Search NASA⌕ Search

SEARCH · Search NASA

Results for “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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Pair density wave in the doped three-band Hubbard model on two-leg square cylinders

A pair density wave (PDW) is a superconducting (SC) state with a spatially modulated order parameter. Although much is known about the properties of the PDW state, its realization in microscopic models with divergent susceptibility has been challenging. Here, in this work, we report a density-matrix renormalization group study of a three-band Hubbard model (also known as the Emery model) for cuprates on long two-leg square cylinders. Upon light doping, we find that the ground state of the system is consistent with that of a PDW state with mutually commensurate and power-law SC, charge (CDW), and spin (SDW) density wave correlations. The SC correlations are dominant between neighboring Cu sites with d-wave pairing symmetry. Interestingly, we find that the near-neighbor interactions, especially the near-neighbor attractive V pd interaction between neighboring Cu and oxygen sites, can notably enhance the SC correlations while simultaneously suppressing the CDW correlations. For a modestly strong attractive V pd , the SC correlations become quasi-long-ranged with a divergent PDW susceptibility.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Influence of Deformation on the Energy and Optical Absorption Spectra of Fullerene C{sub 20} within the Hubbard Model

Abstract—Anticommutator Green’s functions and energy spectra of fullerene C{sub 20} with the I{sub h}, D{sub 5d}, and D{sub 3d} symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of fullerene C{sub 20} with the I{sub h}, D{sub 5d}, and D{sub 3d} symmetry groups have been determined. It is also shown how the energy levels of fullerene C{sub 20} with the I{sub h} symmetry group are split with the symmetry reduction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Full self-consistency versus quasiparticle self-consistency in diagrammatic approaches: Exactly solvable two-site Hubbard model

Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ₁ from the first-order perturbation theory, and the exact vertex Γ E ). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. Results obtained with the exact vertex are directly related to the present open question—which approximation is more advantageous for future implementations, GW + DMFT or QPGW + DMFT. It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on Perturbation Theory systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Gapless spin liquid and pair density wave of the Hubbard model on three-leg triangular cylinders

We study the ground state properties of the Hubbard model on three-leg triangular cylinders using large-scale density-matrix renormalization group simulations. At half-filling, we identify an intermediate gapless spin liquid phase, which has one gapless spin mode and algebraic spin–spin correlations but exponential decay scalar chiral–chiral correlations, between a metallic phase at weak coupling and Mott insulating dimer phase at strong interaction. Upon light doping the gapless spin liquid, the system exhibits power-law charge-density-wave (CDW) correlations but short-range single-particle, spin–spin, and chiral–chiral correlations. Similar to CDW correlations, the superconducting correlations also decay in power-law but oscillate in sign as a function of distance, which is consistent with the striped pair-density wave. When further doping the gapless spin liquid phase or doping the dimer order phase, another phase takes over, which has similar CDW correlations but all other correlations decay exponentially.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1999

Phase Diagram of the Two-Chain Hubbard Model

We have calculated the charge gap and spin gap for the two-chain Hubbard model as a function of the on-site Coulomb interaction and the interchain hopping amplitude. We used the density matrix renormalization group method and developed a method to calculate separately the gaps numerically for the symmetric and antisymmetric modes with respect to the exchange of the chain indices. We have found very different behaviors for the weak and strong interaction cases. Our calculated phase diagram is compared to the one obtained by Balents and Fisher using the weak coupling renormalization group technique.

Park, Youngho↗
DOE OSTI2015

Attractive Hubbard model with disorder and the generalized Anderson theorem

Using the generalized DMFT+Σ approach, we study the influence of disorder on single-particle properties of the normal phase and the superconducting transition temperature in the attractive Hubbard model. A wide range of attractive potentials U is studied, from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong-coupling region, where the superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the superconducting transition temperature. We study two typical models of the conduction band with semi-elliptic and flat densities of states, respectively appropriate for three-dimensional and two-dimensional systems. For the semi-elliptic density of states, the disorder influence on all single-particle properties (e.g., density of states) is universal for an arbitrary strength of electronic correlations and disorder and is due to only the general disorder widening of the conduction band. In the case of a flat density of states, universality is absent in the general case, but still the disorder influence is mainly due to band widening, and the universal behavior is restored for large enough disorder. Using the combination of DMFT+Σ and Nozieres-Schmitt-Rink approximations, we study the disorder influence on the superconducting transition temperature T{sub c} for a range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong-coupling. Disorder can either suppress T{sub c} (in the weak-coupling region) or significantly increase T{sub c} (in the strong-coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of the superconducting critical temperature are essentially due to only the general disorder widening of the conduction band.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Charge Order of Strongly Bounded Electron Pairs on the Triangular Lattice: the Zero-Bandwidth Limit of the Extended Hubbard Model with Strong Onsite Attraction

The inhomogeneous distribution of charged particles is known as charge-order phenomena. Recent experimental studies of (quasi-) two-dimensional materials found different ordered patterns on the triangular lattice. In this work, the preliminary studies of the extended Hubbard model (with the intersite Coulomb density-density repulsion) in the atomic limit on the triangular lattice are presented. The model is investigated within the mean-field approach that treats the onsite term exactly. The finite temperature phase diagrams including metastable phases and some characteristics of the model are determined for the limit of strong onsite attraction. It is shown that in the limit considered all transitions between stable phases are discontinuous (for fixed chemical potential), which is totally different from the model on the alternate lattices. Continuous transitions between metastable phases are also found.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Anyon superconductivity from topological criticality in a Hofstadter–Hubbard model

We argue that the combination of strong repulsive interactions and high magnetic fields can generate electron pairing and superconductivity. Inspired by the large lattice constants of moiré materials, which make large flux per unit cell accessible at laboratory fields, we study the triangular lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette, where previous literature has argued that a chiral spin liquid separates a weak-coupling integer quantum Hall phase and a strong-coupling topologically trivial antiferromagnetic insulator at a density of one electron per site. We argue that topological superconductivity emerges upon doping in the vicinity of the integer quantum Hall to chiral spin liquid transition. We employ exact diagonalization and density matrix renormalization group methods to examine this theoretical scenario and find that electronic pairing indeed occurs on both sides of criticality over a remarkably broad range of interaction strengths. On the chiral spin liquid side, our results provide a concrete model realization of the long-hypothesized mechanism of anyon superconductivity. Our study thus establishes a beyond-Bardeen-Cooper-Schrieffer route to electron pairing in a well-controlled limit, relying crucially on the interplay between electron correlations and band topology.

Hubbard model↗
DOE OSTI2022

Simulating Lindbladian evolution with non-Abelian symmetries: Ballistic front propagation in the SU(2) Hubbard model with a localized loss

In this work, we develop a non-Abelian time evolving block decimation (NA-TEBD) approach to study open systems governed by Lindbladian time evolution, while exploiting an arbitrary number of Abelian or non-Abelian symmetries. We illustrate this method in a one-dimensional fermionic SU(2) Hubbard model on a semi-infinite lattice with localized particle loss at one end. We observe a ballistic front propagation with strongly renormalized front velocity, and a hydrodynamic current density profile. For large loss rates, a suppression of the particle current is observed, as a result of the quantum Zeno effect. Operator entanglement is found to propagate faster than the depletion profile, preceding the latter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Dynamics of the quantum phase transition in the one-dimensional Bose-Hubbard model: Excitations and correlations induced by a quench

The ground state of the one-dimensional Bose-Hubbard model at unit filling undergoes the Mott-superfluid quantum phase transition. It belongs to the Kosterlitz-Thouless universality class with an exponential divergence of the correlation length in place of the usual power law. Here, we present numerical simulations of a linear quench both from the Mott insulator to superfluid and back. The results satisfy the scaling hypothesis that follows from the Kibble-Zurek mechanism (KZM). In the superfluid-to-Mott quenches there is no significant excitation in the superfluid phase despite its gaplessness. And since all critical superfluid ground states are qualitatively similar, the excitation begins to build up only after crossing the critical point when the ground state begins to change fundamentally. The last process falls into the KZM framework.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Stripe order enhanced superconductivity in the Hubbard model

Unidirectional (“stripe”) charge density wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high-temperature superconductors, where it generally competes with superconductivity. Nonetheless, on theoretical grounds it has been conjectured that stripe order (or other forms of “optimal” inhomogeneity) may play an essential positive role in the mechanism of high-temperature superconductivity. Here, we report density matrix renormalization group studies of the Hubbard model on long four- and six-leg cylinders, where the hopping matrix elements transverse to the long direction are periodically modulated—mimicking the effect of putative period 2 stripe order. We find that even modest amplitude modulations can enhance the long-distance superconducting correlations by many orders of magnitude and drive the system into a phase with a substantial spin gap and superconducting quasi–long-range order with a Luttinger exponent, K sc ~ 1.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Fluctuating intertwined stripes in the strange metal regime of the Hubbard model

Strongly correlated electron systems host a variety of poorly understood correlations in their high-temperature normal state. Unlike ordered phases defined by order parameters, regions of the normal state are often defined through unconventional properties such as strange metallic transport or spectroscopic pseudogaps. Characterizing the microscopic correlations in the normal state is necessary to elucidate mechanisms that lead to these properties and their connection to ground-state orders. Here, in this paper, we establish the presence of intertwined charge and spin stripes in the strange metal normal state of the Hubbard model using determinant quantum Monte Carlo calculations. The charge and spin density waves constituting the stripes are fluctuating and short ranged; yet they obey a mutual commensurability relation and remain microscopically interlocked, as evidenced through measurements of three-point spin-spin-hole correlation functions. Our findings demonstrate the ability of many-body numerical simulations to unravel the microscopic correlations that define quantum states of matter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Machine learning to alleviate Hubbard-model sign problems

Lattice Monte Carlo calculations of interacting systems on nonbipartite lattices exhibit an oscillatory imaginary phase known as the phase or sign problem, even at zero chemical potential. One method to alleviate the sign problem is to analytically continue the integration region of the state variables into the complex plane via holomorphic flow equations. For asymptotically large flow times, the state variables approach manifolds of constant imaginary phase known as Lefschetz thimbles. Furthermore, flowing such variables and calculating the ensuing Jacobian is a computationally demanding procedure. In this paper, we demonstrate that neural networks can be trained to parametrize suitable manifolds for this class of sign problem and drastically reduce the computational cost for different severely afflicted small volume systems. In particular, we apply our method to the Hubbard model on the triangle and tetrahedron, both of which are nonbipartite. At strong interaction strengths and modest temperatures, the tetrahedron suffers from a severe sign problem that cannot be overcome with standard reweighting techniques, while it quickly yields to our method. We benchmark our results with exact calculations and comment on future directions of this work.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1989

Phase diagram of the two-dimensional negative-U Hubbard model

Theoretical arguments and numerical calculations are used to discuss the phase diagram of the two-dimensional negative-U Hubbard model. The results are consistent with (1) a vanishing transition temperature at half-filling but with a ground state having both superconducting and charge-density-wave long-range order, and (2) a Kosterlitz-Thouless transition at a finite temperature into a superconducting state with power-law decay of the pairing correlations away from half-filling.

Scalettar, R. T.↗
DOE OSTI2024

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

The complicated ways in which electrons interact in many-body systems such as molecules and materials have long been viewed through the lens of local electron correlation and associated correlation functions. However, quantum information science has demonstrated that more global diagnostics of quantum states like the entanglement entropy can provide a complementary and clarifying lens on electronic behavior. One particularly useful measure that can be used to distinguish between quantum and classical sources of entanglement is the accessible entanglement, the entanglement available as a quantum resource for systems subject to conservation laws, such as fixed particle number, due to superselection rules. In this work, we introduce an algorithm and demonstrate how to compute accessible and symmetry-resolved entanglements for interacting fermion systems. This is accomplished by combining an incremental version of the swap algorithm with a recursive auxiliary field quantum Monte Carlo algorithm recently developed by the authors. We apply these tools to study the pairing and charge density waves exhibited in the paradigmatic attractive Hubbard model via entanglement. We find that the particle and spin symmetry-resolved entanglements and their related full probability distribution functions show very clear—and unique—signatures of the underlying electronic behavior even when those features are less pronounced in conventional correlation functions. Altogether, this work provides a systematic means of characterizing the entanglement within quantum systems that can grant a deeper understanding of the complicated electronic behavior that underlies quantum phase transitions and crossovers in many-body systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices

Here, we calculate the bipartite R enyi entanglement entropy of an L x L x 2 bilayer Hubbard model using a determinantal quantum Monte Carlo method recently proposed by Grover [Phys. Rev. Lett. 111, 130402 (2013)]. Two types of bipartition are studied: (i) One that divides the lattice into two L x L planes, and (ii) One that divides the lattice into two equal-size (L x L=2 x 2) bilayers. Furthermore, we compare our calculations with those for the tight-binding model studied by the correlation matrix method. As expected, the entropy for bipartition (i) scales as L 2 , while the latter scales with L with possible logarithmic corrections. The onset of the antiferromagnet to singlet transition shows up by a saturation of the former to a maximal value and the latter to a small value in the singlet phase. We also comment on the large uncertainties in the numerical results with increasing U, which would have to be overcome before the critical behavior and logarithmic corrections can be quanti ed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Transport and optical conductivity in the Hubbard model: A high-temperature expansion perspective

We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the high-temperature series expansion. We consider generic dimension d as well as the infinite- d limit, arbitrary electron density n, and both finite and infinite repulsion U. We use moment-reconstruction methods to obtain the one-electron spectral function, the self-energy, and the optical conductivity. They are all smooth functions at high temperature and, at large U, they are featureless with characteristic widths of the order of the lattice hopping parameter t. In the infinite-d limit, we compare the series expansion results with accurate numerical renormalization group and interaction expansion quantum Monte Carlo results. We find excellent agreement down to surprisingly low temperatures, throughout most of the bad-metal regime, which applies for T≳ (1 - n)D, the Brinkman-Rice scale. The resistivity increases linearly in T at high temperature without saturation. This results from the 1/T behavior of the compressibility or kinetic energy, which play the role of the effective carrier number. In contrast, the scattering time (or diffusion constant) saturates at high T. We find that σ( n,T) ≈ (1 - n)σ(n = 0,T) to a very good approximation for all n, with σ(n = 0,T) ∝ t/T at high temperatures. The saturation at small n occurs due to a compensation between the density dependence of the effective number of carriers and that of the scattering time. The T dependence of the resistivity displays a kneelike feature which signals a crossover to the intermediate-temperature regime where the diffusion constant (or scattering time) starts increasing with decreasing T. At high temperatures, the thermopower obeys the Heikes formula, while the Wiedemann-Franz law is violated with the Lorenz number vanishing as 1/T 2 . The relevance of our calculations to experiments probing high-temperature transport in materials with strong electronic correlations or ultracold atomic gases in an optical lattice is briefly discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Magnetic field dependent dynamics and field-driven metal-to-insulator transition of the half-filled Hubbard model: A DMFT+DMRG study

Here, we study the magnetic field-driven metal-to-insulator transition in half-filled Hubbard model on the Bethe lattice, using the dynamical mean-field theory by solving the quantum impurity problem with density-matrix renormalization group algorithm. The method enables us to obtain a high-resolution spectral densities in the presence of a magnetic field. It is found that the Kondo resonance at the Fermi level splits at relatively high magnetic field: the spin-up and -down components move away from the Fermi level and finally form a spin-polarized band insulator. By calculating the magnetization and spin susceptibility, we clarify that an applied magnetic field drives a transition from a paramagnetic metallic phase to a band insulating phase. In the weak interaction regime, the nature of the transition is continuous and captured by the Stoner's description, while in the strong interaction regime the transition is very likely to be metamagnetic, evidenced by the hysteresis curve. Furthermore, we determine the phase boundary by tracking the kink in the magnetic susceptibility, and the steplike change of the entanglement entropy and the entanglement gap closing. Interestingly, the phase boundaries determined from these two different ways are largely consistent with each other.

36 MATERIALS SCIENCE↗