Recent progress on cluster and meron algorithms for strongly correlated systems

Abstract

Ab-initio studies of strongly interacting bosonic and fermionic systems is greatly facilitated by efficient Monte Carlo algorithms. This article emphasizes this requirement, and outlines the ideas behind the construction of the cluster algorithms and illustrates them via specific examples. Numerical studies of fermionic systems at finite densities and at real-times are sometimes hindered by the infamous sign problem, which is also discussed. The construction of meron cluster algorithms, which can solve certain sign problems are discussed. Cluster algorithms which can simulate certain pure Abelian gauge theories (realized as quantum link models) are also discussed.

Submitted to Indian Journal of Physics memorial issue for Pushan Majumdar. 20 pages, 6 figures. Matches the published version

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Interfaces, Strings, and a Soft Mode in the Square Lattice Quantum Dimer Model
• Real-time dynamics of open quantum spin systems driven by dissipative processes
• Real-Time Simulation of Large Open Quantum Spin Systems driven by Measurements
• Solving the quantum dimer and six vertex models one electric field line at a time

Cited by in corpus (5)

• Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
• Weak universality induced by $Q=\pm 2e$ charges at the deconfinement transition of a (2+1)-d $U(1)$ lattice gauge theory
• Crystalline phases at finite winding densities in a quantum link ladder
• Geometric fragmentation and anomalous thermalization in cubic dimer model
• Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d