pages, 10 figures; typos in text correcte

QCD at non-zero density and canonical partition functions with Wilson fermions

We present a reduction method for Wilson Dirac fermions with non-zero chemical potential which generates a dimensionally reduced fermion matrix. The size of the reduced fermion matrix is independent of the temporal lattice extent and the dependence on the chemical potential is factored out. As a consequence the reduced matrix allows a simple evaluation of the Wilson fermion determinant for any value of the chemical potential and hence the exact projection to the canonical partition functions.Comment: 22 pages, 11 figures, 1 table; references added, figure size reduce

Simulation of supersymmetric models on the lattice without a sign problem

Simulations of supersymmetric models on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. The formulation is based on the exact hopping expansion of the fermionic action and allows the explicit decomposition of the partition function into bosonic and fermionic contributions. We devise a simulation algorithm which separately samples the fermionic and bosonic sectors, as well as the relative probabilities between them. The latter then allows a direct calculation of the Witten index and the corresponding Goldstino mode. Finally, we present results from simulations on the lattice for the spectrum and the Witten index for N=2 supersymmetric quantum mechanics.Comment: 14 pages, 4 figures, Talks presented at the XXVIII International Symposium on Lattice Field Theory, Lattice2010, Villasimius, Italy, June 14-19, 201

Canonical simulations of supersymmetric SU(N) Yang-Mills quantum mechanics

The fermion loop formulation naturally separates partition functions into their canonical sectors. Here we discuss various strategies to make use of this for supersymmetric SU(N) Yang-Mills quantum mechanics obtained from dimensional reduction in various dimensions and present numerical results for the separate canonical sectors with fixed fermion numbers. We comment on potential problems due to the sign of the contributions from the fermions and due to flat directions.Comment: 7 pages, 3 figure