Green's Functions from Quantum Cluster Algorithms

Abstract

We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a cluster algorithm for the partition function has been constructed. To explain the idea, we consider the quantum XY model and compute its two point Green's function in various ways, showing that all of them are equivalent. We also provide numerical evidence confirming the analytic arguments. Similar techniques are applicable to other models. In particular, in the recently constructed quantum link models, the new technique allows us to construct improved estimators for Wilson loops and may lead to a very precise determination of the glueball spectrum.

arXiv comment15 pages, LaTeX, with four figures. Added preprint number

References in corpus (4)

• Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems
• Cluster Algorithm for Vertex Models
• Quantum Link Models: A Discrete Approach to Gauge Theories
• Cluster algorithms

Cited by in corpus (17)

• The Loop Algorithm
• Recent Developments of World-Line Monte Carlo Methods
• Quantum Monte Carlo study of S=1/2 weakly-anisotropic antiferromagnets on the square lattice
• Single hole dynamics in the t-J model on a square lattice
• Low-temperature transport in Heisenberg chains
• Chiral Limit of Strongly Coupled Lattice Gauge Theories
• Finite-size Scaling of Correlation Ratio and Generalized Scheme for the Probability-Changing Cluster Algorithm
• Conductivity of quantum-spin chains: A Quantum Monte Carlo approach
• Meron-Cluster Approach to Systems of Strongly Correlated Electrons
• Path-integral Monte Carlo method for the local Z_2 Berry phase
• Machine-Learning Study using Improved Correlation Configuration and Application to Quantum Monte Carlo Simulation
• Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems
• Real-time simulation of non-equilibrium transport of magnetization in large open quantum spin systems driven by dissipation
• Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions
• Green's function theory for spin-1/2 ferromagnets with an easy-plane exchange anisotropy
• Structural and magnetic instabilities of layered magnetic systems
• Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries