A numerical algorithm to calculate exact finite-temperature spectra of<br />
many-body lattice Hamiltonians is formulated by combining the typicality<br />
approach and the shifted Krylov subspace method. The combined algorithm, which<br />
we name finite-temperature shifted Krylov subspace method for simulating<br />
spectra (FTK$\omega$), efficiently reproduces the canonical-ensemble<br />
probability distribution at finite temperatures with the computational cost<br />
proportional to the Fock space dimension. The present FTK$\omega$ enables us to<br />
exactly calculate finite-temperature spectra of many-body systems whose system<br />
sizes are twice larger than those handled by the canonical ensemble average and<br />
allows us to access the frequency domain without sequential real-time evolution<br />
often used in previous studies. By employing the reweighting method with the<br />
present algorithm, we obtain significant reduction of the numerical costs for<br />
temperature sweeps. Application to the Kiteav-Heisenberg model (KHM) on a<br />
honeycomb lattice demonstrates the capability of the FTK$\omega$. The KHM shows<br />
quantum phase transitions from the quantum spin liquid (QSL) phase to<br />
magnetically ordered phases when the finite Heisenberg exchange coupling is<br />
introduced. We examine temperature dependence of dynamical spin structure<br />
factors of the KHM in proximity to the QSL. It is clarified that the crossover<br />
from a spin-excitation continuum, which is a characteristic of the QSL, to a<br />
damped high-energy magnon mode occurs at temperatures higher than the energy<br />
scale of the Heisenberg couplings or the spin gap that is a signature of the<br />
QSL at zero temperature. The crossover and the closeness to the Kitaev&#039;s QSL<br />
are quantitatively measured by the width of the excitation continuum or the<br />
magnon spectrum. The present results shed new light on analysis of neutron<br />
scattering and other spectroscopy measurements on QSL candidates.