鈴木 隆史

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.

We study the boundary nature of trapped bosonic Mott insulators in optical<br /> square lattices, by performing quantum Monte Carlo simulation. We show that a<br /> finite superfluid density generally emerges in the incommensurate-filling (IC)<br /> boundary region around the bulk Mott state, irrespectively of the width of the<br /> IC region. Both off-diagonal and density correlation functions in the IC<br /> boundary region exhibit a nearly power-law decay. The power-law behavior and<br /> superfluidity are well developed below a characteristic temperature. These<br /> results indicate that a gapless boundary mode always emerges in any atomic Mott<br /> insulators on optical lattices. This further implies that if we consider a<br /> topological insulating state in Bose or Fermi atomic systems, its boundary<br /> possesses at least two gapless modes (or coupled modes) of an above IC edge<br /> state and the intrinsic topologically-protected edge state.

We performed variational calculation based on the multi-scale entanglemnt<br /> renormalization ansatz, for the antiferromagnetic Heisenberg model on a Shastry<br /> Sutherland lattice (SSL). Our results show that at coupling ratio J&#039;/J=<br /> 0.687(3), the system undergoes a quantum phase transition from the orthogonal<br /> dimer order to the plaquette valence bond solid phase, which then transits into<br /> the antiferromagnetic order above J&#039;/J=0.75. In the presence of an external<br /> magnetic field, our calculations show clear evidences of various magnetic<br /> plateaux in systems with different coupling ratios range from 0.5 to 0.69. Our<br /> calculations are not limited to the small coupling ratio region, and we are<br /> able to show strong evidence of the presence of several supersolid phases,<br /> including ones above 1/2 and 1/3 plateaux. Such supersolid phases, which<br /> feature the coexistence of compressible superfluidity and crystalline long<br /> range order in triplet excitations, emerge at relatively large coupling ratio<br /> (J&#039;/J&gt;0.5). A schematic phase diagram of the SSL model in the presence of<br /> magnetic field is provided.