Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations

Abstract

We apply the Average Spectrum Method to the problem of getting the excitation spectrum from imaginary-time quantum Monte Carlo simulations. We show that with high quality QMC data this method reproduces the dominant spectral features very well. It is also capable of giving information on the spectrum in regions dominated by the many-particle continuum of excitations.

v2: Major revision. Title and abstract as well as the focus of the paper have been changed. Added a figure about the dynamics of 1D Heisenberg chain

References in corpus (24)

• Quantum Monte Carlo with Directed Loops
• Spin waves and electronic interactions in La2CuO4
• Feedback-optimized parallel tempering Monte Carlo
• Computation of dynamical correlation functions of Heisenberg chains in a field
• Critical Properties of gapped spin-1/2 chains and ladders in a magnetic field
• Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures
• Magnetic excitation spectrum of dimerized antiferromagnetic chains
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• High-energy magnon dispersion and multi-magnon continuum in the two-dimensional Heisenberg antiferromagnet
• A Study of the S=1/2 Alternating Chain using Multiprecision Methods
• Triplet Waves in a Quantum Spin Liquid
• Strong-Coupling Expansions for Multiparticle Excitations: Continuum and Bound States
• Double gap and solitonic excitations in the spin-Peierls chain CuGeO3
• 1/S-expansion study of spin waves in a two-dimensional Heisenberg antiferromagnet
• Further Series Studies of the Spin-1/2 Heisenberg Antiferromagnet at T=0: Magnon Dispersion and Structure Factors
• Spin-wave excitation spectra and spectral weights in square lattice antiferromagnets
• Spin wave dispersion in La2CuO4
• A neutron scattering study of two-magnon states in the quantum magnet copper nitrate
• Dynamical Structure Factor for the Alternating Heisenberg Chain: A Linked Cluster Calculation
• Quantum renormalization of high energy excitations in the 2D Heisenberg antiferromagnet
• Magnetic Excitation Spectrum of the Square Lattice S=1/2 Heisenberg Antiferromagnet K2V3O8
• Deconfinement Transition and Bound States in Frustrated Heisenberg Chains: Regimes of Forced and Spontaneous Dimerization
• Finite Temperature Dynamics of the Spin 1/2 Bond Alternating Heisenberg Antiferromagnetic Chain

Cited by in corpus (63)

• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Ab-initio low-energy dynamics of superfluid and solid 4He
• Constrained sampling method for analytic continuation
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Artificial Neural Network Approach to the Analytic Continuation Problem
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Dynamics of Topological Excitations in a Model Quantum Spin Ice
• Dynamical Signature of Symmetry Fractionalization in Frustrated Magnets
• Triangular lattice quantum dimer model with variable dimer density
• The amplitude mode in three-dimensional dimerized antiferromagnets
• Topological phase transition and single/multi anyon dynamics of $Z_2$ spin liquid
• A machine learning approach to dynamical properties of quantum many-body systems
• Dynamical properties of collective excitations in twisted bilayer Graphene
• Superconductivity and bosonic fluid emerging from Moiré flat bands
• Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo
• Dynamical properties of the $S=\frac{1}{2}$ random Heisenberg chain
• The Average Spectrum Method for Analytic Continuation: Efficient Blocked Modes Sampling and Dependence on Discretization Grid
• Dynamic structure factor of superfluid He-4 from Quantum Monte Carlo: Maximum Entropy revisited
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• $\text{TRIQS}/\text{SOM}$: Implementation of the Stochastic Optimization Method for Analytic Continuation
• Quantum Monte Carlo sign bounds, topological Mott insulator and thermodynamic transitions in twisted bilayer graphene model
• Fractional and composite excitations of antiferromagnetic quantum spin trimer chains
• Finite-size effects in transport data from Quantum Monte Carlo simulations
• Finite-Temperature Dynamics and Thermal Intraband Magnon Scattering in Haldane Spin-One Chains
• Tracking the effects of interactions on spinons in gapless Heisenberg chains
• Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid
• Vestigial anyon condensation in kagome quantum spin liquids
• Extending the average spectrum method: Grid points sampling and density averaging
• Imaginary Time Correlations and the phaseless Auxiliary Field Quantum Monte Carlo
• Analytical solution for time-integrals in diagrammatic expansions: application to real-frequency diagrammatic Monte Carlo
• Analytic continuation average spectrum method for quantum liquids
• Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets
• Chebyshev expansion of spectral functions using restricted Boltzmann machines
• NMR relaxation in the spin-1 Heisenberg chain
• Excitation spectrum in two-dimensional superfluid 4He
• Quantum and thermal ionic motion, oxygen isotope effect, and superexchange distribution in La${}_2$CuO${}_4$
• Spin excitation spectra of the two dimensional $S=1/2$ Heisenberg model with a checkerboard structure
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Stochastic pole expansion method
• Dynamical spin excitations of topological Haldane gapped phase in the $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy
• Beyond perturbation theory: A time-dependent approach to inelastic scattering spectroscopies in- and away from equilibrium
• Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Connecting Tikhonov regularization to the maximum entropy method for the analytic continuation of quantum Monte Carlo data
• Magnetic field-induced soft mode in spin-gapped high-Tc superconductors
• Magnon, doublon and quarton excitations in 2D S=1/2 trimerized Heisenberg models
• Unifying static and dynamic properties in 3D quantum antiferromagnets
• Barycentric rational function approximation made simple: A fast analytic continuation method for Matsubara Green's functions
• Single-Particle Dispersion and Density of States of the Half-Filled 2D Hubbard Model
• Analytical Continuation Approaches to Electronic Transport: The Resonant Level Model
• Cross Validation in Stochastic Analytic Continuation
• Cubic* criticality emerging from a quantum loop model on triangular lattice
• Temperature dependence of the $(\pi ,0)$ anomaly in the excitation spectrum of the 2D quantum Heisenberg antiferromagnet
• Formation of paired phases of bosons and their excitations in a square lattice
• Least square based method for obtaining one particle spectral functions from temperature Green functions
• Accessing Excitation of Many-body Systems via Single-Mode Approximation within Quantum Monte Carlo Simulations
• Bell sampling in Quantum Monte Carlo simulations
• Universal collective Larmor-Silin mode emerging in magnetized correlated Dirac fermions