Hubbard Model Research Articles

Singlet Even-Frequency and Triplet Odd-Frequency Superconductivity in the Two-Band Hubbard Model Based on the Dynamical Mean-Field Theory

Singlet Even-Frequency and Triplet Odd-Frequency Superconductivity in the Two-Band Hubbard Model Based on the Dynamical Mean-Field Theory

Hidden symmetry of Bogoliubov de Gennes quasi-particle eigenstates and universal relations in flat band superconducting bipartite lattices

Unconventional flat band (FB) superconductivity, as observed in van der Waals heterostructures, could open promising avenues towards high-T_cc materials. In FBs, pairings and superfluid weight scale linearly with the interaction parameter, such an unusual behaviour justifies and encourages strategies to promote FB engineering. Bipartite lattices (BLs) which naturally host FBs could be particularly interesting candidates. Within Bogoliubov de Gennes theory and in the framework of the attractive Hubbard model in BLs, a hidden symmetry of the quasi-particle eigenstates is revealed. As a consequence, we demonstrate universal relations for the pairings and the superfluid weight that are independent of the characteristics of the hopping term. Remarkably, it is shown that these general properties are insensitive to disorder as long as the bipartite character is protected.

Phase diagram and critical behavior of the Hubbard model on the square-hexagon-octagon lattice

Phase diagram and critical behavior of the Hubbard model on the square-hexagon-octagon lattice

Antiferromagnetically ordered topological semimetals in Hubbard model with spin-orbit coupling

We examine the possible existence of Dirac semimetal with magnetic order in a two-dimensional system with a nonsymmorphic symmetry by using the Hartree–Fock mean-field theory within the Hubbard model. We locate the region in the second-neighbor spin–orbit coupling vs Hubbard interaction phase diagram, where such a state is stabilized. The edge states for the ribbons along two orthogonal directions concerning the orientation of in-plane magnetic moments are obtained. Finally, the effect of the in-plane magnetic field, which results in the stabilization of the Weyl semimetallic (WSM) state, and the nature of the edge states corresponding to the WSM state for ribbon geometries are also explored.

Spin correlations in the bilayer Hubbard model with perpendicular electric field

Spin correlations in the bilayer Hubbard model with perpendicular electric field

Bethe ansatz solutions of the 1D extended Hubbard-model

We construct an integrable 1D extended Hubbard model within the framework of the quantum inverse scattering method. With the help of the nested algebraic Bethe ansatz method, the eigenvalue Hamiltonian problem is solved by a set of Bethe ansatz equations, whose solutions are supposed to give the correct energy spectrum.

Half-filled extended Hubbard model on a square lattice: Phase boundaries from determinant quantum Monte Carlo simulations

Half-filled extended Hubbard model on a square lattice: Phase boundaries from determinant quantum Monte Carlo simulations

Ubiquitous light real-space pairing from long-range hopping and interactions

We systematically examine how long-range hopping and its synergy with extended interactions leads to light bound pairs. Pair properties are determined for a dilute extended Hubbard model with large on-site repulsion (U) and both near- and next-nearest neighbour hopping (t and t′) and attraction (V and V′), for cubic and tetragonal lattices. The presence of t′ and V′ promotes light pairs. For tetragonal lattices, t′<0 pairs can be lighter than non-interacting particles, and d-symmetric pairs form. Close packing transition temperatures, T⁎ are estimated for the Bose-Einstein condensation (BEC) of pairs to be kBT⁎∼t‾0.1, where t‾ is the geometric mean of the hoppings on the Cartesian axes. When pairs have d-symmetry, the condensate has d-wave character. Thus, the presence of both t′ and V′ leads ubiquitously to small strongly bound pairs with an inverse mass that is linear in hopping, which could lead to high temperature BECs.

Revisiting pairing of bosons in one-dimensional Bose–Hubbard model with three-body interaction using CMFT+DMRG method

Revisiting pairing of bosons in one-dimensional Bose–Hubbard model with three-body interaction using CMFT+DMRG method

Magnetic supersolid phases of two-dimensional extended Bose–Hubbard model with spin–orbit coupling

We investigate the quantum phases and phase transitions for spin–orbit coupled two-species bosons with nearest-neighbor (NN) interaction in a two-dimensional square lattice using inhomogeneous dynamical Guztwiller mean-field method. Under the effect of spin–orbit coupling and NN interaction, we uncover a rich variety of different magnetic supersolid (SS) phases. In the presence of intraspecies NN interaction, the phase diagram exhibits the phase-twisted double-checkerboard SS (PT-DCSS) and phase-striped double-checkerboard SS (PS-DCSS) phases. For both intra- and interspecies NN interactions, apart from the phase-twisted lattice SS (PT-LSS) and phase-striped lattice SS (PS-LSS) phases, some nontrivial SS phases with interesting properties occur. More importantly, we find that the emergences of these nontrivial SS phases are dependent of the interspecies on-site interaction. To further characterize the SS phases, we also discuss the spin-dependent momentum distributions and magnetic textures. The magnetic textures, such as antiferromagnetic, spiral and stripe orders are shown. Finally, we give the fully analytical insights into the numerical results.

Bands renormalization and superconductivity in the strongly correlated Hubbard model using composite operators method

We use the composite operator method (COM) to analyze the strongly correlated repulsive Hubbard model, investigating the effect of nearest-neighbor hoppings up to fourth order on a square lattice. We consider two sets of self-consistent equations, one enforcing the Pauli principle and the other imposing charge-charge, spin-spin, and pair–pair correlations using a decoupling scheme developed by Roth (1969 Phys. Rev. 184 451–9). We extract three distinct solutions from these equations: COM1 and COM2 by imposing the Pauli principle and one from Roth decoupling. An overview of the method studying the validity of particle-hole symmetry and the Luttinger theorem for each solution is presented. Additionally, we extend the initial basis to study superconductivity, concluding that it is induced by the Van Hove singularity. Finally, we include higher-order hoppings using realistic estimates for tight binding parameters and compare our results with ARPES measurements on cuprates.

Exploring kinetically induced bound states in triangular lattices with ultracold atoms: Spectroscopic approach

Quantum simulations with ultracold fermions in triangular optical lattices have recently emerged as a new platform for studying magnetism in frustrated systems. Experimental realizations of the Fermi Hubbard model revealed striking contrast between magnetism in bipartite and triangular lattices. In bipartite lattices magnetism is strongest at half filling, and doped charge carriers tend to suppress magnetic correlations. In triangular-type lattices for large U/t and t&gt;0, antiferromagnetism (ferromagnetism) gets enhanced by doping away from n=1 with holes (doublons) because kinetic energy of dopants can be lowered through developing magnetic correlations, corresponding to formation of magnetic polarons. Snapshots of many-body states obtained with quantum gas microscopes demonstrated existence of magnetic polarons by revealing the magnetic correlations around dopants at temperatures that considerably exceed superexchange energy scale. In this paper we discuss theoretically that additional insight into properties of magnetic polarons in triangular lattices can be achieved using spectroscopic experiments with ultracold atoms. We consider starting from a spin polarized state with small hole doping and applying a two-photon Raman photoexcitation, which transfers atoms into a different spin state. We show that such magnon injection spectra exhibit a separate peak corresponding to formation of a bound state between a hole and a magnon. This polaron peak is separated from the simple magnon spectrum by energy proportional to single particle tunneling and can be easily resolved with currently available experimental techniques. For some momentum transfer there is an additional peak corresponding to photoexciting a bound state between two holes and a magnon. We point out that in two component Bose mixtures in triangular lattices one can also create dynamical magnetic polarons, with one hole and one magnon forming a repulsive bound state.

A tight-binding model for illustrating exciton confinement in semiconductor nanocrystals.

The Brus equation describes the relation between the lowest energy of an electron-hole pair and the size of a semiconductor crystallite. However, taking the strong confinement regime as a starting point, the equation does not cover the transition from weak to strong confinement, the accompanying phenomenon of charge-carrier delocalization, or the change in the transition dipole moment of the electron-hole pair state. Here, we use a one-dimensional, two-particle Hubbard model for interacting electron-hole pairs that extends the well-known tight-binding approach through a point-like electron-hole interaction. On infinite chains, the resulting exciton states exhibit the known relation between the Bohr radius, the exciton binding energy, and the effective mass of the charge carriers. Moreover, by introducing infinite-well boundary conditions, the model enables the transition of the exciton states from weak to strong confinement to be tracked, while straightforward adaptations provide insights into the relation between defects, exciton localization, and confinement. In addition, by introducing the dipole operator, the variation of the transition dipole moment can be mapped when shifting from electron-hole pairs in strong confinement to delocalized and localized excitons in weak confinement. The proposed model system can be readily implemented and extended to different multi-carrier states, thus providing researchers a tool for exploring, understanding, and teaching confinement effects in semiconductor nanocrystals under different conditions.

Kekulé valence bond order in the Hubbard model on the honeycomb lattice with possible lattice distortions for graphene

Kekulé valence bond order in the Hubbard model on the honeycomb lattice with possible lattice distortions for graphene

Excitonic enhancement of cavity-mediated interactions in a two-band Hubbard model

Excitonic enhancement of cavity-mediated interactions in a two-band Hubbard model

Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moiré WS2/WSe2 heterobilayer

Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a WS2/WSe2 heterobilayer device that hosts this hybrid particle density. We independently tune the fermionic and bosonic populations by electronic doping and optical injection of electron-hole pairs, respectively. This enables us to form strongly interacting excitons that are manifested in a large energy gap in the photoluminescence spectrum. The incompressibility of excitons is further corroborated by observing a suppression of exciton diffusion with increasing pump intensity, as opposed to the expected behavior of a weakly interacting gas of bosons, suggesting the formation of a bosonic Mott insulator. We explain our observations using a two-band model including phase space filling. Our system provides a controllable approach to the exploration of quantum many-body effects in the generalized Bose-Fermi-Hubbard model.

Stabilization of Hubbard-Thouless pumps through nonlocal fermionic repulsion

Thouless pumping represents a powerful concept to probe quantized topological invariants in quantum systems. We explore this mechanism in a generalized Rice-Mele Fermi-Hubbard model characterized by the presence of competing onsite and intersite interactions. Contrary to recent experimental and theoretical results, showing a breakdown of quantized pumping induced by the onsite repulsion, we prove that sufficiently large intersite interactions allow for an interaction-induced recovery of Thouless pumps. Our analysis further reveals that the occurrence of stable topological transport at large interactions is connected to the presence of a spontaneous bond-order-wave in the ground-state phase diagram of the model. Finally, we discuss a concrete experimental setup based on ultracold magnetic atoms in an optical lattice to realize the newly introduced Thouless pump. Our results provide a new mechanism to stabilize Thouless pumps in interacting quantum systems.

Non-Hermitian Strongly Interacting Dirac Fermions.

Exotic quantum phases and phase transition in the strongly interacting Dirac systems have attracted tremendous interests. On the other hand, non-Hermitian physics, usually associated with dissipation arising from the coupling to environment, emerges as a frontier of modern physics in recent years. In this Letter, we investigate the interplay between non-Hermitian physics and strong correlation in Dirac-fermion systems. We generalize the projector quantum Monte-Carlo (PQMC) algorithm to the non-Hermitian interacting fermionic systems. Employing PQMC simulation, we decipher the ground-state phase diagram of the honeycomb Hubbard model with spin resolved non-Hermitian asymmetric hopping processes. The antiferromagnetic (AFM) ordering induced by Hubbard interaction is enhanced by the non-Hermitian asymmetric hopping. Combining PQMC simulation and renormalization group analysis, we reveal that the quantum phase transition between Dirac semi-metal and AFM phases belongs to Hermitian chiral XY universality class, implying that a Hermitian Gross-Neveu transition is emergent at the quantum critical point although the model is non-Hermitian.

Flat band and $\eta $-pairing states in one-dimensional Moiré Hubbard model

Abstract A moiré system is formed when two periodic structures have a slightly mismatched period, resulting in unusual strongly correlated states in the presence of particle-particle interactions. The periodic structures can arise from the intrinsic crystalline order and periodic external field. We investigate a one-dimensional Hubbard models with periodic on-site potential of period $n_{0}$, which is commensurate to the lattice constant. For large $% n_{0}$, exact solution demonstrates that there is a midgap flat band with zero energy in the absence of Hubbard interaction. Each moiré unit cell contributes two zero energy levels to the flat band. In the presence of Hubbard interaction, the midgap physics is demonstrated to be well described by a uniform Hubbard chain, in which the effective hopping and on-site interaction strength, can be controlled by the amplitude and period of the external field. Numerical simulations are performed to demonstrate the correlated behaviors in the finite-sized moiré Hubbard system, including the existence of $\eta $-pairing state, and bound pair oscillation. This finding provides a method to enhance the correlated effect by a spatially periodic external field.

Possible High T_{c} Superconductivity in La_{3}Ni_{2}O_{7} under High Pressure through Manifestation of a Nearly Half-Filled Bilayer Hubbard Model.

Inspired by a recent experiment showing that La_{3}Ni_{2}O_{7} exhibits high T_{c} superconductivity under high pressure, we theoretically revisit the possibility of superconductivity in this material. We find that superconductivity can take place, which is somewhat similar to that of the bilayer Hubbard model consisting of the Ni 3d_{3z^{2}-r^{2}} orbitals. Although the coupling with the 3d_{x^{2}-y^{2}} orbitals degrades superconductivity, T_{c} can still be high enough to understand the experiment thanks to the very high T_{c} reached in the bilayer Hubbard model.