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arXiv:2211.15711

Hall map and breakdown of Fermi liquid theory in the vicinity of a Mott insulator

Ilia Khait, Sauri Bhattacharyya, Abhisek Samanta, Assa Auerbach

Published Nov 28, 2022• 0 citations
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Abstract

The Hall coefficient exhibits anomalous behavior in lightly doped Mott insulators. For strongly interacting electrons its computation has been challenged by analytical and numerical obstacles. We calculate the leading contributions in the recently derived thermodynamic formula for the Hall coefficient. We obtain its doping and temperature dependence for the square lattice tJ-model at high temperatures. The second order corrections are evaluated to be negligible. Quantum Monte Carlo sampling extends our results to lower temperatures. We find a divergence of the Hall coefficient toward the Mott limit and a sign reversal relative to Boltzmann equation's weak scattering prediction. The Hall current near the Mott phase is carried by a low density of spin-entangled vacancies, which should constitute the Cooper pairs in any superconducting phase at lower temperatures.

DOI
10.48550/arxiv.2211.15711

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The Hall coefficient exhibits anomalous behavior in lightly doped Mott insulators. For strongly interacting electrons its computation has been challenged by analytical and numerical obstacles. We calculate the leading contributions in the recently derived thermodynamic formula for the Hall coefficient. We obtain its doping and temperature dependence for the square lattice tJ-model at high temperatures. The second order corrections are evaluated to be negligible. Quantum Monte Carlo sampling extends our results to lower temperatures. We find a divergence of the Hall coefficient toward the Mott limit and a sign reversal relative to Boltzmann equation's weak scattering prediction. The Hall current near the Mott phase is carried by a low density of spin-entangled vacancies, which should constitute the Cooper pairs in any superconducting phase at lower temperatures.
Abstract The Hall coefficient of the strongly interacting square lattice Hubbard model is calculated for temperatures between the antiferromagnetic interaction and the Mott gap scales. The leading order thermodynamic formula is evaluated for all doping concentrations. Second-order corrections of the thermodynamic formula are calculated and found to be negligible. The Hall coefficient diverges toward the Mott insulator. Below 45% doping the Hall sign is reversed relative to band structure-based Boltzmann’s equation. These results elucidate the effects of the Mott insulator on the charge carriers and their non-Fermi liquid transport.
Many metallic quantum materials display anomalous transport phenomena that defy a Fermi liquid description. Here, we use numerical methods to calculate thermal and charge transport in the doped Hubbard model and observe a crossover separating high- and low-temperature behaviors. Distinct from the behavior at high temperatures, the Lorenz number [Formula: see text] becomes weakly doping dependent and less sensitive to parameters at low temperatures. At the lowest numerically accessible temperatures, [Formula: see text] roughly approaches the Wiedemann-Franz constant [Formula: see text], even in a doped Mott insulator that lacks well-defined quasiparticles. Decomposing the energy current operator indicates a compensation between kinetic and potential contributions, which may help to clarify the interpretation of transport experiments beyond Boltzmann theory in strongly correlated metals.
We investigate the Hall effect in two different theoretical models of strongly correlated systems: a system made of weakly coupled Luttinger liquids, in the presence of umklapp scattering, and the 2D triangular lattice, with nearest-neighbor hopping and a local Hubbard interaction. In the first model we use a memory function approach to compute the Hall coefficient as a function of temperature and frequency in the presence of umklapp scattering. We find a power-law correction to the free-fermion value (band value), with an exponent depending on the Luttinger parameter KρK_ρKρ​. At sufficiently high temperature or frequency the Hall coefficient approaches the band value. We discuss the applications to Hall experiments made in quasi 1D organic compounds. In the second model, the complete temperature and doping dependencies of the high-frequency Hall coefficient $\RH$ are evaluated analytically and numerically for small, intermediate, and strong interactions using various approximation schemes. We find that $\RH$ follows the semiclassical 1/qn∗1/qn^*1/qn∗ law near T=0, but exhibits a striking TTT-linear behavior with an interaction- and doping-dependent slope at high temperature. We compare our results with Hall measurements performed in cobaltates.
Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behavior. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the two-dimensional Hubbard model. Because the charge gap arises from on-site correlations, we have been refining the nonperturbative approach of Matsumoto and Mancini [Phys. Rev. B 55, 2095 (1997)] which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbor energy scale J. At half-filling, we find that the spectral function possesses a gap of order U and is devoid of any coherent quasiparticle peaks although ordering or charge fractionalization are absent. At low temperatures, local antiferromagnetic correlations emerge. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. The breakdown of Luttinger's theorem in the underdoped regime is traced both to the dynamically generated Mott gap as well to a nonvanishing of the imaginary part of the self-energy at the Fermi level. Spectral weight transfer across the Mott gap also emerges as a ubiquitous feature of a doped Mott insulator and suggests that high- and low-energy scales are inseparable. Additionally in the underdoped regime, we find that a pseudogap exists in the single-particle density of states as well as in the heat capacity. The pseudogap (which is set by the energy scale t2/U){t}^{2}/U)t2/U) is argued to be a ubiquitous feature of a lightly doped Mott state and simply represents the fact that hole transport involves double occupancy. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a one-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\ifmmode\pm\else\textpm\fi{}y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level x<1/3.x<1/3.x<1/3. The sign change is tied to a termination of strong correlation physics in the doped Mott state.
Understanding the doped Mott insulator is a central challenge in condensed matter physics. In this work, we first explicitly identify a new sign structure in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model on the square lattice that replaces the conventional Fermi statistics for weakly interacting electrons. Then we show that the singular, i.e., the phase-string part of the sign structure in the partition function can be precisely turned off in a modified model. The density matrix renormalization group method is then employed to study these two models comparatively on finite-size systems, which is designed to unveil the consequences of the phase-string component. We find that the hole pairing is present not only in the quasi-long-range superconducting phase but also in the stripe phase of the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model. However, once the phase-string is switched off, both the superconducting and stripe orders together with the underlying hole pairing disappear. The corresponding ground state reduces to a trivial Fermi-liquid-like state with small hole Fermi pockets that is decoupled from the antiferromagnetic spin background. It is in sharp contrast to the original $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model where large Fermi surfaces can be restored in the stripe phase found at ${t}^{\ensuremath{'}}/t<0$ or the superconducting phase at ${t}^{\ensuremath{'}}/t>0$ in the six-leg ladder calculation. Our study clearly demonstrates that the strong correlation effect in doped Mott insulator should be mainly attributed to the long-range quantum entanglement between the spin and charge, which is, nonperturbatively, beyond a simple spin-charge separation under the no double occupancy constraint.
Low energy properties of the metallic state of the two-dimensional t - J model are presented for second neighbor hopping with hole-doping ( ) and electron-doping ( ), with various superexchange energy J . We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory . These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density , implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T 2 behavior at low T , followed by an interesting kink at higher T . The Hall number exhibits strong renormalization due to correlations. Flipping the sign of changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.