Meron-Cluster Solution of Fermion and Other Sign Problems

Abstract

Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Important examples include QCD and other field theories at non-zero chemical potential, at non-zero vacuum angle, or with an odd number of flavors, as well as the Hubbard model for high-temperature superconductivity and quantum antiferromagnets in an external magnetic field. In all these cases standard simulation algorithms require an exponentially large statistics in large space-time volumes and are thus impossible to use in practice. Meron-cluster algorithms realize a general strategy to solve severe sign problems but must be constructed for each individual case. They lead to a complete solution of the sign problem in several of the above cases.

15 pages,LATTICE99

References in corpus (9)

• Axial symmetries in lattice QCD with Kaplan fermions
• Cluster Algorithm for Vertex Models
• Quantum Link Models: A Discrete Approach to Gauge Theories
• The Loop Algorithm
• Meron-Cluster Simulation of the $\theta$-Vacuum in the 2-d $O(3)$-Model
• Dimensional Crossover in Quantum Antiferromagnets
• Bosonization and Cluster Updating of Lattice Fermions
• Blockspin Cluster Algorithms for Quantum Spin Systems
• Blockspin Cluster Algorithms for Quantum Spin Systems

Cited by in corpus (14)

• Quantum Monte Carlo with Directed Loops
• Generic conditions for stable hybrid stars
• The Loop Algorithm
• Solution of the Complex Action Problem in the Potts Model for Dense QCD
• Anatomy of the sign-problem in heavy-dense QCD
• PT Symmetry in Classical and Quantum Statistical Mechanics
• From Spin Ladders to the 2-d O(3) Model at Non-Zero Density
• Ab Initio Simulations of Light Nuclear Systems Using Eigenvector Continuation and Auxiliary Field Monte Carlo
• Quantum Link Models with Many Rishon Flavors and with Many Colors
• Superconductivity with the Meron-Cluster Algorithm
• Mitigating the sign problem for non-relativistic fermions on the lattice
• Topics in Lattice QCD and Effective Field Theory
• Isocliny in spinor space and Wilson fermions
• Simulation of a modified Hubbard model with a chemical potential using a meron-cluster algorithm