Satoshi Nishimoto

Kitaev interactions between j = 1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations

Na2IrO3, a honeycomb 5d5 oxide, has been recently identified as a potential realization of the Kitaev spin lattice. The basic feature of this spin model is that for each of the three metal–metal links emerging out of a metal site, the Kitaev interaction connects only spin components perpendicular to the plaquette defined by the magnetic ions and two bridging ligands. The fact that reciprocally orthogonal spin components are coupled along the three different links leads to strong frustration effects and nontrivial physics. While the experiments indicate zigzag antiferromagnetic order in Na2IrO3, the signs and relative strengths of the Kitaev and Heisenberg interactions are still under debate. Herein we report results of ab initio many-body electronic-structure calculations and establish that the nearest-neighbor exchange is strongly anisotropic with a dominant ferromagnetic Kitaev part, whereas the Heisenberg contribution is significantly weaker and antiferromagnetic. The calculations further reveal a strong sensitivity to tiny structural details such as the bond angles. In addition to the large spin–orbit interactions, this strong dependence on distortions of the Ir2O2 plaquettes singles out the honeycomb 5d5 oxides as a new playground for the realization of unconventional magnetic ground states and excitations in extended systems.

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb alpha-RuCl3

Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d5 honeycomb halide α-RuCl3. From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d5 halides and oxides in general.Ravi Yadav, Nikolay A. Bogdanov, Vamshi M. Katukuri, Satoshi Nishimoto, 2 Jeroen van den Brink, 2, 3 and Liviu Hozoi Institute for Theoretical Solid State Physics, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany Department of Physics, Technical University Dresden, Helmholtzstrasse 10, 01069 Dresden, Germany Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA (Dated: March 5, 2018)

Tomonaga-Luttinger parameters for doped Mott insulators

The Tomonaga-Luttinger parameter Kρ determines the critical behavior in quasi–one-dimensional correlated electron systems, e.g., the exponent α for the density of states near the Fermi energy. We use the numerical density-matrix renormalization group method to calculate Kρ from the slope of the density-density correlation function in momentum space at zero wave vector. We check the accuracy of our new approach against exact results for the Hubbard and XXZ Heisenberg models. We determine Kρ in the phase diagram of the extended Hubbard model at quarter filling, nc = 1/2, and confirm the bosonization results Kρ = nc2 = 1/4 on the critical line and KρCDW = nc2/2 = 1/8 at infinitesimal doping of the charge-density-wave (CDW) insulator for all interaction strengths. The doped CDW insulator exhibits exponents α > 1 only for small doping and strong correlations.

Phase Diagram of the One-Dimensional Half-Filled Extended Hubbard Model

We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).

Fourth-order perturbation theory for the half-filled Hubbard model in infinite dimensions

Abstract.We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction U for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth W, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at U/W = 0.4 agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal the limited resolution of the Numerical Renormalization Group approach in treating the Hubbard bands. The momentum distributions from all approximate studies of the model are very similar in the regime where perturbation theory is applicable,

Intrinsic coupling of orbital excitations to spin fluctuations in Mott insulators.

U/W le 0.6

Density-matrix renormalization group approach to quantum impurity problems

. Iterated Perturbation Theory overestimates the quasiparticle weight above such moderate interaction strengths.

Dynamical density-matrix renormalization group for the Mott-Hubbard insulator in high dimensions

We show how the general and basic asymmetry between two fundamental degrees of freedom present in strongly correlated oxides, spin and orbital, has very profound repercussions on the elementary spin and orbital excitations. Whereas the magnons remain largely unaffected, orbitons become inherently coupled with spin fluctuations in spin-orbital models with antiferromagnetic and ferro-orbital ordered ground states. The composite orbiton-magnon modes that emerge fractionalize again in one dimension, giving rise to spin-orbital separation in the peculiar regime where spinons are faster than orbitons.

Application of the density matrix renormalization group in momentum space

A dynamic density-matrix renormalization group approach to the spectral properties of quantum impurity problems is presented. The method is demonstrated on the spectral density of the flat-band symmetric single-impurity Anderson model. We show that this approach provides the impurity spectral density for all frequencies and coupling strengths. In particular, Hubbard satellites at high energy can be obtained with a good resolution. The main difficulties are the necessary discretization of the host band hybridized with the impurity and the resolution of sharp spectral features such as the Abrikosov–Suhl resonance.

Spectral density of the two-impurity Anderson model

We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy approach to the DMFT (FE-DMFT). In FE-DMFT, the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth W = 4t at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling Uc/t = 4.45 ± 0.05. At U = 4.5t, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at Uc.