Accuracy of the typicality approach using Chebyshev polynomials

Abstract

Trace estimators allow to approximate thermodynamic equilibrium observables with astonishing accuracy. A prominent representative is the finite-temperature Lanczos method (FTLM) which relies on a Krylov space expansion of the exponential describing the Boltzmann weights. Here we report investigations of an alternative approach which employs Chebyshev polynomials. This method turns out to be also very accurate in general, but shows systematic inaccuracies at low temperatures that can be traced back to an improper behavior of the approximated density of states with and without smoothing kernel. Applications to archetypical quantum spin systems are discussed as examples.

arXiv comment11 pages, 16 figures

References in corpus (38)

• Correlated Electrons in High Temperature Superconductors
• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
• The Kernel Polynomial Method
• Canonical Thermal Pure Quantum State
• Thermal Pure Quantum States at Finite Temperature
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• One-Dimensional Magnetism
• Ground State and Finite Temperature Lanczos Methods
• Chebyshev matrix product state approach for spectral functions
• Magnetism of the N=42 kagome lattice antiferromagnet
• Clues and criteria for designing Kitaev spin liquid revealed by thermal and spin excitations of honeycomb iridates Na${}_2$IrO${}_3$
• Frustrated two dimensional quantum magnets
• Self-energy-functional theory
• Dynamical and thermal magnetic properties of the Kitaev spin liquid candidate $\alpha$-RuCl${}_3$
• Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method
• Low Temperature Lanczos Method
• Typicality approach to the optical conductivity in thermal and many-body localized phases
• Improved bounds on sample size for implicit matrix trace estimators
• Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase
• Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations
• Quantum spin liquid at finite temperature: proximate dynamics and persistent typicality
• Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
• Magnon crystallization in the kagome lattice antiferromagnet
• Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate
• Delta chain with ferromagnetic and antiferromagnetic interactions at the critical point
• Matrix product state formulation of frequency-space dynamics at finite temperatures
• Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods
• Large-scale numerical investigations of the antiferromagnetic Heisenberg icosidodecahedron
• Topological spin excitations in Harper-Heisenberg spin chains
• Advanced Finite-Temperature Lanczos Method for anisotropic spin systems
• Finite-temperature properties of the extended Heisenberg model on a triangular lattice
• Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures
• Kondo Lattice Model with Finite Temperature Lanczos Method
• Thermodynamics of delta-chain with ferro- and antiferromagnetic interactions
• Effective S=1/2 description of the S=1 chain with strong easy plane anisotropy
• Finite-size scaling of typicality-based estimates
• Approximating spectral densities of large matrices
• Loop-gas description of the localized-magnon states on the kagome lattice with open boundary conditions

Cited by in corpus (5)

• Magnetism of the $s=1/2$ $J_1$-$J_2$ square-kagome lattice antiferromagnet
• Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
• A spectrum adaptive kernel polynomial method
• Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
• Faster randomized partial trace estimation