Standard Hubbard Model Research Articles

Moiré Kanamori-Hubbard model for transition metal dichalcogenide homobilayers

Ab initio and continuum model studies predicted that the $\mathrm{\ensuremath{\Gamma}}$ valley transition metal dichalcogenide (TMD) homobilayers could simulate the conventional multiorbital Hubbard model on the moir\'e honeycomb lattice. Here, we perform the Wannierization starting from the continuum model and show that a more general moir\'e Kanamori-Hubbard model emerges, beyond the extensively studied standard multiorbital Hubbard model, which can be used to investigate the many-body physics in the $\mathrm{\ensuremath{\Gamma}}$ valley TMD homobilayers. Using the unrestricted Hartree-Fock and Lanczos techniques, we study these half-filled multiorbital moir\'e bands. By constructing the phase diagrams we predict the presence of an antiferromagnetic state and in addition we found unexpected and dominant states, such as a $S=1$ ferromagnetic insulator and a charge density wave state. Our theoretical predictions made using this model can be tested in future experiments on the $\mathrm{\ensuremath{\Gamma}}$ valley TMD homobilayers.

Hall Effect in Doped Mott–Hubbard Insulator

We present theoretical analysis of Hall effect in doped Mott–Hubbard insulator, considered as a prototype of cuprate superconductor. We consider the standard Hubbard model within DMFT approximation. As a typical case we consider the partially filled (hole doping) lower Hubbard band. We calculate the doping dependence of both the Hall coefficient and Hall number and determine the value of carrier concentration, where Hall effect changes its sign. We obtain a significant dependence of Hall effect parameters on temperature. Disorder effects are taken into account in a qualitative way. We also perform a comparison of our theoretical results with some known experiments on doping dependence of Hall number in the normal state of YBCO and Nd-LSCO, demonstrating rather satisfactory agreement of theory and experiment. Thus the doping dependence of Hall effect parameters obtained within Hubbard model can be considered as an alternative to a popular model of the quantum critical point.

Hall Effect in Doped Mott–Hubbard Insulator

We present theoretical analysis of Hall effect in doped Mott-Hubbard insulator, considered as a prototype of cuprate superconductor. We consider the standard Hubbard model within DMFT approximation. As a typical case we consider the partially filled (hole doping) lower Hubbard band. We calculate the doping dependence of both the Hall coefficient and Hall number and determine the value of carrier concentration, where Hall effect changes its sign. We obtain a significant dependence of Hall effect parameters on temperature. Disorder effects are taken into account in a qualitative way.We also perform a comparison of our theoretical results with some known experiments on doping dependence of Hall number in the normal state of YBCO and Nd-LSCO, demonstrating rather satisfactory agreement of theory and experiment. Thus the doping dependence of Hall effect parameters obtained within Hubbard model can be considered as an alternative to a popular model of the quantum critical point.

Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation

It is pointed out that the low energy effective theory of a generalized spin system relates to the more generalized system shown by the Hubbard-like model. When the onsite repulsion is assumed to be provided by hard-core repulsion, a generalized fermion with flavour and colour degrees of freedom is used to define the Hubbard-like Hamiltonian in this case. In the strong coupling limit and at half filling this reduces to an antiferromagnet. The <I>D</I>-theory then helps us to associate the continuum limit of the <i>(4+1)D </i>aniferromagnet to <i>4D </i>principal chiral model. It has been observed that in the strong coupling limit the problem of finding the ground state of lattice QCD is identical to that of solving the generalized antiferromagnet with Neel order playing the role of chiral symmetry breaking. In view of this, now formulate the Hubbard-like model Hamiltonian in terms of the gener- alized fermions with flavor and color degrees of freedom also shall consider the<i> D</i>-theoretical framework to show that the antiferromagnetic system which arises in the strong coupling limit and at half filling corresponds to the principal chiral model in the continuum limit with dimensional reduction. Also pointed out that at strong coupling and half filling the system reduces to a Heisenberg antiferromagnet. This result is analogous to the result obtained in standard Hubbard model.

Pairing in the Hubbard model on the honeycomb lattice with hopping up to the third-nearest-neighbor

The electronic properties of graphene can be approximately described by the standard Hubbard model on the honeycomb lattice. It was argued that the d+id-wave pairing is the dominant pairing symmetry in such a system. However, in the standard Hubbard model, only the nearest-neighbor hopping t1 is considered, while the second-nearest-neighbor hopping t2 and third-nearest-neighbor hopping t3 are ignored. In this paper, by doing the determinant quantum Monte Carlo simulations of the Hubbard model with hopping up to the third-nearest-neighbor, we examine the effect of t2 and t3 on the pairing symmetries. We find that the second- and third-nearest-neighbor hopping amplitudes have strong effect on the d+id-wave pairing symmetry.

Competing Nodal d-Wave Superconductivity and Antiferromagnetism.

Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here, we report unbiased quantum MonteCarlo (QMC) simulations on a sign-problem-free repulsive toy model with same on site symmetries as the standard Hubbard model on a 2D square lattice. Using QMC simulations, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.

Superconducting pairing symmetries of the Hubbard model on the honeycomb lattice with inhomogeneous hopping strength

Using finite-temperature determinantal quantum Monte Carlo calculations, we find that the dominant pairing symmetries in the standard Hubbard model on the honeycomb lattice depend on the electron filling. When the electron density $\ensuremath{\rho}$ is larger than around 0.25, the dominant pairing symmetry is the $d+id$-wave; when the electron density is low enough ($\ensuremath{\rho}\ensuremath{\lesssim}0.25$), the dominant pairing symmetry is the $p+ip$ wave. For two electron densities $\ensuremath{\rho}=0.1$ and $\ensuremath{\rho}=0.4$, where the dominant pairing symmetries are $p+ip$ wave and $d+id$ wave separately, we study the effect of two types of hopping inhomogeneities (the plaquette and the quasi-$1\mathrm{D}$ hopping inhomogeneities) on the pairing symmetries. For $\ensuremath{\rho}=0.1$, the plaquette hopping inhomogeneity drives the dominant $p+ip$-wave pairing symmetry into the $d+id$-wave; while the quasi-$1\mathrm{D}$ hopping inhomogeneity almost does not affect the $p+ip$ wave, and arises the $f$ wave, causing the coexistence of $p+ip$-wave and $f$-wave pairing. For $\ensuremath{\rho}=0.4$, both the plaquette and the quasi-$1\mathrm{D}$ hopping inhomogeneities destroy the $d+id$-wave pairing symmetry, without causing other pairing symmetry. Our results suggest that the effect of hopping inhomogeneity on the pairing symmetries is robust and depends on the electron filling. This finding may be useful for the design of artificial graphene superconductors with different kinds of pairing, especially for the realization of the $d+id$-wave, $p+ip$-wave, or $f$-wave superconductors at low filling.

The Mott transition as a topological phase transition

We show that the Mott metal-insulator transition in the standard one-band Hubbard model can be understood as a topological phase transition. Our approach is inspired by the observation that the mid-gap pole in the self-energy of a Mott insulator resembles the zero-energy spectral pole of the localized surface state in a topological insulator. We use NRG-DMFT to solve the infinite-dimensional Hubbard model, and represent the resulting local self-energy in terms of the boundary Green's function of an auxiliary tight-binding chain without interactions. The auxiliary system is of generalized SSH model type; the Mott transition corresponds to a dissociation of domain walls.

Solitonic in-gap modes in a superconductor-quantum antiferromagnet interface

Bound states at interfaces between superconductors and other materials are a powerful tool to characterize the nature of the involved systems, and to engineer elusive quantum excitations. In-gap excitations of conventional s-wave superconductors occur, for instance, at magnetic impurities with net magnetic moment breaking time-reversal symmetry. Here we show that interfaces between a superconductor and a quantum antiferromagnet can host robust in-gap excitations, without breaking time-reversal symmetry. We illustrate this phenomenon in a one-dimensional model system with an interface between a conventional s-wave superconductor and a one-dimensional Mott insulator described by a standard Hubbard model. This genuine many-body problem is solved exactly by employing a combination of kernel polynomial and tensor network techniques. We unveil the nature of such zero modes by showing that they can be adiabatically connected to solitonic solutions between a superconductor and a classical antiferromagnet. Our results put forward a new class of in-gap excitations between superconductors and a disordered quantum spin phase can be relevant for a wider range of heterostructures.

High-precision analysis of Feshbach resonances in a Mott insulator

We show that recent high-precision measurements of relative on-site interaction energies $\Delta U$ in a Mott insulator require a theoretical description beyond the standard Hubbard-model interpretation, when combined with an accurate coupled-channels calculation. In contrast to more sophisticated lattice models, which can be elaborate especially for parameter optimization searches, we introduce an easy to use effective description of $U$ valid over a wide range of interaction strengths modeling atomic pairs confined to single lattice sites. This concise model allows for a straightforward combination with a coupled-channels analysis. With this model we perform such a coupled-channels analysis of high-precision $^7$Li spectroscopic data on the on-site interaction energy $U$, which spans over four Feshbach resonances and provide an accurate and consistent determination of the associated resonance positions. Earlier experiments on three of the Feshbach resonances are consistent with this new analysis. Moreover, we verify our model with a more rigorous numerical treatment of the two atom system in an optical lattice.

Quantum Integrability of 1D Ionic Hubbard Model

AbstractThe quantum integrability of the 1D ionic Hubbard model (IHM) is established using two independent numerical methods, namely i) energy level spacing statistics and ii) occupation profile of one‐particle density matrix (OPDM) eigen‐values. Both methods suggest that the 1D IHM is integrable. The calculations of energy level statistics reproduce the known results for the standard Hubbard model. Upon turning on the the ionic term, the energy level spacing distribution of this model continues to obey the Poissonian distribution. Occupation patterns as extracted from OPDM indicate that quasi‐particles are sharpened upon increasing the ionic potential. This is evidenced by a larger jump in the occupation number distribution.

Extended dynamical mean field theory combined with the two-particle irreducible functional renormalization-group approach as a tool to study strongly correlated systems

We propose new approach for treatment of local and non-local interactions in correlated electronic systems, which uses self-energy and the two-particle irreducible vertices, obtained from (extended) dynamical mean-field theory, as an input of two-particle irreducible functional renormalization-group (2PI-fRG) approach. Using 2PI-fRG approach allows us to treat both, local and non-local interactions. In case of purely local interaction the corresponding equations have similar (although not identical) structure to the earlier developed DMF$^2$RG approach. In a simplest truncation, neglecting scale-dependence of the two-particle irreducible vertices, we reproduce the results for the two-particle vertices/susceptibilities in the ladder approximation of the dual boson or D$\Gamma$A approach; in more sophisticated truncations the method allows us to consider non-local corrections to the self-energy, as well as the interplay of charge- and spin correlations. treatment of vertex renormalizations. The proposed scheme is tested on the two-dimensional standard and extended $U$-$V$ half-filled Hubbard models. For the standard Hubbard model we obtain non-local self-energy, which is in agreement with numerical studies; for the extended Hubbard model we obtain the boundary of charge instability, which agrees well with the results of the dual boson (DB) approach. We also find that the effect of spin correlations on electron interaction in the charge channel, not considered previously in the DB approach, only slightly reduces critical next-nearest-neighbor interaction of charge instability of the extended Hubbard model at the considered finite small temperature, yielding better agreement with dynamic cluster approximation. The considered method is rather general and can be applied to study various phenomena in strongly-correlated electronic systems.

Hidden Charge Orders in Low-Dimensional Mott Insulators

The opening of a charge gap driven by interaction is a fingerprint of the transition to a Mott insulating phase. In strongly correlated low-dimensional quantum systems, it can be associated to the ordering of hidden non-local operators. For Fermionic 1D models, in the presence of spin–charge separation and short-ranged interaction, a bosonization analysis proves that such operators are the parity and/or string charge operators. In fact, a finite fractional non-local parity charge order is also capable of characterizing some two-dimensional Mott insulators, in both the Fermionic and the bosonic cases. When string charge order takes place in 1D, degenerate edge modes with fractional charge appear, peculiar of a topological insulator. In this article, we review the above framework, and we test it to investigate through density-matrix-renormalization-group (DMRG) numerical analysis the robustness of both hidden orders at half-filling in the 1D Fermionic Hubbard model extended with long range density-density interaction. The preliminary results obtained at finite size including several neighbors in the case of dipolar, screened and unscreened repulsive Coulomb interactions, confirm the phase diagram of the standard extended Hubbard model. Besides the trivial Mott phase, the bond ordered and charge density wave insulating phases are also not destroyed by longer ranged interaction, and still manifest hidden non-local orders.

Hubbard models with nearly flat bands: Ground-state ferromagnetism driven by kinetic energy

We consider the standard repulsive Hubbard model with a flat lowest-energy band for two one-dimensional lattices (diamond chain and ladder) as well as for a two-dimensional lattice (bilayer) at half filling of the flat band. The considered models do not fall in the class of Mielke-Tasaki flat-band ferromagnets, since they do not obey the connectivity conditions. However, the ground-state ferromagnetism can emerge, if the flat band becomes dispersive. To study this kinetic-energy-driven ferromagnetism we use perturbation theory and exact diagonalization of finite lattices. We find as a typical scenario that small and moderate dispersion may lead to a ferromagnetic ground state for sufficiently large on-site Hubbard repulsion $U>U_c$, where $U_c$ increases monotonically with the acquired bandwidth. However, we also observe for some specific parameter cases, that (i) ferromagnetism appears at already very small $U_c$, (ii) ferromagnetism does not show up at all, (iii) the critical on-site repulsion $U_c$ is a nonmonotonic function of the bandwidth, or that (iv) a critical bandwidth is needed to open the window for ground-state ferromagnetism.

Communication: Fragment-based Hamiltonian model of electronic charge-excitation gaps and gap closure.

Capturing key electronic properties such as charge excitation gaps within models at or above the atomic scale presents an ongoing challenge to understanding molecular, nanoscale, and condensed phase systems. One strategy is to describe the system in terms of properties of interacting material fragments, but it is unclear how to accomplish this for charge-excitation and charge-transfer phenomena. Hamiltonian models such as the Hubbard model provide formal frameworks for analyzing gap properties but are couched purely in terms of states of electrons, rather than the states of the fragments at the scale of interest. The recently introduced Fragment Hamiltonian (FH) model uses fragments in different charge states as its building blocks, enabling a uniform, quantum-mechanical treatment that captures the charge-excitation gap. These gaps are preserved in terms of inter-fragment charge-transfer hopping integrals T and on-fragment parameters U((FH)). The FH model generalizes the standard Hubbard model (a single intra-band hopping integral t and on-site repulsion U) from quantum states for electrons to quantum states for fragments. We demonstrate that even for simple two-fragment and multi-fragment systems, gap closure is enabled once T exceeds the threshold set by U((FH)), thus providing new insight into the nature of metal-insulator transitions. This result is in contrast to the standard Hubbard model for 1d rings, for which Lieb and Wu proved that gap closure was impossible, regardless of the choices for t and U.

Correlated Dirac semimetal by periodized cluster dynamical mean-field theory

The periodized cluster dynamical mean-field theory (PCDMFT) combined with exact diagonalization as impurity solver has been applied to the half-filled standard Hubbard model on the honeycomb lattice. A correlated Dirac semimetal is found for weak interactions and it transforms into an antiferromagnetic insulating phase for strong interactions via a first-order quantum phase transition, not intervened by a spin liquid phase in between. In this application, the PCDMFT introduces the partial translation symmetry, but cures well the problem due to the translation symmetry breaking in the cluster dynamical mean-field theory studies for the same model, which give rise to a spurious insulating phase in the weakly interacting region.

Exploring unconventional Hubbard models with doubly modulated lattice gases.

Recent experiments show that periodic modulations of cold atoms in optical lattices may be used to engineer and explore interesting models. We show that double modulation combining lattice shaking and modulated interactions allows for the engineering of a much broader class of lattice with correlated hopping, which we study for the particular case of one-dimensional systems. We show, in particular, that by using this double modulation it is possible to study Hubbard models with asymmetric hopping, which, contrary to the standard Hubbard model, present insulating phases with both parity and string order. Moreover, double modulation allows for the simulation of lattice models in unconventional parameter regimes, as we illustrate for the case of the spin-1/2 Fermi-Hubbard model with correlated hopping, a relevant model for cuprate superconductors.

Search for ferromagnetism in doped semiconductors in the absence of transition metal ions

In contrast to semiconductors doped with transition metal magnetic elements (e.g., ${\text{Ga}}_{1\ensuremath{-}x}{\text{Mn}}_{x}\text{As}$), which become ferromagnetic at temperatures below $\ensuremath{\sim}{10}^{2}\text{ }\text{K}$, semiconductors doped with nonmagnetic ions (e.g., silicon doped with phosphorous) have not shown evidence of ferromagnetism down to millikelvin temperatures. This is despite the fact that for low densities the system is expected to be well modeled by the Hubbard model, which is predicted to have a ferromagnetic ground state at $T=0$ on two-dimensional (2D) or three-dimensional bipartite lattices in the limit of strong correlation near half-filling. We examine the impurity band formed by hydrogenic centers in semiconductors at low densities, and show that it is described by a generalized Hubbard model which has, in addition to strong electron-electron interaction and disorder, an intrinsic electron-hole asymmetry. With the help of mean-field methods as well as exact diagonalization of clusters around half filling, we can establish the existence of a ferromagnetic ground state, at least on the nanoscale, which is more robust than that found in the standard Hubbard model. This ferromagnetism is most clearly seen in a regime inaccessible to bulk systems but attainable in quantum dots and 2D heterostructures. If observed, this would be the first experimental realization of a system exhibiting Nagaoka ferromagnetism. We present extensive numerical results for small systems that demonstrate the occurrence of high-spin ground states in both periodic and positionally disordered 2D systems. We examine how properties of real doped semiconductors, such as positional disorder and electron-hole asymmetry, affect the ground state spin of small 2D systems, and use the results to infer properties at longer length scales.

Extended Hubbard model on a C20 molecule

The electronic correlations on aC20 molecule,as described by an extended Hubbard Hamiltonian with a nearest-neighbor Coulomb interaction ofstrength V, are studied using quantum Monte Carlo and exact diagonalization methods. For electron-dopedC20, it isknown that pair binding arising from a purely electronic mechanism is absent within the standard Hubbardmodel (V = 0). Here we show that this is also the case for hole doping for0<U/t≤3 and that, for both electron and hole doping, the effect of a non-zeroV is to work against pair binding. We also study the magnetic properties of the neutralmolecule, and find transitions between spin singlet and triplet ground states for either fixedU orV values. In addition, spin, charge and pairing correlation functions onC20 are computed. The spin–spin and charge–charge correlations are very short-range, althougha weak enhancement in the pairing correlation is observed for a distance equal to themolecular diameter.

Quantum degenerate Bose-Fermi mixtures on one-dimensional optical lattices

We study numerically and analytically the phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional lattice. In particular, along a symmetry plane in the parameter space, we obtain the exact boundary of the boson-demixing transition from the Bethe ansatz solution of the standard Hubbard model. For a region of parameter space, we prove the existence of boson-fermion mixed phase at all densities. This phase is a two-component Luttinger liquid for weak couplings or for incommensurate total density, otherwise it has a charge gap but retains a gapless mode of mixture composition fluctuations. We show that the static density correlations in these two regimes are markedly different.