We identify a new kind of elementary excitations, spin-rotons, in the doped Mott insulator. They play a central role in deciding the superconducting transition temperature Tc, resulting in a simple Tc formula,Tc=Eg/6, with Eg as the characteristic en
ergy scale of the spin rotons. We show that the degenerate S=1 and S=0 rotons can be probed by neutron scattering and Raman scattering measurements, respectively, in good agreement with the magnetic resonancelike mode and the Raman A1g mode observed in the high-Tc cuprates.
We numerically demonstrate that a supersolid phase exists in a frustrated hard-core boson system on a triangular lattice over a wide range of interaction strength. In the infinite repulsion (Ising) limit, we establish a mapping to the same problem wi
th unfrustrated hopping, which connects the supersolid to the known results in that case. The weak superfluidity can be destroyed or strongly enhanced by a next nearest neighbor hopping term, which provides valuable information for experimental realization of a supersolid phase on optical lattice.
We have proposed a novel numerical method to calculate accurately the physical quantities of the ground state with the tensor-network wave function in two dimensions. We determine the tensor network wavefunction by a projection approach which applies
iteratively the Trotter-Suzuki decomposition of the projection operator and the singular value decomposition of matrix. The norm of the wavefunction and the expectation value of a physical observable are evaluated by a coarse grain renormalization group approach. Our method allows a tensor-network wavefunction with a high bond degree of freedom (such as D=8) to be handled accurately and efficiently in the thermodynamic limit. For the Heisenberg model on a honeycomb lattice, our results for the ground state energy and the staggered magnetization agree well with those obtained by the quantum Monte Carlo and other approaches.
We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagom{e} lattice using the density-matrix renormalization group (DMRG) method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exp
onential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commersurate antiferromangetic wavevectors. We obtain a spin triplet excitation gap $Delta E(S=1)=0.055pm 0.005$ by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.
We study the superfluid-Mott-insulator transition of ultracold bosonic atoms in a one-dimensional optical lattice with a double-well confining trap using the density-matrix renormalization group. At low density, the system behaves similarly as two se
parated ones inside harmonic traps. At high density, however, interesting features appear as the consequence of the quantum tunneling between the two wells and the competition between the superfluid and Mott regions. They are characterized by a rich step-plateau structure in the visibility and the satellite peaks in the momentum distribution function as a function of the on-site repulsion. These novel properties shed light on the understanding of the phase coherence between two coupled condensates and the off-diagonal correlations between the two wells.
We present a topological description of quantum spin Hall effect (QSHE) in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be characterize
d by a $2times 2$ traceless matrix of first Chern integers. The nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM). A spin Chern number is derived from the CNM, which is conserved in the presence of finite disorder scattering and spin nonconserving Rashba coupling. By using the Laughlins gedanken experiment, we numerically calculate the spin polarization and spin transfer rate of the conducting edge states, and determine a phase diagram for the QSHE.
