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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Robust charge-density-wave correlations in the electron-doped single-band Hubbard model

There is growing evidence that the hole-doped single-band Hubbard and t–J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Quantum many-body simulations of the two-dimensional Fermi-Hubbard model in ultracold optical lattices

Understanding quantum many-body states of correlated electrons is one main theme in modern condensed-matter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, was recently realized in ultracold optical lattices, it is highly desirable to have controlled numerical methodology to provide precise finite-temperature results upon doping to directly compare with experiments. Here, we demonstrate the exponential tensor renormalization group (XTRG) algorithm [Chen et al., Phys. Rev. X 8, 031082 (2018)], complemented by independent determinant quantum Monte Carlo, offers a powerful combination of tools for this purpose. XTRG provides full and accurate access to the density matrix and thus various spin and charge correlations, down to an unprecedented low temperature of a few percent of the tunneling energy. Finally, we observe excellent agreement with ultracold fermion measurements at both half filling and finite doping, including the sign-reversal behavior in spin correlations due to formation of magnetic polarons, and the attractive hole-doublon and repulsive hole-hole pairs that are responsible for the peculiar bunching and antibunching behaviors of the antimoments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Optical conductivity of the two-dimensional Hubbard model: Vertex corrections, emergent Galilean invariance, and the accuracy of the single-site dynamical mean field approximation

We compute the frequency-dependent conductivity of the two-dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single-site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the model exhibits an emergent Galilean invariance. The DMFT approximation also becomes qualitatively inaccurate very near half filling if nesting is important.

2-dimensional systems↗
DOE OSTI2022

Doped Mott insulators in the triangular-lattice Hubbard model

Here we investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping δ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping δ ≲ 10%, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well-defined Fermi surface. On further doping, δ ≈ 10%~20% SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping δ ≳ 20%, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Metal-insulator transition in a random Hubbard model

In this work, we examine the metal-insulator transition in a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange, and an on-site nonrandom repulsion, the Hubbard $\textit{U}$. We argue that recent numerical results of Cha et al. can be understood in terms of a deconfined critical point between a disordered Fermi liquid and an insulating spin glass. We find a deconfined critical point in a previously proposed large $\textit{M}$ theory, which generalizes the SU(2) spin symmetry to SU($\textit{M}$) and obtains exponents for the electron and spin correlators which agree with those of Cha et al. This critical point is expected to have the maximal quantum Lyapunov exponent. We also present a renormalization group analysis, and argue for the presence of an additional metallic spin glass phase at half-filling and small $\textit{U}$.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 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 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 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 OSTI2023

Non-Fermi Liquid Behavior in the Three-Dimensional Hubbard Model

We present a numerical study on the non-Fermi liquid behavior of a three-dimensional strongly correlated system. The Hubbard model in a simple cubic lattice is simulated by the dynamical cluster approximation; in particular, the quasi-particle weight is calculated at finite dopings for a range of temperatures. By fitting the quasi-particle weight to the marginal Fermi liquid form at finite doping near the putative quantum critical point, we find evidence of a separatrix between Fermi liquid and non-Fermi liquid regions. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point exist in the non-symmetry broken solution of the three-dimensional interacting electron systems. We also calculate the spectral function, close to the half-filling, and we obtain evidence of pseudogap.

Kellar, Samuel↗
NASA NTRSDate not supplied

Simulating a Low-Weight Encoding of the Fermi-Hubbard Model Feedback and Support with QAOA

Recent work [1] has proposed a compact fermion-to-qubit mapping for the Fermi-Hubbard model (FHM), potentially lowering the overhead needed to simulate such a system on quantum hardware. In prior work [2], we numerically investigated how well a quantum annealer could prepare ground states of the FHM encoded using the resource-efficient mapping. In order to compare these results to gate-model systems, we turn to a QAOA-style approach and replace the annealing schedule with both Trotterizations thereof and also more general Hamiltonian-variational ansatze based on the terms of the mapped FH Hamiltonian. We investigate the achievable ground state fidelities of these gate sequences, consider various optimizations of the ansatze structure, and offer resource estimations of the optimized QAOA protocols for near-term hardware.

quantum computing↗