Superexchange in Mott-Hubbard Insulators

Arianna Montorsi, Mario Rasetti

Mingzhong Lu, Yu-Feng Song, Youjin Deng +1 more

Abstract The interaction-driven crossover from a Slater insulator to a Mott insulator in the Néel-ordered ground state of the Hubbard model is a fundamental paradigm of strongly correlated electrons, yet its quantitative characterization has remained elusive. Here we establish a clear and experimentally accessible thermal criterion for this crossover via the sign change of the temperature derivative of double occupancy, ( ∂D / ∂T ) U , near zero temperature. In the Slater regime, ( ∂D / ∂T ) U > 0 reflects the major role of charge fluctuations; in the Mott regime, the anomalous ( ∂D / ∂T ) U < 0, a manifestation of the Pomeranchuk effect, signals the dominance of low-energy spin superexchange physics. Using exact diagonalization and numerically exact quantum Monte Carlo simulations, we demonstrate that this criterion determines the crossover boundary at U cross / t = 4.0(2) for the half-filled two-dimensional Hubbard model. Furthermore, we obtain a consistent boundary independently from the maximum in the antiferromagnetic correlation length, which also arises from the superexchange physics. These two thermal signatures are theoretically unified through the local minimum of thermal entropy versus interaction U at low temperatures. Our results offer a direct, measurable, and physically intuitive framework to identify the SlaterMott crossover in optical lattice experiments.

B. H. Brandow

Wen O. Wang, Jixun K. Ding, Brian Moritz +2 more

Whether or not anomalies in the thermal conductivity from insulating cuprates can be attributed to antiferromagnetic order and magnons in a 2D Mott insulator remains an intriguing open question. To shed light on this issue, we investigate the thermal conductivity $\kappa$ and specific heat $c_v$ of the half-filled 2D single-band Hubbard model using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. Both $c_v$ and $\kappa$ possess two peaks as a function of temperature, with scales related to the Hubbard interaction energy $U$ and spin superexchange energy $J$, respectively. At low temperatures where the charge degrees of freedom are gapped-out, our results for the contribution to both $c_v$ and the Drude weight associated with $\kappa$ from the kinetic energy agree well with spin-wave theory for the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model.

R. Bulla, Thomas Pruschke, Alex C. Hewson

Alexis Reymbaut, M. Charlebois, Marco Fellous-Asiani +4 more

The nearest-neighbor superexchange-mediated mechanism for ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the one-band Hubbard model faces the challenge that nearest-neighbor Coulomb repulsion can be larger than superexchange. To answer this question, we use cellular dynamical mean-field theory (CDMFT) with a continuous-time quantum Monte Carlo solver to determine the superconducting phase diagram as a function of temperature and doping for on-site repulsion $U=9t$ and nearest-neighbor repulsion $V=0,2t,4t$. In the underdoped regime, $V$ increases the CDMFT superconducting transition temperature ${T}_{c}^{d}$ even though it decreases the superconducting order parameter at low temperature for all dopings. However, in the overdoped regime $V$ decreases ${T}_{c}^{d}$. We gain insight into these paradoxical results through a detailed study of the frequency dependence of the anomalous spectral function, extracted at finite temperature via the MaxEntAux method for analytic continuation. A systematic study of dynamical positive and negative contributions to pairing reveals that even though $V$ has a high-frequency depairing contribution, it also has a low frequency pairing contribution since it can reinforce superexchange through $J=4{t}^{2}/(U\ensuremath{-}V)$. Retardation is thus crucial to understanding pairing in doped Mott insulators, as suggested by previous zero-temperature studies. We also comment on the tendency to charge order for large $V$ and on the persistence of $d$-wave superconductivity over extended-$s$ or $s+d$ wave.