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.

11 pages, 16 figures

References in corpus (13)

• The Kernel Polynomial Method
• Chebyshev matrix product state approach for spectral functions
• Frustrated two dimensional quantum magnets
• Low Temperature Lanczos Method
• Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations
• Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
• 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
• Advanced Finite-Temperature Lanczos Method for anisotropic spin systems
• 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
• 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