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Results for “Extended Hubbard model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems

The generalized Wigner crystal (GWC) is a novel quantum phase of matter driven by further-range interaction at fractional fillings of a lattice. The role of further-range interaction as the driver for the incompressible state is akin to the Wigner crystal. On the other hand, the significant role of commensurate filling is akin to the Mott insulator. Recent progress in simulator platforms presents unprecedented opportunities to investigate quantum melting in the strongly interacting regime through synergy between theory and experiments. However, the earlier theory literature presents diverging predictions. We study the quantum freezing of GWC through large-scale density matrix renormalization group simulations of a triangular lattice extended Hubbard model. We find a single first-order phase transition between the Fermi liquid and the √3×√3 GWC state. Furthermore, the GWC state shows long-range antiferromagnetic 120° Néel order. Our results present the simplest answers to the question of the quantum phase transition into the GWC phase and the properties of the GWC phase.

Density matrix renormalization group↗
DOE OSTI2024

Extracting off-diagonal order from diagonal basis measurements

Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multiscale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments. Published by the American Physical Society 2024

1-dimensional systems↗
DOE OSTI2024

Spin transport of a doped Mott insulator in moiré heterostructures

Moiré superlattices of semiconducting transition metal dichalcogenide heterobilayers are model systems for investigating strongly correlated electronic phenomena. Specifically, WSe 2 /WS 2 moiré superlattices have emerged as a quantum simulator for the two-dimensional extended Hubbard model. Experimental studies of charge transport have revealed correlated Mott insulator and generalized Wigner crystal states, but spin transport of the moiré heterostructure has not yet been sufficiently explored. Here, we use spatially and temporally resolved circular dichroism spectroscopy to directly image the spin transport as a function of carrier doping and temperature in WSe 2 /WS 2 moiré heterostructures. We observe diffusive spin transport at all hole concentrations at 11 Kelvin — including the Mott insulator at one hole per moiré unit cell — where charge transport is strongly suppressed. At elevated temperatures the spin diffusion constant remains unchanged in the Mott insulator state, but it increases significantly at finite doping away from the Mott state. The doping- and temperature-dependent spin transport can be qualitatively understood using a t–J model, where spins can move via the hopping of spin-carrying charges and via the exchange interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Improving Spectral Resolution from Real-time Evolution for Correlated Systems

Abstract The quality of numerically simulated spectra using real-time evolution methods for strongly correlated systems is affected by both the length of simulation time and the system size, limiting resolution in both frequency and momentum. In this work, we propose a computationally cheap, linear autoregressive machine learning-based framework to extend short-time and short-distance results over a wider range. We use the proposed method to extend the lesser Green’s function for both the Hubbard model and the much more computationally challenging Hubbard-extended Holstein model. This technique significantly improves both the frequency and momentum resolution of the single-particle removal spectrum $${\mathcal{A}}(k,\omega )$$ A ( k , ω ) , allowing the observation of otherwise obscured spectral features due to electron-phonon coupling.

Tang, Ta↗
DOE OSTI2024

Luther-Emery liquid and dominant singlet superconductivity in the hole-doped Haldane spin-1 chain

We investigate the pairing tendencies in the hole-doped Haldane spin-1 chain. To allow for doping, we extend the original spin chain Hamiltonian into a fermionic model involving a two-orbital Hubbard chain at intermediate or strong repulsive interaction strengths U and for degenerate orbitals. At half filling and large U, the ferromagnetic Hund's coupling, J H , generates effective spin-1 moments, with antiferromagnetic correlations between sites. Using large-scale density matrix renormalization group calculations, we accurately study the system's behavior under light hole-doping. For U = 1.6 in units of the noninteracting bandwidth and for J H /U ≳ 0.275, we find that singlet pairing dominates the long-distance physics, establishing this system as a promising platform for repulsively mediated superconductivity. We provide concrete examples of materials that could realize the physics described here. We also provide evidence that the system approaches a Luther-Emery liquid state at large system sizes, reminiscent of the behavior of doped one-orbital two-leg ladders at weak coupling, which also have superconducting tendencies. The numerically calculated central charge approaches one in the thermodynamic limit, indicating a single gapless mode as is expected for the Luther-Emery state. Exponents characterizing the power-law decays of singlet pair-pair and charge density-density correlations are determined, and found to approximately satisfy the Luther-Emery identity.

1-dimensional systems↗
DOE OSTI2025

Particle-hole asymmetric phases in doped twisted bilayer graphene

Twisted bilayer graphene (TBG) has emerged as a paradigmatic platform for exploring the interplay between strong interactions in a multi-band system with nearly flat bands, while offering unprecedented control over the filling fraction of electron/hole carriers. Despite much theoretical work, developing a comprehensive ab initio model for this system has proven challenging due to the inherent trade-off between accurately describing the band structure and incorporating the interactions within the Hamiltonian. Here, we constructed an extended multi-orbital Hubbard model, and performed Hartree-Fock (HF) calculations to explore its phase diagram across commensurate fillings. We found several nearly-degenerate insulating states at charge neutrality, all of which exhibit orbital orders. We also observed that most of the Hartree–Fock ground states exhibit a generalized valley Hund’s-like rule, resulting in valley polarization. Importantly, we show that the incorporation of the intra-valley and inter-valley exchange interactions is crucial to properly stabilize the ordered symmetry-broken states. In agreement with experiments, we find significant particle-hole asymmetry, which underscores the importance of using particle-hole asymmetric models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Quantum utility in simulating the real-time dynamics of the Fermi–Hubbard model using superconducting quantum computers

The Fermi–Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi–Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi–Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi–Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Lastly, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Exploring thermal equilibria of the Fermi-Hubbard model with variational quantum algorithms

Here, this study investigates the thermal properties of the repulsive Fermi-Hubbard model with chemical potential using variational quantum algorithms, crucial in comprehending particle behaviour within lattices at heightened temperatures in condensed matter systems. Conventional computational methods encounter challenges, especially in managing chemical potential, prompting exploration into Hamiltonian approaches. Despite the promise of quantum algorithms, their efficacy is hampered by coherence limitations when simulating extended imaginary time evolution sequences. To overcome these constraints, this research focuses on optimizing variational quantum algorithms to probe the thermal properties of the Fermi-Hubbard model. Physics-inspired circuit designs are tailored to alleviate coherence constraints, facilitating a more comprehensive exploration of materials at elevated temperatures. Our study demonstrates the potential of variational algorithms in simulating the thermal properties of the Fermi-Hubbard model while acknowledging limitations stemming from error sources in quantum devices and encountering barren plateaus.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Transformer-based operator learning framework for self-energy in strongly correlated systems

We introduce Σ-Attention, a transformer-based operator-learning framework for approximating the self-energy operator of strongly correlated electronic systems. By creating a batched dataset that combines results from three complementary approaches, i.e., many-body perturbation theory, strong-coupling expansion, and exact diagonalization, each effective in specific parameter regimes, Σ-Attention is applied to learn an accurate approximation for the self-energy operator that is valid across a wide range of parameter regimes. This hybrid strategy leverages the strengths of existing methods while relying on the transformer's ability to generalize beyond individual limitations. More importantly, the scalability of the transformer architecture allows the learned self-energy to be extended to systems with larger sizes, leading to much improved computational scaling. Using the one-dimensional Hubbard model, we demonstrate that Σ-Attention can accurately predict the Matsubara Green's function of large systems with a wide range of coupling strength. Our framework offers a promising and scalable pathway for studying strongly correlated systems with many possible generalizations.

Zhu, Yuanran↗
DOE OSTI2024

Localization in Energy Materials (Final Project Report)

The last year of this award we have continued our research on using quantum machine learning to identify phase transitions. By combining quantum machine learning with quantum computing, we extended a hybrid classical-quantum algorithm to capture the metal-insulator quantum phase transition of the Hubbard model. We have also continued our studies of non-equilibrium dynamics of interacting disordered systems. In particular, we studied the non-equilibrium transient dynamics of a system described by the Anderson-Hubbard model following an interaction and disorder quench, and the effect of disorder on the out-of-time-order correlator on the Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Auxiliary field Quantum Monte Carlo for dilute neutrons on the lattice

We employ constrained path Auxiliary Field Quantum Monte Carlo (AFQMC) in the pursuit of studying physical nuclear systems using a lattice formalism. Since AFQMC has been widely used in the study of condensed-matter systems such as the Hubbard model, we benchmark our method against published results for both one- and two-dimensional Hubbard model calculations. We then turn our attention to cold atomic and nuclear systems. We use an onsite contact interaction that can be tuned in order to reproduce the known scattering length and effective range of a given interaction. Developing this machinery allows us to extend our calculations to study nuclear systems within a lattice formalism. In conclusion, we perform initial calculations for a range of nuclear systems from two- to few-body neutron systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Influence of extended interactions on spin dynamics in one-dimensional cuprates

Quasi-one-dimensional (1D) materials provide a unique platform for understanding the importance and influence of extended interactions on the physics of strongly correlated systems due to their relative structural simplicity and the existence of powerful theoretical tools well-adapted to one spatial dimension. Recently, this was highlighted by anomalous observations in the single-particle spectral function A(q, ω) of 1D cuprate chain compounds, measured by angle-resolved photoemission spectroscopy (ARPES), which were explained by the presence of a long-range attractive interaction. Such an extended interaction should leave its fingerprints on other observables, notably the dynamical spin structure factor S(q, ω), measured by neutron scattering or resonant inelastic x-ray scattering (RIXS). Starting from a simple Hubbard Hamiltonian in 1D and using time-dependent density matrix renormalization group (tDMRG) methods, we show that the presence of long-range attractive coupling, directly through an instantaneous Coulomb interaction V or retarded electron phonon (el-ph) coupling, can introduce significant spectral weight redistribution in S(q, ω) across a wide range of doping. Here, this underscores the significant impact that extended interactions can have on dynamical correlations among particles, and the importance of properly incorporating this influence in modeling. Our results demonstrate that S(q, ω) can provide a sensitive experimental constraint, which complements ARPES measurements, in identifying key interactions in 1D cuprates, beyond the standard Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Global phase diagram of D-wave superconductivity in the square-lattice t-J model

The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.

Chen, Feng (ORCID:000000018196030X)↗
DOE OSTI2025

A resonant valence bond spin liquid in the dilute limit of doped frustrated Mott insulators

Abstract Ideas about resonant valence bond liquids and spin–charge separation have led to key concepts in physics such as quantum spin liquids, emergent gauge symmetries, topological order and fractionalization. Despite extensive efforts to demonstrate the existence of a resonant valence bond phase in the Hubbard model that originally motivated the concept, a definitive realization has yet to be achieved. Here we present a solution to this long-standing problem by uncovering a resonant valence bond phase exhibiting spin–charge separation in realistic Hamiltonians. We show analytically that this ground state emerges in the dilute-doping limit of a half-filled Mott insulator on corner-sharing tetrahedral lattices with frustrated hopping, in the absence of exchange interactions. We confirm numerically that the results extend to finite exchange interactions, finite-sized systems and finite dopant density. Although much attention has been devoted to the emergence of unconventional states from geometrically frustrated interactions, our work demonstrates that kinetic energy frustration in doped Mott insulators may be essential for stabilizing robust, topologically ordered states in real materials.

Physics↗
DOE OSTI2025

Almost strong zero modes at finite temperature

Interacting fermionic chains exhibit extended regions of topological degeneracy of their ground states as a result of the presence of Majorana or parafermionic zero modes localized at the edges. In the opposite limit of infinite temperature, the corresponding nonintegrable spin chains, obtained via generalized Jordan-Wigner mapping, are known to host so-called almost strong zero modes, which are long-lived with respect to any bulk excitations. Here we study the fairly unexplored territory that bridges these two extreme cases of zero and infinite temperature. We blend two established techniques for states, the Lanczos series expansion and a tensor network ansatz, uplifting them to the level of operator algebra. This allows us to efficiently simulate large system sizes for arbitrarily long timescales and to extract the temperature-dependent decay rates. We observe that for the Kitaev-Hubbard model, the decay rate of the edge mode depends exponentially on the inverse temperature 𝛽, and on an effective energy scale Δ eff that is greater than the thermodynamic gap of the system Δ.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Direct estimation of the density of states for fermionic systems

Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic properties by estimating the density of states (DOS), which is a central object in quantum statistical mechanics. We introduce several key innovations that significantly improve the practicality and extend the generality of previous techniques. First, our approach allows one to estimate the DOS only for a specific subspace of the full Hilbert space. This is crucial for fermionic systems, since both canonical and grand canonical ensemble thermal equilibrium properties depend on subspaces of fixed number. Second, in our approach, by time evolving very simple, random initial states, such as randomly chosen computational basis states, we can exactly recover the DOS on average. Third, due to circuit-depth limitations, we only reconstruct the DOS up to a convolution with a Gaussian window—thus all imperfections that shift the energy levels by less than the width of the convolution window will not significantly affect the estimated DOS. For these reasons, we find the approach is a promising candidate for early quantum advantage as even short-time, noisy dynamics can yield a semiquantitative reconstruction of the DOS (convolution with a broad Gaussian window), while early fault-tolerant devices will likely enable higher-resolution DOS reconstruction through longer time evolutions. We demonstrate the practicality of our approach in representative Fermi-Hubbard and spin models and indeed find that our approach is highly robust against algorithmic errors in the time evolution and against gate noise. We further demonstrate that our approach is compatible with noisy intermediate-scale quantum (NISQ) computing NISQ-friendly variational techniques, introducing and leveraging a technique for variational time evolution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Design Rules for Open-Shell Molecular Wires: Insights from Correlated Many-Body Transport

Open-shell π-conjugated systems have emerged as promising molecular wires that can sustain unusually high low-bias conductance over tens of nanometers. However, predictive design rules remain limited because near-degeneracy and spin polarization give rise to correlated electronic states that are not reliably captured by standard density functional theory and Landauer transport descriptions. Here, we establish physically transparent design rules for long-range, weakly length-dependent charge transport based on the interplay between bond-length alternation and electron–electron interactions. Using a fully correlated transport framework that combines density matrix renormalization group calculations with nonequilibrium Green’s function embedding, we show that weak dimerization maintains spatially extended edge states, while moderate on-site interaction stabilizes open-shell character without excessively separating transport-relevant resonances. This balance yields zero-bias transmission that is largely insensitive to molecular length, providing a route to connect chemically tunable structure to correlated transport beyond mean-field descriptions.

Charge transport↗
DOE OSTI2025

Entanglement Structure of Non-Gaussian States and How to Measure It

Rapidly growing capabilities of quantum simulators to probe quantum many-body phenomena require new methods to characterize increasingly complex states. Here, we present a protocol that constrains quantum states using experimentally measured correlation functions. This method enables measurement of a quantum state’s entanglement structure, opening a new route to study entanglement-related phenomena. Our approach extends Gaussian state parameterizations by systematically incorporating higher-order correlations. We show the protocol’s usefulness in conjunction with current and forthcoming experimental capabilities, focusing on weakly interacting fermions as a proof of concept. Here, the lowest nontrivial expansion quantitatively predicts early time thermalization dynamics, including signaling the onset of quantum chaos indicated by the entanglement Hamiltonian.

Fermi gases↗