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arXiv:2112.04718 · Physical review. B./Physical review. B

Sign-free determinant quantum Monte Carlo study of excitonic density orders in a two-orbital Hubbard-Kanamori model

Xu-Xin Huang, Brian Moritz, Martin Claassen, Thomas Devereaux

Published Apr 15, 2022• 9 citations
arXivHTMLPDF

Abstract

While excitonic instabilities in multiorbital systems recently have come under scrutiny in a variety of transition-metal compounds, understanding the emergence of these instabilities from strong electronic interactions has remained a challenge. Here, we present a sign-problem-free determinant quantum Monte Carlo study of excitonic density orders in a half-filled two-orbital Hubbard-Kanamori model with broken orbital degeneracy, which accounts for the role of Hund's coupling in transition-metal compounds. For strong inverted (negative) Hund's exchange, we find numerical evidence for the emergence of excitonic density order, with competition between anti-ferro-orbital order and $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$ excitonic density order as a function of orbital splitting and Hund's coupling. While inverted Hund's coupling stabilizes a spin-singlet excitonic density phase for weak orbital splitting, positive Hund's coupling favors a spin-triplet excitonic density phase.

DOI
10.1103/physrevb.105.165124

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While excitonic instabilities in multiorbital systems recently have come under scrutiny in a variety of transition-metal compounds, understanding the emergence of these instabilities from strong electronic interactions has remained a challenge. Here, we present a sign-problem-free determinant quantum Monte Carlo study of excitonic density orders in a half-filled two-orbital Hubbard-Kanamori model with broken orbital degeneracy, which accounts for the role of Hund's coupling in transition-metal compounds. For strong inverted (negative) Hund's exchange, we find numerical evidence for the emergence of excitonic density order, with competition between anti-ferro-orbital order and Q=(\ensuremathπ,\ensuremathπ)\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})Q=(\ensuremathπ,\ensuremathπ) excitonic density order as a function of orbital splitting and Hund's coupling. While inverted Hund's coupling stabilizes a spin-singlet excitonic density phase for weak orbital splitting, positive Hund's coupling favors a spin-triplet excitonic density phase.
Excitonic condensation and stripe formation are two distinct manifestations of electronic correlations. While excitonic order naturally arises in multi-orbital systems, stripe order is a prominent feature of doped correlated-electron models. Here, we investigate an excitonic analogue of stripe order in the two--orbital Hubbard-Kanamori model on the square lattice, characterized by a spatial modulation of inter-orbital particle-hole coherence and, in the orbital-parity-symmetric limit, spontaneous breaking of a relative orbital Z2\mathbb{Z}_2Z2​ symmetry. Using unrestricted real-space Hartree-Fock calculations complemented by random-phase-approximation instability analysis, we determine how the Kanamori interactions select different excitonic channels. The sign of Hund's exchange controls the spin character of the condensate: ferromagnetic Hund coupling favors triplet excitonic order, whereas antiferromagnetic Hund coupling stabilizes singlet excitonic order. Upon doping, commensurate excitonic density waves develop incommensurate textures, including excitonic stripes and, in the triplet sector, spiral excitonic density waves. We further show that crystal-field splitting strongly reorganizes the excitonic instability by modifying inter-orbital nesting and can stabilize triplet excitonic order even in the absence of pair hopping. Our results establish excitonic stripes as a distinct symmetry-broken state of multi-orbital correlated systems and identify microscopic routes for their stabilization.
Excitonic phases described by the quantum condensation of electron-hole pairs (or excitons) are studied in the two-orbital Hubbard model with the Hund's rule coupling J . Using the variational cluster approximation, we calculate the ground-state energy and order parameters, and show that the Hund's rule coupling always stabilizes the excitonic spin-density- wave state and destabilizes the excitonic charge-density-wave state. The pair coherence lengths calculated in the spin-singlet and spin-triplet states indicate that only the spin-triplet excitons are paired more tightly with increasing J . The single-particle spectrum and density of states are also calculated to clarify the characters of these excitonic density-wave states.
In order to numerically study electron correlation effects in multiorbital systems, we propose a new type of discrete transformation for the exchange (Hund's coupling) and pair-hopping interactions to be used in the dynamical mean field theory+quantum\text{theory}+\text{quantum}theory+quantum Monte Carlo method. The transformation, which is real and exact, turns out to suppress the sign problem in a wide parameter region including non-half-filled bands. This enables us to obtain the dominant pairing symmetry in the double-orbital Hubbard model, which shows that the spin-triplet, orbital-antisymmetric pairing that exploits Hund's coupling is stable in a wide region of the band filling.
We study the electronic spectral properties at zero temperature of the one-dimensional (1D) version of the degenerate two-orbital Kanamori-Hubbard model, one of the well-established frameworks to study transition metal compounds, using state-of-the-art numerical techniques based on the density matrix renormalization group. While the system is Mott insulating for the half-filled case, as expected for an interacting 1D system, we find interesting and rich structures in the single-particle density of states (DOS) for the hole-doped system. In particular, we find the existence of in-gap states which are pulled down to lower energies from the upper Hubbard band with increasing the interorbital Coulomb interaction VVV. We analyze the composition of the DOS by projecting it onto different local excitations, and we observe that for large dopings these in-gap excitations are formed mainly by interorbital holon-doublon (HD) states and their energies follow approximately the HD states in the atomic limit. We observe that the Hund interaction JJJ increases the width of the in-gap band, as expected from the two-particle fluctuations in the Hamiltonian. The observation of a finite density of states within the gap between the Hubbard bands for this extended 1D model indicates that these systems present a rich excitation spectra which could help us understand the microscopic physics behind multiorbital compounds.
The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and interlayer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing (π,π) charge density wave state. We extract the Berezinskii-Kosterlitz-Thouless transition temperature from superfluid density and a finite-size scaling analysis of the correlation functions and explain our results in terms of an effective biexcitonic hard-core boson model.
An antiferromagnetic Hund coupling in multiorbital Hubbard systems induces orbital freezing and an associated superconducting instability, as well as unique composite orders in the case of an odd number of orbitals. While the rich phase diagram of the half-filled three-orbital model has recently been explored in detail, the properties of the doped system remain to be clarified. Here, we complement the previous studies by computing the entropy of the half-filled model, which exhibits an increase in the orbital-frozen region and a suppression in the composite ordered phase. The doping-dependent phase diagram shows that the composite ordered state can be stabilized in the doped Mott regime, if conventional electronic orders are suppressed by frustration. While antiferro-orbital order dominates the filling range $2\ensuremath{\lesssim}n\ensuremath{\le}3$ and ferro-orbital order dominates the strongly interacting region for $1\ensuremath{\lesssim}n<2$, we find superconductivity with a remarkably high Tc{T}_{c}Tc​ around n=1.5n=1.5n=1.5 (quarter filling). Also in the doped system, there is a close connection between the orbital-freezing crossover and superconductivity.