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arXiv:2004.00471 · Physical review. B./Physical review. B

Entropy and specific heat of the infinite-dimensional three-orbital Hubbard model

Changming Yue, Philipp Werner

Published Aug 3, 2020• 5 citations
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Abstract

The Hund's coupling in multiorbital Hubbard systems induces spin freezing and associated Hund metal behavior. Using dynamical mean-field theory, we explore the effect of local moment formation, spin, and charge excitations on the entropy and specific heat of the three-orbital model. For fillings $2\ensuremath{\lesssim}n<3$ and low temperature, we demonstrate a substantial enhancement of the entropy in the spin-frozen metal phase to values comparable to the half-filled Mott insulator. We also discuss the appearance of entropy plateaus and peaks in the specific heat associated with the activation of spin and charge fluctuations at high temperature. The temperature scale for charge excitations is almost independent of filling and given by $\ensuremath{\approx}0.2U$, with $U$ the intraorbital repulsion. Local spin excitations become relevant for filling $n>1$ and their characteristic temperature is proportional to the Hund coupling $J$, with a filling-dependent prefactor. The analysis of the specific heat in the atomic limit yields accurate predictions for these features in the strong-coupling regime.

DOI
10.1103/physrevb.102.085102

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The Hund's coupling in multiorbital Hubbard systems induces spin freezing and associated Hund metal behavior. Using dynamical mean-field theory, we explore the effect of local moment formation, spin, and charge excitations on the entropy and specific heat of the three-orbital model. For fillings 2\ensuremath≲n<32\ensuremath{\lesssim}n<32\ensuremath≲n<3 and low temperature, we demonstrate a substantial enhancement of the entropy in the spin-frozen metal phase to values comparable to the half-filled Mott insulator. We also discuss the appearance of entropy plateaus and peaks in the specific heat associated with the activation of spin and charge fluctuations at high temperature. The temperature scale for charge excitations is almost independent of filling and given by \ensuremath≈0.2U\ensuremath{\approx}0.2U\ensuremath≈0.2U, with UUU the intraorbital repulsion. Local spin excitations become relevant for filling n>1n>1n>1 and their characteristic temperature is proportional to the Hund coupling JJJ, with a filling-dependent prefactor. The analysis of the specific heat in the atomic limit yields accurate predictions for these features in the strong-coupling regime.
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.
We investigate the phase diagram of the spin-orbit-coupled three orbital Hubbard model at arbitrary filling by means of dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. We find that the spin-freezing crossover occurring in the metallic phase of the nonrelativistic multiorbital Hubbard model can be generalized to a J-freezing crossover, with J=L+S, in the spin-orbit-coupled case. In the J-frozen regime the correlated electrons exhibit a nontrivial flavor selectivity and energy dependence. Furthermore, in the regions near n=2 and n=4 the metallic states are qualitatively different from each other, which reflects the atomic Hund's third rule. Finally, we explore the appearance of magnetic order from exciton condensation at n=4 and discuss the relevance of our results for real materials.
We propose a way to identify strongly Hund-correlated materials by unveiling a key signature of Hund correlations at the two-particle level. The defining feature is the sign of the response of the frozen spin ratio (the long-time local spin-spin correlation function divided by the instantaneous value) under variation of electron density. The underlying physical reason is that the sign is closely related to the strength of charge fluctuations between the dominant atomic multiplets and higher-spin ones in a neighboring charge subspace. It is the predominance of these fluctuations that promotes Hund metallicity. The temperature dependence of the frozen spin ratio can further reveal a non-Fermi-liquid behavior and thus the Hund metal states. We analyze both degenerate and nondegenerate multiorbital Hubbard models and corroborate our argument by taking doped La2CuO4{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}La2​CuO4​ and LaFeAsO as representative material examples, respectively, of Mott and Hund metals. Our proposal should be applicable to systems with non-half-filled integer electron fillings and their doped cases provided the doping drove the electron density toward the half filling.
We study the Mott transition in the three-orbital Hubbard model. To investigate how the orbital level splitting and the Ising-type Hund's coupling affect the Mott transition in the case of two electrons per site, we use the dynamical mean-field theory combined with continuous-time quantum Monte Carlo simulations. The calculation of the double occupancy reveals that the critical interaction strength separating a metallic phase and two kinds of insulating phases shows a nonmonotonic behavior as a function of the level splitting. We find that this behavior is characteristic for 1/31/31/3 filling, in comparison with the preceding results for different fillings and for two-orbital models. Strong competition between the two insulators results in an intriguing first-order transition to an insulating phase having intermediate characters between Mott and band insulators. It is also found that the two insulators show different behaviors in the phase boundary with the metallic phase in the interaction-temperature plane, which is reflected in a difference in the quasiparticle behavior around the transition. We also discuss the orbital selective Mott transition for larger Hund's coupling, which is compared with previous study at zero temperature.
For many years, strong electronic correlations in metals have mainly been associated with `Mottness' driven by the Coulomb repulsion, which suppresses charge fluctuations. Recently, `Hundness', induced by Hund's rule coupling that affects spin dynamics, has gained recognition as another route to strong correlations. Using dynamical mean-field theory and the numerical renormalization group, the authors identify numerous fingerprints distinguishing Hundness from Mottness in the temperature dependence of various physical quantities for a minimal model of Hund metals.
We solve the orbitally degenerate two-band Hubbard model within dynamical mean field theory and map out the instabilities to various symmetry-broken phases based on an analysis of the corresponding lattice susceptibilities. Phase diagrams as a function of the Hund coupling parameter JJJ are obtained both for the model with rotationally invariant interaction and for the model with Ising-type anisotropy. For negative JJJ, an intraorbital spin-singlet superconducting phase appears at low temperatures, while the normal state properties are characterized by an orbital-freezing phenomenon. This is the negative-J\text{negative-}Jnegative-J analog of the recently discovered fluctuating-moment induced s-waves\text{-wave}s-wave spin-triplet superconductivity in the spin-freezing regime of multiorbital models with J>0J>0J>0.