Continuous-time Monte Carlo Renormalization Group

Abstract

We implement Monte Carlo Renormalization Group (MCRG) in the continuous-time Monte Carlo simulation of a quantum system. We demonstrate numerically the emergent isotropy between space and time at large distances for the systems that exhibit Lorentz invariance at quantum criticality. This allows us to estimate accurately the sound velocity for these quantum systems. $Q$-state Potts models in one and two space dimensions are used to illustrate the method.

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Entropy and Quantum Field Theory
• Exact, Complete, and Universal Continuous-Time Worldline Monte Carlo Approach to the Statistics of Discrete Quantum Systems
• Excitation spectrum and Density Matrix Renormalization Group iterations
• Shadow of complex fixed point: Approximate conformality of Q>4 Potts model
• Novel Monte Carlo method to calculate the central charge and critical exponents
• A Variational Approach to Monte Carlo Renormalization Group
• Lecture notes on Diagrammatic Monte Carlo for the Fröhlich polaron
• Determination of the Critical Manifold Tangent Space and Curvature with Monte Carlo Renormalization Group
• Entanglement entropy of the $Q\ge 4$ quantum Potts chain
• The Tangent Space to the Manifold of Critical Classical Hamiltonians Representable by Tensor Networks

Cited by in corpus (3)

• Inverse Renormalization Group based on Image Super-Resolution using Deep Convolutional Networks
• Extracting the Speed of Light from Matrix Product States
• Exploring the limit of the Lattice-Bisognano-Wichmann form describing the Entanglement Hamiltonian: A quantum Monte Carlo study