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arXiv:2109.01119 · Physical review. B./Physical review. B

Magnon heat transport in a two-dimensional Mott insulator

Wen O. Wang, Jixun K. Ding, Brian Moritz, Edwin W. Huang, Thomas Devereaux

Published Apr 18, 2022• 10 citations
arXivHTMLPDF

Abstract

Whether or not anomalies in the thermal conductivity in 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 $\ensuremath{\kappa}$ and its relationship with the specific heat ${c}_{v}$ in the half-filled 2D single-band Hubbard model, using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. At low temperatures where the charge degrees of freedom are gapped-out and ${c}_{v}$ exhibits a clear magnon peak, we observe that thermal conductivity $\ensuremath{\kappa}$ also tends to form a peak at similar temperatures. Reducing temperature further produces a sharp upturn in $\ensuremath{\kappa}$, associated with an increasing mean-free path. We identify this as the high-temperature side of the anomalous peak in insulating cuprates, where the mean-free path eventually is cut off by other scattering effects, including phonons, disorder, and physical size. Different scattering effects in our model are identified and analyzed in the thermal diffusivity.

DOI
10.1103/physrevb.105.l161103

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Whether or not anomalies in the thermal conductivity in 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 \ensuremathκ\ensuremath{\kappa}\ensuremathκ and its relationship with the specific heat cv{c}_{v}cv​ in the half-filled 2D single-band Hubbard model, using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. At low temperatures where the charge degrees of freedom are gapped-out and cv{c}_{v}cv​ exhibits a clear magnon peak, we observe that thermal conductivity \ensuremathκ\ensuremath{\kappa}\ensuremathκ also tends to form a peak at similar temperatures. Reducing temperature further produces a sharp upturn in \ensuremathκ\ensuremath{\kappa}\ensuremathκ, associated with an increasing mean-free path. We identify this as the high-temperature side of the anomalous peak in insulating cuprates, where the mean-free path eventually is cut off by other scattering effects, including phonons, disorder, and physical size. Different scattering effects in our model are identified and analyzed in the thermal diffusivity.
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 κ\kappaκ and specific heat cvc_vcv​ of the half-filled 2D single-band Hubbard model using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. Both cvc_vcv​ and κ\kappaκ possess two peaks as a function of temperature, with scales related to the Hubbard interaction energy UUU and spin superexchange energy JJJ, respectively. At low temperatures where the charge degrees of freedom are gapped-out, our results for the contribution to both cvc_vcv​ and the Drude weight associated with κ\kappaκ from the kinetic energy agree well with spin-wave theory for the spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg model.
Recent experiments on cuprates show that as a function of doping, the normal-state specific heat sharply peaks at the doping ${\ensuremath{\delta}}^{*}$, where the pseudogap ends at low temperature. This finding is taken as the thermodynamic signature of a quantum critical point, whose nature has not yet been identified. Here we present calculations for the two-dimensional Hubbard model in the doped Mott insulator regime, which indicate that the specific heat anomaly can arise from the finite-temperature critical end point of a first-order transition between a pseudogap phase with dominant singlet correlations and a metal. As a function of doping at the temperature of the end point, the specific heat diverges. Upon increasing temperature, the peak becomes broader. The diverging correlation length is associated with uniform density fluctuations. No broken symmetries are needed. These anomalies also occur at half-filling as a function of interaction strength, and are relevant for organic superconductors and ultracold atoms.
Quantum Monte Carlo results for the specific heat c of the two-dimensional Hubbard model are presented. At half filling it was observed that c\ensuremath{\sim}T2{\mathrm{T}}^{2}T2 at very low-temperatures. Two distinct features were also identified: a low-temperature peak related to the spin degrees of freedom and a higher-temperature broad peak related to the charge degrees of freedom. Away from half filling the spin-induced feature slowly disappears as a function of hole doping while the charge feature moves to lower temperature. A comparison with experimental results for the high-temperature cuprates is discussed.
In light of recent experimental data indicating a substantial thermal Hall effect in square lattice antiferromagnetic Mott insulators, we investigate whether a simple Mott insulator can sustain a finite thermal Hall effect. We verify that the answer is "no" if one performs calculations within a spin-only low-energy effective spin model with noninteracting magnons. However, by performing determinant quantum Monte Carlo simulations, we show the single-band t-t^{'}-U Hubbard model coupled to an orbital magnetic field does support a finite thermal Hall effect when t^{'}≠0 and B≠0 in the Mott insulating phase. We argue that the (carrier agnostic) necessary conditions for observing a finite thermal Hall effect are time-reversal and particle-hole symmetry breaking. By considering magnon-magnon scattering using a semiclassical Boltzmann analysis, we illustrate a physical mechanism by which finite transverse thermal conductivity may arise, consistent with our symmetry argument and numerical results. Our results indicate that square and triangular lattices with SU(2) symmetry can support a finite thermal Hall effect and call for a critical reexamination of thermal Hall effect data in insulating magnets, as the magnon contribution should not be excluded a priori.
We study the electronic thermal conductivity ${\ensuremath{\kappa}}_{\text{el}}$ and the thermal diffusion constant DQ,el{D}_{\text{Q,el}}DQ,el​ in the square lattice Hubbard model using the finite-temperature Lanczos method. We make use of the Nernst-Einstein relation for thermal transport and connect the strong nonmonotonous temperature dependence of ${\ensuremath{\kappa}}_{\text{el}}$ to that of DQ,el{D}_{\text{Q,el}}DQ,el​ and the electronic specific heat cel{c}_{\text{el}}cel​. We present also the results for the Heisenberg model on a square lattice and ladder geometries. We study the effects of doping and consider the doped case also with the dynamical mean-field theory. We show that ${\ensuremath{\kappa}}_{\text{el}}$ is below the corresponding Mott-Ioffe-Regel value in almost all calculated regimes, while the mean free path is typically above or close to lattice spacing. We discuss the opposite effect of quasiparticle renormalization on charge and heat diffusion constants. We calculate the Lorenz ratio and show that it differs from the Sommerfeld value. We discuss our results in relation to experiments on cuprates. Additionally, we calculate the thermal conductivity of overdoped cuprates within the anisotropic marginal Fermi liquid phenomenological approach.
In order to investigate the thermal properties (specific heat, magnetic susceptibility, entropy, internal energy, and some correlation functions) of the one-dimensional half-filled-band Hubbard model, we have studied linear chains and rings containing two to six atoms, by performing machine calculations. Supplementing the low-temperature behavior obtained from the exact solution for the infinite chain by Lieb and Wu, our results should be suggestive of the properties of the infinite system throughout the entire temperature domain. It is shown that when the ratio of the correlation energy UUU to the total width $\ensuremath{\Delta}$ of the band of single-particle excitations is larger than 1, the specific heat has two peaks. The high-temperature peak arises from the gradual metal-insulator transition (or the gradual formation of local moments), while the low-temperature peak is associated with the antiferromagnetic short-range ordering. When $\frac{U}{\ensuremath{\Delta}}$ becomes small, the two peaks merge into one. This picture is consistent with all other thermal properties, including correlation functions. The high-temperature properties are compared with the results predicted by Hubbard's approximate theory based on the truncation of the equations of motion of the Green's functions.