Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates

Abstract

We study trace estimators for equilibrium thermodynamic observables that rely on the idea of typicality and derivatives thereof such as the finite-temperature Lanczos method (FTLM). As numerical examples quantum spin systems are studied. Our initial aim was to identify pathological examples or circumstances, such as strong frustration or unusual densities of states, where these methods could fail. Instead we failed with the attempt. All investigated systems allow such approximations, only at temperatures of the order of the lowest energy gap the convergence is somewhat slower in the number of random vectors over which observables are averaged.

arXiv comment11 pages, 14 figures, minor improvements, thicker lines in figures, new error estimate (13)

References in corpus (49)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Correlated Electrons in High Temperature Superconductors
• An efficient, multiple range random walk algorithm to calculate the density of states
• Many body localization and thermalization in quantum statistical mechanics
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Many-body localization, thermalization, and entanglement
• The Kernel Polynomial Method
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Canonical Thermal Pure Quantum State
• Thermal Pure Quantum States at Finite Temperature
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• Dynamical typicality of quantum expectation values
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Wang-Landau algorithm for continuous models and joint density of states
• Typical fast thermalization processes in closed many-body systems
• Spin-current autocorrelations from single pure-state propagation
• Magnetism of the N=42 kagome lattice antiferromagnet
• Frustrated two dimensional quantum magnets
• Regression relation for pure quantum states and its implications for efficient computing
• Random phase vector for calculating the trace of a large matrix
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• 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
• Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
• 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
• Frustration effects in magnetic molecules
• Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• Delta chain with ferromagnetic and antiferromagnetic interactions at the critical point
• Multiple nearest-neighbor exchange model for the frustrated magnetic molecules Mo72Fe30 and Mo72Cr30
• Large-scale numerical investigations of the antiferromagnetic Heisenberg icosidodecahedron
• Advanced Finite-Temperature Lanczos Method for anisotropic spin systems
• Why are macroscopic experiments reproducible? Imitating the behavior of an ensemble by single pure states
• Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures
• Interpolation between low and high temperatures of the specific heat for spin systems
• Finite-temperature properties of the extended Heisenberg model on a triangular lattice
• Frustration effects in antiferromagnetic molecules: the cuboctahedron
• Delta chain with anisotropic ferromagnetic and antiferromagnetic interactions
• Combined use of translational and spin-rotational invariance for spin systems
• Kondo Lattice Model with Finite Temperature Lanczos Method
• Thermodynamics of delta-chain with ferro- and antiferromagnetic interactions
• Sampling the two-dimensional density of states g(E,M) of a giant magnetic molecule using the Wang-Landau method
• Effective S=1/2 description of the S=1 chain with strong easy plane anisotropy

Cited by in corpus (36)

• Magnon crystallization in the kagome lattice antiferromagnet
• Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
• Random State Technology
• Selected applications of typicality to real-time dynamics of quantum many-body systems
• Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
• Thermodynamics of the spin-half square-kagome lattice antiferromagnet
• Thermodynamic properties of an $S=1/2$ ring-exchange model on the triangular lattice
• Thermal Pure Quantum Matrix Product States Recovering a Volume Law Entanglement
• Flat-band physics in the spin-1/2 sawtooth chain
• Frustrated magnetism of spin-1/2 Heisenberg diamond and octahedral chains as a statistical-mechanical monomer-dimer problem
• Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets
• Magnetism of the $s=1/2$ $J_1$-$J_2$ square-kagome lattice antiferromagnet
• Krylov-aware stochastic trace estimation
• Melting of magnetization plateaus for kagome and square-kagome lattice antiferromagnets
• Density dynamics in the mass-imbalanced Hubbard chain
• Quantum half-orphans in kagome antiferromagnets
• Stability of the 1/3 magnetization plateau of the $J_1-J_2$ kagome Heisenberg model
• Accuracy of the typicality approach using Chebyshev polynomials
• Spin-half Heisenberg antiferromagnet on a symmetric sawtooth chain: Rotation-invariant Green's functions and high-temperature series
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
• Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
• Thermodynamics of the $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet
• Finite-size scaling of typicality-based estimates
• Isothermal and adiabatic magnetization processes of the spin-$\frac{1}{2}$ Heisenberg model on an anisotropic triangular lattice
• Magneto- and barocaloric properties of the ferro-antiferromagnetic sawtooth chain
• Frustrated kagome-lattice bilayer quantum Heisenberg antiferromagnet
• A spectrum adaptive kernel polynomial method
• Escaping the Krylov space during finite precision Lanczos
• Sample complexity of matrix product states at finite temperature
• A posteriori error bounds for the block-Lanczos method for matrix function approximation
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• Towards lattice-gas description of low-temperature properties above the Haldane and cluster-based Haldane ground states of a mixed spin-(1,1/2) Heisenberg octahedral chain
• Itinerant magnetism in Hubbard models with long-range interactions
• Faster randomized partial trace estimation
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures
• Field-induced states and thermodynamics of the frustrated Heisenberg antiferromagnet on a square lattice