Luttinger Liquid Physics and Spin-Flip Scattering on Helical Edges

We investigate electronic correlation effects on edge states of quantum spin-Hall insulators within the Kane-Mele-Hubbard model by means of quantum Monte Carlo simulations. Given the U(1) spin symmetry and time-reversal invariance, the low-energy theory is the helical Tomanaga-Luttinger model, with forward scattering only. For weak to intermediate interactions, this model correctly describes equal-time spin and charge correlations, including their doping dependence. As apparent from the Drude weight, bulk states become relevant in the presence of electron-electron interactions, rendering the forward-scattering model incomplete. Strong correlations give rise to slowly decaying transverse spin fluctuations, and inelastic spin-flip scattering strongly modifies the single-particle spectrum, leading to graphene-like edge state signatures. The helical Tomanaga-Luttinger model is completely valid only asymptotically in the weak-coupling limit.Comment: 5 pages, 5 figures (modified version with additional data

Critical Exponents of the Metal-Insulator Transition in the Two-Dimensional Hubbard Model

We study the filling-controlled metal-insulator transition in the two-dimensional Hubbard model near half-filling with the use of zero temperature quantum Monte Carlo methods. In the metallic phase, the compressibility behaves as $\kappa \propto |\mu - \mu_c|^{-0.58\pm0.08}$ where $\mu_c$ is the critical chemical potential. In the insulating phase, the localization length follows $\xi_l \propto |\mu - \mu_c|^{-\nu_l}$ with $\nu_l = 0.26 \pm 0.05$. Under the assumption of hyperscaling, the compressibility data leads to a correlation length exponent $\nu_\kappa = 0.21 \pm 0.04$. Our results show that the exponents $\nu_\kappa$ and $\nu_l$ agree within statistical uncertainty. This confirms the assumption of hyperscaling with correlation length exponent $\nu = 1/4$ and dynamical exponent $z = 4$. In contrast the metal-insulator transition in the generic band insulators in all dimensions as well as in the one-dimensional Hubbard model satisfy the hyperscaling assumption with exponents $\nu = 1/2$ and $z = 2$.Comment: Two references added. The DVI file and PS figure files are also available at http://www.issp.u-tokyo.ac.jp/labs/riron/imada/furukawa/; to appear in J. Phys. Soc. Jpn 65 (1996) No.

Quantum Transition between an Antiferromagnetic Mott Insulator and dx2−y2d_{x^2 - y^2} Superconductor in Two Dimensions

We consider a Hubbard model on a square lattice with an additional interaction, $W$, which depends upon the square of a near-neighbor hopping. At half-filling and a constant value of the Hubbard repulsion, increasing the strength of the interaction $W$ drives the system from an antiferromagnetic Mott insulator to a $d_{x^2 -y^2}$ superconductor. This conclusion is reached on the basis of zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$.Comment: 4 pages (latex) and 4 postscript figure

Charge and Spin Structures of a dx2−y2d_{x^2 - y^2} Superconductor in the Proximity of an Antiferromagnetic Mott Insulator

To the Hubbard model on a square lattice we add an interaction, $W$, which depends upon the square of a near-neighbor hopping. We use zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$, to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a $d_{x^2 -y^2}$ superconductor. With a combination of finite temperature quantum Monte Carlo simulations and the Maximum Entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite temperature Kosterlitz-Thouless transition to the $d_{x^2 -y^2}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, $T_{KT}$, we compute the one-electron density of states, $N(\omega)$, the spin relaxation rate $1/T_1$, as well as the imaginary and real part of the spin susceptibility $\chi(\vec{q},\omega)$. The spin dynamics are characterized by the vanishing of $1/T_1$ and divergence of $Re \chi(\vec{q} = (\pi,\pi), \omega = 0)$ in the low temperature limit. As $T_{KT}$ is approached $N(\omega)$ develops a pseudo-gap feature and below $T_{KT}$ $Im \chi(\vec{q} = (\pi,\pi), \omega)$ shows a peak at finite frequency.Comment: 46 pages (latex) including 14 figures in encapsulated postscript format. Submitted for publication in Phys. Rev.

Asymmetric spin-1/2 two-leg ladders

We consider asymmetric spin-1/2 two-leg ladders with non-equal antiferromagnetic (AF) couplings J_|| and \kappa J_|| along legs (\kappa <= 1) and ferromagnetic rung coupling, J_\perp. This model is characterized by a gap \Delta in the spectrum of spin excitations. We show that in the large J_\perp limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at \kappa=1, admits a linear scaling for the spin gap \Delta ~ J_\perp. The second class appears for a strong asymmetry of the coupling along legs, \kappa J_|| << J_\perp << J_|| and is characterized by two energy scales: the exponentially small spin gap \Delta ~ J_\perp \exp(-J_|| / J_\perp), and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange ~ J_\perp^2 /J_|| . We report numerical results obtained by exact diagonalization, density matrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetry. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.Comment: 18 pages, 11 figure

Dynamic Exponent of t-J and t-J-W Model

Drude weight of optical conductivity is calculated at zero temperature by exact diagonalization for the two-dimensional t-J model with the two-particle term, $W$. For the ordinary t-J model with $W$=0, the scaling of the Drude weight $D \propto \delta^2$ for small doping concentration $\delta$ is obtained, which indicates anomalous dynamic exponent $z$=4 of the Mott transition. When $W$ is switched on, the dynamic exponent recovers its conventional value $z$=2. This corresponds to an incoherent-to-coherent transition associated with the switching of the two-particle transfer.Comment: LaTeX, JPSJ-style, 4 pages, 5 eps files, to appear in J. Phys. Soc. Jpn. vol.67, No.6 (1998

Doping induced metal-insulator transition in two-dimensional Hubbard, t−Ut-U, and extended Hubbard, t−U−Wt-U-W, models

We show numerically that the nature of the doping induced metal-insulator transition in the two-dimensional Hubbard model is radically altered by the inclusion of a term, $W$, which depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length, $\xi_l$, in the insulating state. At finite values of $W$ we find results consistent with $\xi_l \sim | \mu - \mu_c|^{- 1/2}$ where $\mu_c$ is the critical chemical potential. In contrast, $\xi_l \sim | \mu - \mu_c|^{-1/4}$ for the Hubbard model. At finite values of $W$, the presented numerical results imply that doping the antiferromagnetic Mott insulator leads to a $d_{x^2 - y ^2}$ superconductor.Comment: 19 pages (latex) including 7 figures in encapsulated postscript format. Submitted for publication in Phys. Rev.