Hubbard Model Research Articles

Effects of Magnetic Fields and Orbital Angular Momentum on Excitonic Condensation in Two-Orbital Hubbard Model

Effects of Magnetic Fields and Orbital Angular Momentum on Excitonic Condensation in Two-Orbital Hubbard Model

Coexistence of superconductivity with partially filled stripes in the Hubbard model

The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature ( T c ) superconductivity.

Observation of Nagaoka polarons in a Fermi-Hubbard quantum simulator.

Quantum interference can deeply alter the nature of many-body phases of matter1. In the case of the Hubbard model, Nagaoka proved that introducing a single itinerant charge can transform a paramagnetic insulator into a ferromagnet through path interference2-4. However, amicroscopic observation of this kinetic magnetism induced by individually imaged dopants has been so far elusive. Here we demonstrate the emergence of Nagaoka polarons in a Hubbard system realized with strongly interacting fermions in a triangular optical lattice5,6. Using quantum gas microscopy, we image these polarons asextended ferromagnetic bubbles around particle dopants arising from the local interplay of coherent dopant motion and spin exchange. By contrast, kinetic frustration due to the triangular geometry promotes antiferromagnetic polarons around hole dopants7. Our work augurs the exploration of exotic quantum phases driven by charge motion in strongly correlated systems and over sizes that are challenging for numerical simulation8-10.

Disentangling the physics of the attractive Hubbard model as a fully interacting model of fermions via the accessible and symmetry-resolved entanglement entropies

Disentangling the physics of the attractive Hubbard model as a fully interacting model of fermions via the accessible and symmetry-resolved entanglement entropies

Tensor Renormalization Group for fermions.

We review the basic ideas of the Tensor Renormalization Group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. 
We discuss recent progress for entanglement filtering, 
loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson--Majorana fermions and multi-flavor 
Gross--Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

Insulating-to-conducting state transition in the bilayer Hubbard model induced by a perpendicular quench field

A many-body quantum system with varying parameters can exhibit two distinct quantum states within the same energy shell. This allows for a dynamic transition from the ground state of the pre-quench Hamiltonian to a steady state of the post-quench Hamiltonian. We investigate the dynamic response of the ground states in a two-layer half-filled Hubbard model to a perpendicular electric field. We demonstrate that the steady state exhibits conductivity when the field is in resonance with the on-site repulsion, while the initial state is a Mott-insulating state. Additionally, the two layers exhibit identical conducting behavior due to the formation of long-lived dopings, as evidenced by the charge fluctuation. The key factor in achieving this dynamic transition is the cooperative interplay between on-site interactions and the resonant field, rather than the individual roles they play. Our findings offer an alternative mechanism for field-induced conductivity in strongly correlated systems.

Unconventional superconductivity and charge ordering in an extended ionic Hubbard model on the triangular lattice

To address the issues of superconducting and charge properties in hydrated sodium cobalt, we investigate an extended ionic Hubbard model on the triangular lattice, which includes off-site attractions between sites with minor charges. Our quantum Monte Carlo simulations show that close to quarter filling, the off-site attractions induce a significant enhancement of d-wave and extended s-wave pairing correlations. Simultaneously, they render an increase of the charge structure factor at most of wave vectors. A combination with charge correlations in real space indicates the development of short-range finite-q charge density waves on the sites with minor charges. Our findings provide a new perspective on the superconducting mechanism in hydrated sodium cobalt based on the electronic structure which explicitly takes the effect of sodium atoms into account.

Long-Range Effects in Topologically Defective Arm-Chair Graphene Nanoribbons.

The electronic structure of 7/9-AGNR superlattices with up to eight unit cells has been studied by means of state-of-the-art Density Functional Theory (DFT) and also by two model Hamiltonians, the first one including only local interactions (Hubbard model, Hu) while the second one is extended to allow long-range Coulomb interactions (Pariser, Parr and Pople model, PPP). Both are solved within mean field approximation. At this approximation level, our calculations show that 7/9 interfaces are better described by spin non-polarized solutions than by spin-polarized wavefunctions. Consequently, both Hu and PPP Hamiltonians lead to electronic structures characterized by a gap at the Fermi level that diminishes as the size of the system increases. DFT results show similar trends although a detailed analysis of the density of states around the Fermi level shows quantitative differences with both Hu and PPP models. Before improving model Hamiltonians, we interpret the electronic structure obtained by DFT in terms of bands of topological states: topological states localized at the system edges and extended bulk topological states that interact between them due to the long-range Coulomb terms of Hamiltonian. After careful analysis of the interaction among topological states, we find that the discrepancy between ab initio and model Hamiltonians can be resolved considering a screened long-range interaction that is implemented by adding an exponential cutoff to the interaction term of the PPP model. In this way, an adjusted cutoff distance λ=2 allows a good recovery of DFT results. In view of this, we conclude that the correct description of the density of states around the Fermi level (Dirac point) needs the inclusion of long-range interactions well beyond the Hubbard model but not completely unscreened as is the case for the PPP model.

Low-depth simulations of fermionic systems on square-grid quantum hardware

We present a general strategy for mapping fermionic systems to quantum hardware with square qubit connectivity which yields low-depth quantum circuits, counted in the number of native two-qubit fSIM gates. We achieve this by leveraging novel operator decomposition and circuit compression techniques paired with specifically chosen low-depth fermion-to-qubit mappings and allow for a high degree of gate cancellations and parallelism. Our mappings retain the flexibility to simultaneously optimize for qubit counts or qubit operator weights and can be used to investigate arbitrary fermionic lattice geometries. We showcase our approach by investigating the tight-binding model, the Fermi-Hubbard model as well as the multi-orbital Hubbard-Kanamori model. We report unprecedentedly low circuit depths per single Trotter layer with up to a 70% improvement upon previous state-of-the-art. Our compression technique also results in significant reduction of two-qubit gates. We find the lowest gate-counts when applying the XYZ-formalism to the DK mapping. Additionally, we show that our decomposition and compression formalism produces favourable circuits even when no native parameterized two-qubit gates are available.

Origins of multi-sublattice magnetism and superexchange interactions in double–double perovskite CaMnCrSbO6

The multi-sublattice magnetism and electronic structure in double–double perovskite compound CaMnCrSbO6 is explored using density functional theory. The bulk magnetization and neutron diffraction suggest a ferrimagnetic order ( TC∼ 49 K) between between Mn2+ and Cr3+ spins. Due to the non-equivalent Mn atoms (labelled as Mn(1) and Mn(2) which have tetrahedral and planar oxygen coordinations, respectively) and the Cr atom in the centre of distorted oxygen octahedron in the unit cell, the exchange interactions are more complex than that expected from a two sublattice magnetic system. The separations between the on-site energies of the d-orbitals of Mn(1), Mn(2) and Cr obtained from Wannier function analysis are in agreement with their expected crystal field splitting. While the DOS obtained from non spin-polarized calculations show a metallic character, starting from Hubbard U = 0 eV the spin-polarized electronic structure calculations yield a ferrimagnetic insulating ground state. The band gap increases with Ueff (U − J), thereby showing a Mott–Hubbard nature of the system. The inclusion of anti-site disorder in the calculations show decrease in band-gap and also reduction in the total magnetic moment. Due to the ∼90∘ superexchange, nearest neighbour exchange constants obtained from DFT are an order of magnitude smaller than those reported for various magnetic perovskite and double-perovskite compounds. The Mn(1)–O–Mn(2) (out of plane and in-plane), Mn(1)–O–Cr and Mn(2)–O–Cr superexchange interactions are found to be anti-ferromagnetic, while the Cr–O–O–Cr super-superexchange is found to be ferromagnetic. The Mn(2)–O–Cr superexchange is weaker than the Mn(1)–O–Cr super-exchange, thus effectively resulting in ferrimagnetism. From a simple 3-site Hubbard model, we derived expressions for the antiferromagnetic superexchange strength JAFM and also for the weaker ferromagnetic JFM . The relative strengths of JAFM for the various superexchange interactions are in agreement with those obtained from DFT. The expression for Cr–O–O–Cr super-superexchange strength ( J~SS ), which has been derived considering a 4-site Hubbard model, predicts a ferromagnetic exchange in agreement with DFT. Finally, our mean field calculations reveal that assuming a set of four magnetic sub-lattices for Mn2+ spins and a single magnetic sublattice for Cr3+ spins yields a much improved T C , while a simple two magnetic sublattice model yields a much higher T C .

Hunting for quantum-classical crossover in condensed matter problems

The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question of when and how will quantum computers outperform classical computers. The next milestone is undoubtedly the realization of quantum acceleration in practical problems. Here we provide a clear evidence and arguments that the primary target is likely to be condensed matter physics. Our primary contributions are summarized as follows: 1) Proposal of systematic error/runtime analysis on state-of-the-art classical algorithm based on tensor networks; 2) Dedicated and high-resolution analysis on quantum resource performed at the level of executable logical instructions; 3) Clarification of quantum-classical crosspoint for ground-state simulation to be within runtime of hours using only a few hundreds of thousand physical qubits for 2d Heisenberg and 2d Fermi-Hubbard models, assuming that logical qubits are encoded via the surface code with the physical error rate of p = 10−3. To our knowledge, we argue that condensed matter problems offer the earliest platform for demonstration of practical quantum advantage that is order-of-magnitude more feasible than ever known candidates, in terms of both qubit counts and total runtime.

Effect of next-nearest neighbor hopping on the single-particle excitations at finite temperature

In the half-filled one-orbital Hubbard model on a square lattice, we study the effect of next-nearest neighbor hopping on the single-particle spectral function at finite temperature using an exact-diagonalization + Monte-Carlo based approach to the simulation process. We find that the pseudogap-like dip, existing in the density of states in between the Néel temperature T_NTN and a relatively higher temperature scale T^*T*, is accompanied with a significant asymmetry in the hole- and particle-excitation energy along the high-symmetry directions as well as along the normal-state Fermi surface. On moving from (\pi/2, \pi/2π/2,π/2) toward (\pi, 0)(π,0) along the normal state Fermi surface, the hole-excitation energy increases, a behavior remarkably similar to what is observed in the dd-wave state and pseudogap phase of high-T_cTc cuprates, whereas the particle-excitation energy decreases. The quasiparticle peak height is the largest near (\pi/2, \pi/2π/2,π/2) whereas it is the smallest near (\pi, 0)(π,0). These spectral features survive beyond T_NTN. The temperature window T_N ≲ T ≲ T^*TN≲T≲T* shrinks with an increase in the next-nearest neighbor hopping, which indicates that the next-nearest neighbor hopping may not be supportive to the pseudogap-like features.

High-Density, Nonvolatile, Flexible Multilevel Organic Memristor Using Multilayered Polymer Semiconductors.

Nonvolatile organic memristors have emerged as promising candidates for next-generation electronics, emphasizing the need for vertical device fabrication to attain a high density. Herein, we present a comprehensive investigation of high-performance organic memristors, fabricated in crossbar architecture with PTB7/Al-AlOx-nanocluster/PTB7 embedded between Al electrodes. PTB7 films were fabricated using the Unidirectional Floating Film Transfer Method, enabling independent uniform film fabrication in the Layer-by-Layer (LbL) configuration without disturbing underlying films. We examined the charge transport mechanism of our memristors using the Hubbard model highlighting the role of Al-AlOx-nanoclusters in switching-on the devices, due to the accumulation of bipolarons in the semiconducting layer. By varying the number of LbL films in the device architecture, the resistance of resistive states was systematically altered, enabling the fabrication of novel multilevel memristors. These multilevel devices exhibited excellent performance metrics, including enhanced memory density, high on-off ratio (>108), remarkable memory retention (>105 s), high endurance (87 on-off cycles), and rapid switching (∼100 ns). Furthermore, flexible memristors were fabricated, demonstrating consistent performance even under bending conditions, with a radius of 2.78 mm for >104 bending cycles. This study not only demonstrates the fundamental understanding of charge transport in organic memristors but also introduces novel device architectures with significant implications for high-density flexible applications.

Stark Many-Body Localization in Interacting Infinite Dimensional Systems.

We study bulk particle transport in a Fermi-Hubbard model on an infinite-dimensional Bethe lattice, driven by a constant electric field. Previous numerical studies showed that one dimensional analogs of this system exhibit a breakdown of diffusion due to Stark many-body localization at least up to time that scales exponentially with the system size. Here, we consider systems initially in a spin density wave state using a combination of numerically exact and approximate techniques. We show that for sufficiently weak electric fields, the wave's momentum component decays exponentially with time in a way consistent with normal diffusion. By studying different wavelengths, we extract the dynamical exponent and the generalized diffusion coefficient at each field strength. Interestingly, we find a nonmonotonic dependence of the dynamical exponent on the electric field. As the field increases toward a critical value proportional to the Hubbard interaction strength, transport slows down, becoming subdiffusive. At large interaction strengths, however, transport speeds up again with increasing field, exhibiting superdiffusive characteristics when the electric field is comparable to the interaction strength. Eventually, at the large field limit, localization occurs and the current through the system is suppressed.

Selected Nonorthogonal Configuration Interaction with Compressed Single and Double Excitations.

Addressing both dynamic and static correlations accurately is a primary goal in electronic structure theory. Nonorthogonal configuration interaction (NOCI) is a versatile tool for treating static correlation, offering chemical insights by combining diverse reference states. Nevertheless, achieving quantitative accuracy requires the inclusion of the missing dynamic correlation. This work introduces a framework for compressing orthogonal single and double excitations into a NOCI of a much smaller dimension. This compression is repeated with each Slater determinant in a reference NOCI, resulting in another NOCI that includes all of its single and double excitations (NOCISD), effectively recovering the missing dynamic correlations from the reference. This compressed NOCISD is further refined through a selection process using metric and energy tests (SNOCISD). We validate the effectiveness of SNOCISD through its application to the dissociation of the nitrogen molecule and the hole-doped two-dimensional Hubbard model at various interaction strengths.

Dynamics of the atom-polyatomic molecule conversion with quantum decoherence

Based on the mean-field approximation and the two-mode Bose–Hubbard model, we investigate the dynamical properties of atom-polyatomic molecule conversion systems under dissipation and dephasing. For such a many-body system problem, we partition phase space based on the states of fixed points, study the movement of fixed points and the transition to attractors in an open system. Additionally, for all the atoms that constitute a molecule, depending on whether the species of these atoms are identical or not, we introduce the innovative concepts of unbiased and biased systems. We discover that in biased conversion systems under particle losses, the evolution trajectories are distributed on a three-dimensional Bloch sphere with an internal structure. There exists a significant difference from the two-dimensional Hilbert space of an unbiased system. Finally, we discuss the sweeping rate of the time-varying magnetic field applied externally to the conversion system, and analyze a feasible scheme for the quantum coherent synthesis of triatomic molecules.

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

Exact Diagonalization of SU(N) Fermi-Hubbard Models.

We show how to perform exact diagonalizations of SU(N) Fermi-Hubbard models on L-site clusters separately in each irreducible representation (irrep) of SU(N). Using the representation theory of the unitary group U(L), we demonstrate that a convenient orthonormal basis, on which matrix elements of the Hamiltonian are very simple, is given by the set of semistandard Young tableaux (or, equivalently, the Gelfand-Tsetlin patterns) corresponding to the targeted irrep. As an application of this color factorization, we study the robustness of some SU(N) phases predicted in the Heisenberg limit upon decreasing the on-site interaction U on various lattices of size L≤12 and for 2≤N≤6. In particular, we show that a long-range color ordered phase emerges for intermediate U for N=4 at filling 1/4 on the triangular lattice.

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