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arXiv:2104.10158 · Physical review. B./Physical review. B

Charge dynamics in magnetically disordered Mott insulators

Philip Bleicker, Dag-Björn Hering, Götz Silvester Uhrig

Published Feb 14, 2022• 2 citations
arXivHTMLPDF

Abstract

With the aid of both a semianalytical and a numerically exact method, we investigate the charge dynamics in the vicinity of half-filling in the one- and two-dimensional $t\text{\ensuremath{-}}J$ model derived from a Fermi-Hubbard model in the limit of large interaction $U$ and hence small exchange coupling $J$. The spin degrees of freedom are taken to be disordered. So we consider the limit $0<J\ensuremath{\ll}T\ensuremath{\ll}W$, where $W$ is the bandwidth. We focus on evaluating the local spectral density of a single hole excitation and the charge gap that separates the upper and the lower Hubbard band. We find indications that no band edges exist if the magnetic exchange is taken into account; instead of band edges, Gaussian tails seem to appear. A discussion of the underlying physics is provided.

DOI
10.1103/physrevb.105.085121

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With the aid of both a semianalytical and a numerically exact method, we investigate the charge dynamics in the vicinity of half-filling in the one- and two-dimensional t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model derived from a Fermi-Hubbard model in the limit of large interaction UUU and hence small exchange coupling JJJ. The spin degrees of freedom are taken to be disordered. So we consider the limit 0<J\ensuremath≪T\ensuremath≪W0<J\ensuremath{\ll}T\ensuremath{\ll}W0<J\ensuremath≪T\ensuremath≪W, where WWW is the bandwidth. We focus on evaluating the local spectral density of a single hole excitation and the charge gap that separates the upper and the lower Hubbard band. We find indications that no band edges exist if the magnetic exchange is taken into account; instead of band edges, Gaussian tails seem to appear. A discussion of the underlying physics is provided.
We study the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange interaction analytically and numerically. The bosonization and transfer-matrix renormalization group methods are used in the corresponding coupling regimes. At half-filling, the system is a Mott insulator with a finite spin excitation gap if the on-site Coulomb repulsion is fairly smaller than the antiferromagnetic exchange JJJ. This Mott insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is ${U}_{c}\ensuremath{\sim}J∕2$. However, as JJJ increases, the spin-charge couplings become important and the critical point Uc{U}_{c}Uc​ is significantly suppressed and eventually tends to zero as $J\ensuremath{\rightarrow}\ensuremath{\infty}$. Away from half-filling, the charge gap completely collapses but the spin gap persists.
We show exactly that the only charged excitations that exist in the strong-coupling limit of the half-filled Hubbard model are gapped composite excitations generated by the dynamics of the charge 2e2e2e boson that appears upon explicit integration of the high-energy scale. At every momentum, such excitations have nonzero spectral weight at two distinct energy scales separated by the on-site repulsion UUU. The result is a gap in the spectrum for the composite excitations accompanied by a discontinuous vanishing of the density of states at the chemical potential when UUU exceeds the bandwidth. Consequently, we resolve the long-standing problem of the cause of the charge gap in a half-filled band in the absence of symmetry breaking.
We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.
We analyse the thermodynamic Bethe Ansatz equations of the one-dimensional half-filled Hubbard model in the ‘spin-disordered regime’, which is characterized by the temperature being much larger than the magnetic energy scale, but small compared to the Mott–Hubbard gap. In this regime the thermodynamics of the Hubbard model can be thought of in terms of gapped charged excitations with an effective dispersion and spin degrees of freedom that only contribute entropically. In particular, the internal energy and the effective dispersion become essentially independent of temperature. An interpretation of this regime in terms of a putative interacting-electron system at zero temperature leads to a metal–insulator transition at a finite interaction strength above which the gap opens linearly. We relate these observations to studies of the Mott–Hubbard transition in the limit of infinite dimensions.
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.
We study spin and charge dynamics of stripes in doped Mott insulators by considering a two-dimensional Hubbard model with N fermion flavors. For N = 2 we recover the normal one-band model while for N → ∞ a spin density wave mean-field solution. For all band fillings, lattice topologies and N = 4 n , the model may be solved by means of quantum Monte Carlo methods without encountering the sign problem. At N = 4 and in the vicinity of the Mott insulator we find a stripe phase. This phase has a quasiparticle gap but conducts due to long-wavelength low-lying collective charge modes.