We calculate the Hubbard bands for the half-filled Hubbard model on a Bethe lattice with infinite coordination number up to and including third order in the inverse Hubbard interaction. We employ the Kato--Takahashi perturbation theory to solve the self-consistency equation of the Dynamical Mean-Field Theory analytically for the single-impurity Anderson model in multi-chain geometry. The weight of the secondary Hubbard sub-bands is of fourth order so that the two-chain geometry is sufficient for our study. Even close to the Mott--Hubbard transition, our results for the Mott--Hubbard gap agree very well with those from numerical Dynamical Density-Matrix Renormalization Group (DDMRG) calculations. The density of states of the lower Hubbard band also agrees very well with DDMRG data, apart from a resonance contribution at the upper band edge which cannot be reproduced in low-order perturbation theory.
We investigate the momentum distribution function near the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model (the zig-zag Hubbard chain), with the density-matrix renormalization-group technique. We show that for strong interactions the Mott-Hubbard transition occurs between the metallic-phase and an insulating dimerized phase with incommensurate spin excitations, suggesting a decoupling of magnetic and charge excitations not present in weak coupling. We illustrate the signatures for the Mott-Hubbard transition and the commensurate-incommensurate transition in the insulating sp…
We propose an order parameter for the one dimensional Mott-Hubbard transition and provide numerical evidence and general theoretical arguments for the correctness of our proposal. In addition, we discuss some of the implications of this picture of the one dimensional Mott-Hubbard transition and speculate about possible higher dimensional analogs.
We investigate the nature of the interaction-driven Mott-Hubbard transition of the half-filled $t_1{-}t_2$ Hubbard model in one dimension, using a full-fledged variational Monte Carlo approach including a distance-dependent Jastrow factor and backflow correlations. We present data for the evolution of the magnetic properties across the Mott-Hubbard transition and on the commensurate to incommensurate transition in the insulating state. Analyzing renormalized excitation spectra, we find that the Fermi surface renormalizes to perfect nesting right at the Mott-Hubbard transition in the insulating…
In view of a recent controversy we investigated the Mott-Hubbard transition in D=infinity with a novel cluster approach. i) We show that any truncated Bethe lattice of order n can be mapped exactly to a finite Hubbard-like cluster. ii) We evaluate the self-energy numerically for n=0,1,2 and compare with a series of self-consistent equation-of-motion solutions. iii) We find the gap to open continously at the critical U_c~2.5t* (t = t* / sqrt{4d}). iv) A low-energy theory for the Mott-Hubbard transition is developed and relations between critical exponents are presented.
I investigate band and Mott insulating states in a two-band Hubbard model, with the aim of understanding the differences between the idealised one-orbital model and the more realistic multi-band case. Using a projection ansatz I show that additional orbitals suppress the metal-insulator transition, leading to a critical coupling of approximately eight times the bare band-width. I also demonstrate the effects of orbital ordering, which hinder Mott-Hubbard states and open a band gap. Since multi-band correlations are common in real materials, this work suggests that the existence of very strongl…
We investigate the Mott transitions in the multi-orbital Hubbard model at half-filling by means of the self-energy functional approach. The phase diagrams are obtained at finite temperatures for the Hubbard model with up to four-fold degenerate bands. We discuss how the first-order Mott transition points $U_{c1}$ and $U_{c2}$ as well as the critical temperature $T_c$ depend on the orbital degeneracy. It is elucidated that enhanced orbital fluctuations play a key role to control the Mott transitions in the multi-orbital Hubbard model.
We apply the nested algebraic Bethe ansatz method to solve the eigenvalue problem for the SU(4) extension of the Hubbard model. The Hamiltonian is equivalent to the SU(4) graded permutation operator. The graded Yang-Baxter equation and the graded Quantum Inverse Scattering Method are used to obtain the eigenvalue of the SU(4) extension of the Hubbard model.
We study the low energy behavior of the one dimensional Hubbard model across the Mott metal-insulator phase transition in an external magnetic field. In particular we calculate elements of the dressed charge matrix at the critical point of the Mott transition for arbitrary Hubbard repulsion and magnetization numerically and, in certain limiting cases, analytically. These results are combined with a non-perturbative effective field theory approach to reveal how the breaking of time reversal symmetry influences the Mott transition.
We calculate the one-particle density of states for the Mott-Hubbard insulating phase of the Hubbard model on a Bethe lattice in the limit of infinite coordination number. We employ the Kato-Takahashi perturbation theory around the strong-coupling limit to derive the Green function. We show that the Green function for the lower Hubbard band can be expressed in terms of polynomials in the bare hole-hopping operator. We check our technique against the exact solution of the Falicov-Kimball model and give explicit results up to and including second order in the inverse Hubbard interaction. Our res…
We present a calculation of the recombination rate of the excited holon-doublon pairs based on the two-dimensional model relevant for undoped cuprates which shows that fast processes, observed in pump-probe experiments on Mott-Hubbard insulators in picosecond range, can be explained even quantitatively with the multi-magnon emission. The precondition is the existence of the Mott-Hubbard bound exciton of the s-type. We find that its decay is exponentially dependent on the Mott-Hubbard gap and on the magnon energy, with a small prefactor which can be traced back to strong correlations and conseq…
We present experimental evidences for a ferro-electric transition in the family of quasi one- dimensional conductors (TMTTF)2X. We interpret this new transition in the frame of the combined Mott-Hubbard state taking into account the double action of the spontaneous charge disproportionation on the TMTTF molecular stacks and of the X anionic potentials.
Strong repulsive interactions between electrons can lead to a Mott metal-insulator transition. The Dynamical Mean-Field Theory (DMFT) explains the critical end-point and hysteresis region with single-particle concepts such as the spectral function and the quasiparticle weight. In this work, we reconsider the critical end point of the metal-insulator transition on the two-particle level. We show that the relevant eigenvalue and eigenvector of the non-local Bethe-Salpeter kernel provide a unified picture of the hysteresis region and of the critical end point of the Mott transition. In particular…
We investigate the Hubbard model on the anisotropic triangular lattice by means of the cellular dynamical mean field theory. The phase diagram determined in the Hubbard interaction versus temperature plane shows novel reentrant behavior in the Mott transition due to the competition between Fermi-liquid formation and magnetic correlations under geometrical frustration. We demonstrate that the reentrant behavior is characteristic of the Mott transition with intermediate geometrical frustration and indeed consistent with recent experimental results of organic materials.
A recent paper by Bluemer et al. [cond-mat/0609758] again criticizes earlier QMC/DMFT results by Liebsch [Phys. Rev. B {\bf 70}, 165103 (2004)]. This criticism is shown to be unfounded.
We calculate the zero-temperature gap and quasiparticle weight of the half-filled Hubbard model with a random dispersion relation. After extrapolation to the thermodynamic limit, we obtain reliable bounds on these quantities for the Hubbard model in infinite dimensions. Our data indicate that the Mott-Hubbard transition is continuous, i.e., that the quasiparticle weight becomes zero at the same critical interaction strength at which the gap opens.
We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the statistics is equivalent to the presence of a magnetic field produced by the particles themselves, which is present also in a ``free gas'' of these particles.
We study antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model at low temperature. Collective spin fluctuations are governed by a non-linear sigma model that we derive from the Hubbard model for any value of the Coulomb repulsion. As the Coulomb repulsion increases, the ground state progressively evolves from a Slater to a Mott-Heisenberg antiferromagnet. At finite temperature, we find a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling.
Mott transitions are studied in the two-dimensional Hubbard model by a non-perturbative theory of correlator projection that systematically includes spatial correlations into the dynamical mean-field approximation. Introducing a nonzero second-neighbor transfer, a first-order Mott transition appears at finite temperatures and ends at a critical point or curve.
We investigate the Mott transition in the Kagomé lattice Hubbard model using a cluster extension of dynamical mean field theory. The calculation of the double occupancy, the density of states, the static and dynamical spin correlation functions demonstrates that the system undergoes the first-order Mott transition at the Hubbard interaction $U/W \sim 1.4$ ($W$:bandwidth). In the metallic phase close to the Mott transition, we find the strong renormalization of three distinct bands, giving rise to the formation of heavy quasiparticles with strong frustration. It is elucidated that the quasipart…
We have studied the impact of non-local electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte-Carlo and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling -- irrespectively of the preformation of localized or short-ranged magnetic moments. This is the reason, why the two-dimensional Hubbard model is insulating at low …
We investigate the Mott transitions in two-band Hubbard models with different bandwidths. Applying dynamical mean field theory, we discuss the stability of itinerant quasi-particle states in each band. We demonstrate that separate Mott transitions occur at different Coulomb interaction strengths in general, which merge to a single transition only under special conditions. This kind of behavior may be relevant for the physics of the single-layer ruthenates, Ca$_{2-x}$Sr$_x$RuO$_4$.
By comparing the responses to an in-plane magnetic field near the metal-insulator transition (MIT), we find that the observed MIT in Si MOSFETs can be described by the non-perturbative Mott-Hubbard scenario. Interrelations between independent measurables are uncovered and confirmed by replotting the experimental data. A universal critical energy scale vanishing at the MIT is extracted from the experimental data and the critical exponent found.
We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and three-dimensional cubic lattices by means of a recently proposed variational wave function. In one dimension, the variational results agree with the expected Berezinskii-Kosterlitz-Thouless scenario of the interaction-driven Mott transition. In two and three dimensions, we find evidences that, across the transition,most of the spectral weight is concentrated at high energies, suggestive of pre-formed Mott-Hubbard side-bands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. …
The spectral weight evolution of the low-dimensional Mott insulator TiOCl upon alkali-metal dosing has been studied by photoelectron spectroscopy. We observe a spectral weight transfer between the lower Hubbard band and an additional peak upon electron-doping, in line with quantitative expectations in the atomic limit for changing the number of singly and doubly occupied sites. This observation is an unconditional hallmark of correlated bands and has not been reported before. In contrast, the absence of a metallic quasiparticle peak can be traced back to a simple one-particle effect.
Determining the nature of band gaps in transition-metal compounds remains challenging. We present a first-principles study on electronic and optical properties of CoO using hybrid functional pseudopotentials. We show that optical absorption spectrum can provide a clear fingerprint to distinguish between Mott-Hubbard, intermediate and charge-transfer insulators. This discrimination is reflected by the qualitative difference in peak satellites due to unique interplay between $d$-$d$ and $p$-$d$ excitations, thus allowing identification from experimental data alone, unlike the existing methods th…
The magnetic properties and Mott transition of the half-filled Hubbard model on the 1/5 depleted square lattice with frustration is studied at zero temperature by the variational cluster approximation. The $(π,π)$ Néel ordering (AF) is stable in a wide region of the phase diagram and almost completely veils the non-magnetic Mott transition for the unfrustrated case. However, AF is severely suppressed by the frustration and even with moderate frustrations the non-magnetic Mott transition takes place in the range where the intra-dimer hoppings are larger than the intra-plaquette hoppings.
The Mott transition in a two-band Hubbard model involving subbands of different widths is studied as a function of temperature using dynamical mean field theory combined with exact diagonalization. The phase diagram is shown to exhibit two successive first-order transitions if the full Hund's rule coupling is included. In the absence of spin-flip and pair-exchange terms the lower transition remains first-order while the upper becomes continuous.
We investigate the bandwidth-controlled Mott transition in the Hubbard model on the checkerboard lattice at half filling using the path-integral renormalization group (PIRG) method. It is demonstrated that the system undergoes a first-order phase transition to the plaquette-singlet insulating phase at a finite Hubbard interaction. This conclusion is drawn via a detailed analysis of the spin and charge correlations around the phase transition point by means of the PIRG method aided with a new iteration scheme introduced in this paper.
We show that the Mott transition occurring in bosonic Hubbard models can be successfully described by a simple variational wave function that contains all important long-wavelength correlations. Within this approach, a smooth metal-insulator transition is made possible by means of a long-range Jastrow correlation term that binds in real space density fluctuations. We find that the Mott transition has similar properties in two and three dimensions but differs in one dimension. We argue that our description of the Mott transition in terms of a binding-unbinding transition is of general validity …
The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions…
We investigate the Mott transitions in two-orbital Hubbard systems. Applying the dynamical mean field theory and the self-energy functional approach, we discuss the stability of itinerant quasi-particle states in each band. It is shown that separate Mott transitions occur at different Coulomb interaction strengths in general. On the other hand, if some special conditions are satisfied for the interactions, spin and orbital fluctuations are equally enhanced at low temperatures, resulting in a single Mott transition. The phase diagrams are obtained at zero and finite temperatures. We also addres…
We study the second order finite temperature Mott transition point in the fully frustrated Hubbard model at half filling, within Dynamical Mean Field Theory. Using quantum Monte Carlo simulations we show the existence of a finite temperature second order critical point by explicitly demonstrating the existence of a divergent susceptibility as well as by finding coexistence in the low temperature phase. We determine the location of the finite temperature Mott critical point in the (U,T) plane. Our study verifies and quantifies a scenario for the Mott transition proposed in earlier studies (Revi…
The magnetic properties and Mott transition of the Hubbard model on the square lattice with frustration are studied at half-filling and zero temperature by the variational cluster approximation. When the on-site repulsion $U$ is large, magnetically disordered state is realized in highly frustrated region between the Néel and collinear phases, and no imcommensurate magnetic states are found there. As for the Mott transition, in addition to the Mott gap and double occupancy, which clarify the nature of the transition, the structure of the self-energy in the spectral representation is studied in …
We argue that the binding between doubly occupied (doublon) and empty (holon) sites governs the incoherent excitations and plays a key role in the Mott transition in strongly correlated Mott-Hubbard systems. We construct a new saddle point solution with doublon-holon binding in the Kotliar-Ruckenstein slave-boson functional integral formulation of the Hubbard model. On the half-filled honeycomb lattice and square lattice, the ground state is found to exhibit a continuous transition from the paramagnetic semimetal/metal to an antiferromagnetic ordered Slater insulator with coherent quasiparticl…
We investigate the Mott transition in the anisotropic kagomé lattice Hubbard model using the cellular dynamical mean field theory combined with continuous-time quantum Monte Carlo simulations. By calculating the double occupancy and the density of states, we determine the interaction strength of the first-order Mott transition and show that it becomes small as the anisotropy increases. We also calculate the spin correlation functions and the single-particle spectrum, and reveal that the quasiparticle and magnetic properties change dramatically around the Mott transition; the spin correlations …
We use determinant Quantum Monte Carlo simulations and exact diagonalization to explore insulating behavior in the Hubbard model with a bimodal distribution of randomly positioned local site energies. From the temperature dependence of the compressibility and conductivity, we show that gapped, incompressible Mott insulating phases exist away from half filling when the variance of the local site energies is sufficiently large. The compressible regions around this Mott phase are metallic only if the density of sites with the corresponding energy exceeds the percolation threshold, but are Anderso…
The one-dimensional extended Peierls-Hubbard model is studied at several band fillings using the density matrix renormalization group method. Results show that the ground state evolves from a Mott-Peierls insulator with a correlation gap at half-filling to a soliton lattice with a small band gap away from half-filling. It is also confirmed that the ground state of the Peierls-Hubbard model undergoes a transition to a metallic state at finite doping. These results show that electronic correlations effects should be taken into account in theoretical studies of doped polyacetylene. They also show…
The zero temperature Mott-Hubbard transition as a function of the Coulomb repulsion U is investigated in the limit of large dimensions. The behavior of the density of states near the transition at U=U_c is analyzed in all orders of the skeleton expansion. It is shown that only two transition scenarios are consistent with the skeleton expansion for U<U_c: (i) The Mott-Hubbard transition is "discontinuous" in the sense that in the density of states finite spectral weight is redistributed at U_c. (ii) The transition occurs via a point at U=U_c where the system is neither a Fermi liquid nor an ins…
We derived a simple metal-insulator criterion in analytical form for the doped Mott-Hubbard materials. Its readings closely related to the orbital and spin nature of the ground states of the unit cell. The available criterion readings (metal or insulator) in the paramagnetic phase points to the possibility of the insulator state of doped materials with the forbidden first removal electron states. According to its physical meaning the result is similar to Wilsons criterion in the itinerant electron systems. An application of the criterion to the high-Tc cuprates discussed.
The Mott-Hubbard transition is studied in the context of the two-dimensional Hubbard model. Analytical calculations show the existence of a critical value Uc of the potential strength which separates a paramagnetic metallic phase from a paramagnetic insulating phase. Calculations of the density of states and double occupancy show that the ground state in the insulating phase contains always a small fraction of empty and doubly occupied sites. The structure of the ground state is studied by considering the probability amplitude of intersite hopping. The results indicate that the ground state of…
We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we repro…
The validity of the Luttinger sum rule is investigated within the prototype tight-binding model of interacting fermions in one dimension, i.e., the t-V model including the next-nearest neighbor hopping t' in order to break the particle-hole symmetry. Scaling analysis of finite-system results at half-filling reveals evident breakdown of the sum rule in the regime of large gap at V >> t, while the sum rule appears to recover together with vanishing of the Mott-Hubbard gap.
We investigate the characteristics of the metallic phase near the Mott transition in the Kagomé lattice Hubbard model using the cellular dynamical mean field theory. By calculating the specific heat and spin correlation functions, we demonstrate that the quasiparticles show anomalous properties in the metallic phase close to the Mott transition. We find clear evidence for the multi-band heavy quasiparticles in the specific heat, which gives rise to unusual temperature dependence of the spin correlation functions.
The density driven Mott transition is studied by means of Dynamical Mean-Field Theory in the Hubbard-Holstein model, where the Hubbard term leading to the Mott transition is supplemented by an electron-phonon (e-ph) term. We show that an intermediate e-ph coupling leads to a first-order transition at T=0, which is accompanied by phase separation between a metal and an insulator. The compressibility in the metallic phase is substantially enhanced. At quite larger values of the coupling a polaronic phase emerges coexisting with a non-polaronic metal.
We study the interplay of strong electron correlations and intra-triangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-$1$ Mott insulator, a metal, and a spin-$0$ Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intra-triangle multi-orbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenou…
We study how the electron hopping reduces the Mott-Hubbard band gap in the limit of a large Coulomb interaction U and as a function of the orbital degeneracy N. The results support the conclusion that the hopping contribution grows as roughly \sqrt{N}W, where W is the one-particle band width, but in certain models a crossover to a \sim NW behavior is found for a sufficiently large N.
We investigated the optical properties of (Ca,Sr)RuO_3 films on the borderline of a metal-insulator (M-I) transition. Our results show all of the predicted characteristics for a metallic Mott-Hubbard system, including (i) a mass enhancement in dc-limit, (ii) an U/2 excitation, and (iii) an U excitation. Also, a self-consistency is found within the Gutzwiller-Brinkman-Rice picture for the Mott transition. Our finding displays that electron correlation should be important even in 4d materials.
Anisotropic optical spectra coupled with antiferromagnetic spin ordering (SO) and orbital ordering (OO) have been investigated for single crystals of LaVO_{3} and YVO_{3}. The orbital-dependent Mott-Hubbard gap transitions are observed around 2 eV. The transitions composed of the two peaks show distinct anisotropy and selection rules, reflecting the respective SO and OO patterns. The temperature dependence of the anisotropic transitions clearly indicates the SO/OO correlation and the evolution of the order parameters.
We study the interplay between Néel-antiferromagnetism and the paramagnetic metal-insulator-transition (PMIT) on a Bethe lattice with nearest and next-nearest eighbor hopping $t_1$ and $t_2$. We concentrate in this paper on the situation at half-filling. For $t_2/t_1\to 1$ the PMIT outgrows the antiferromagnetic phase and shows a scenario similar to V$_2$O$_3$. In this parameter regime we also observe a novel magnetic phase.
Motivated by Heilmann and Lieb's work, we discuss energy level crossings for the one-dimensional Hubbard model through the Bethe ansatz, constructing explicitly the degenerate eigenstates at the crossing points. After showing the existence of solutions for the Lieb--Wu equations with one-down spin, we solve them numerically and construct Bethe ansatz eigenstates. We thus verify all the level crossings in the spectral flows observed by the numerical diagonalization method with one down-spin. For each of the solutions we obtain its energy spectral flow along the interaction parameter U. Then, we…
The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The discontinuity in the chemical potential for the change from hole to electron doping is calculated analytically as a function of the on-site Coulomb interaction $U$, and the charge-transfer energy $Δ$ between the $d$- and $p$-orbitals, transfer integrals $t_{pd}$, $t_{pp}$, $t_{dd}$ between $p$-$d$, $p$-$p$ and $d$-$d$ sites respectively. The critical behaviour of the quasiparticle weight is also obtained analytically.
We study the magnetic properties around the Mott transition in the Kagomé lattice Hubbard model by the cellular dynamical mean field theory combined with quantum Monte Carlo simulations. By investigating the q-dependence of the susceptibility, we find a dramatic change of the dominant spin fluctuations around the Mott transition. The spin fluctuations in the insulating phase favor down to the lowest temperature a spatial spin configuration in which antiferromagnetic correlations are strong only in one chain direction but almost vanishing in the others.
The mass-imbalanced Hubbard model represents a continuous evolution from the Hubbard to the Falicov-Kimball model. We employ dynamical mean field theory and study the paramagnetic metal-insulator transition, which has a very different nature for the two limiting models. Our results indicate that the metal-insulator transition rather resembles that of the Hubbard model as soon as a tiny hopping between the more localized fermions is switched on. At low temperatures we observe a first-order metal-insulator transition and a three peak structure. The width of the central peak is the same for the m…
Bad-Metal (BM) behavior featuring linear temperature dependence of the resistivity extending to well above the Mott-Ioffe-Regel (MIR) limit is often viewed as one of the key unresolved signatures of strong correlation. Here we associate the BM behavior with the Mott quantum criticality by examining a fully frustrated Hubbard model where all long-range magnetic orders are suppressed, and the Mott problem can be rigorously solved through Dynamical Mean-Field Theory. We show that for the doped Mott insulator regime, the coexistence dome and the associated first-order Mott metal-insulator transiti…
In the present paper, we systematically studied the possible Orbital selective Mott transition (OSMT) in the $t_{2g}$ system, which has three orbital degeneracy. The slave Boson mean field theory is generalized to the three band systems with full Hund's rule coupling including spin flip and pair hopping terms. A new type of Mott transition which is driven by the crystal field splitting or the lattice distortion is found is this model. We argue that this new type of Mott transition may relate to the puzzling phase in $Sr_{x}Ca_{2-x}RuO_4$.
