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At least 19 records
All sourcesNASA NTRSDOE OSTI
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 OSTI2021

Study of spin symmetry in the doped t-J model using infinite projected entangled pair states

We study the two-dimensional t-J model on a square lattice using infinite projected entangled pair states (iPEPS). At small doping, multiple orders, such as antiferromagnetic order, stripe order and superconducting order, are intertwined or compete with each other. We demonstrate the role of spin symmetry at small doping by either imposing SU(2) spin symmetry or its U(1) subgroup in the iPEPS ansatz, thereby excluding or allowing spontaneous spin-symmetry breaking, respectively, in the thermodynamic limit. From a detailed comparison of our simulations, we provide evidence that stripe order is pinned by long-range antiferromagnetic order. We also find SU(2) iPEPS, enforcing a spin-singlet state, yields a uniform charge distribution and favors d-wave singlet pairing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1990

Phase separation in the t-J model

A detailed understanding of the motion of 'holes' in an antiferromagnet is of fundamental importance for the theory of high-temperature superconductors. It is shown here that, for the t-J model, dilute holes in an antiferromagnet are unstable against phase separation into a hole-rich and a no-hole phase. When the spin-exchange interaction J exceeds a critical value Jc, the hole-rich phase has no electrons. It is proposed that, for J slightly less than Jc, the hole-rich phase is a low-density superfluid of electron pairs. Phase separation in related models is briefly discussed.

Emery, V. J.↗
DOE OSTI2024

Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice t – J Model

The square-lattice Hubbard and closely related t-J models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended t-J model have identified d-wave SC on the electron-doped side (with the next-nearest-neighbor hopping t 2 > 0) but a dominant charge density wave (CDW) order on the hole-doped side (t 2 < 0), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended t-J model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range δ = 1/16 – 1/8, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and d-wave symmetry. On the wider eight-leg systems, the d-wave SC also emerges on the hole-doped side at the optimal 1=8 doping, demonstrating the winning of SC over CDW by increasing the system width. Furthermore, our results not only suggest a new path to SC in general t-J model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Phase diagram of the one-dimensional t 1 - t 2 - J model: Ferromagnetism, triplet pairing, and charge and pair density waves

Here, we present a density matrix renormalization group (DMRG) study of an extended t-J model with hopping to the first and second neighbors -- the one dimensional t 1 -t 2 -J model. The full phase diagram as a function of the density n and exchange strength J, for both positive and negative values of t 2 , is obtained. For t 2 = -0.5 we observe that, in the strongly interacting region, Nagaoka Ferromagnetism (FM) is accompanied by a triplet pair density wave (PDW) upon doping. As the spin exchange J increases, a charge density wave (CDW) phase emerges and then gives way to singlet superconductivity (SC). This phase behaves as a singlet PDW with vanishing spacial average of the order parameter and a spin gap. When t 2 = 0.5, the physics is basically reminiscent of the conventional t-J model, undergoing a transition from a metallic to a SC phase as a function of J.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Coexistence of antiferromagnetism and topological superconductivity on the honeycomb lattice Hubbard model

In this report, motivated by the recent numerical simulations for doped t-J model on the honeycomb lattice, we study superconductivity of singlet and triplet pairing on the honeycomb lattice Hubbard model. We show that a superconducting state with coexisting spin-singlet and spin-triplet pairings is induced by the antiferromagnetic order near half filling. The superconducting state we obtain has a topological phase transition that separates a topologically trivial state and a nontrivial state with Chern number two. Possible experimental realization of such a topological superconductivity is also discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Superconducting valence bond fluid in lightly doped eight-leg $t-J$ cylinders

Superconductivity in doped quantum paramagnets has been a subject of long theoretical inquiry. In this work, we report a density matrix renormalization group study of lightly doped $t-J$ models on the finite-width square lattice (doped hole densities $δ$ = 1/12 and 1/8) with parameters for which previous studies have suggested that the undoped system in 2D is either a quantum spin liquid or a valence bond crystal. Our studies are performed on cylinders with width up to 8. Here, ground-state correlations are found to be nearly identical for the “doped quantum spin liquid” and “doped valence bond crystal.” Upon increasing the cylinder widths from 4 to 8, we observed a significant strengthening of the quasi-long-range superconducting correlations and a dramatic suppression of any “competing” charge density wave order. Extrapolating from the observed behavior of the width eight cylinders, we speculate that the system has a nodeless $d$-wave superconducting ground state in the 2D limit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Singlet, triplet, and pair density wave superconductivity in the doped triangular-lattice moiré system

Recent experimental progress has established the twisted bilayer transition metal dichalcogenide (TMD) as a highly tunable platform for studying many-body physics. Particularly, the homobilayer TMDs under displacement field are believed to be described by a generalized triangular-lattice Hubbard model with a spin-dependent hopping phase θ. To explore the effects of θ on the system, we perform density matrix renormalization group calculations for the relevant triangular lattice t-J model. By changing θ at small hole doping, we obtain a region of quasi-long-range superconducting order coexisting with charge and spin density wave within 0 < θ < π/3. The superconductivity is composed of a dominant spin singlet d-wave and a subdominant triplet p-wave pairing. Intriguingly, the S z = ±1 triplet pairing components feature pair-density waves. In addition, we find a region of triplet superconductivity coexisting with charge-density wave and ferromagnetism within π/3 < θ < 2π/3, which is related to the former phase at smaller θ by a combined operation of spin-flip and gauge transformation. Furthermore, our findings provide insights and directions for experimental search for exotic superconductivity in twisted TMD systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Robust d-Wave Superconductivity in the Square-Lattice t–J Model

Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. Here, to explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Excitation spectra of quantum matter without quasiparticles. I. Sachdev-Ye-Kitaev models

Here, we study the low-frequency spectra of complex Sachdev-Ye-Kitaev models at general densities. The analysis applies also to SU(M) magnets with random exchange at large M. The spectral densities are computed by numerical analysis of the saddle-point equations on the real frequency ω axis at zero temperature T. The asymptotic low-ω behaviors are found to be in excellent agreement with the scaling dimensions of irrelevant operators which perturb the conformally invariant critical states. Of possible experimental interest is our computation of the universal spin spectral weight of the SU(M) magnets at low ω and T; this includes a contribution from the time reparametrization mode, which is the boundary graviton of the holographic dual. This analysis is extended to a random t-J model in the following paper [M. Tikhanovskaya et al., following paper, Phys. Rev. B 103, 075142 (2021)].

36 MATERIALS SCIENCE↗
DOE OSTI2021

Possible Superconductivity with a Bogoliubov Fermi Surface in a Lightly Doped Kagome U(1) Spin Liquid

Whether the doped t-J model on the Kagome lattice supports exotic superconductivity has not been decisively answered. In this paper, we propose a new class of variational states for this model and perform large-scale variational Monte Carlo simulation on it. The proposed variational states are parameterized by the SU(2)-gauge-rotation angles, as the SU(2)-gauge structure hidden in the Gutzwiller-projected mean-field ansatz for the undoped model is broken upon doping. These variational doped states smoothly connect to the previously studied U(1) π-flux or 0-flux states, and energy minimization among them yields a chiral noncentrosymmetric nematic superconducting state with 2 × 2-enlarged unit cell. Moreover, this pair density wave state possesses a finite Fermi surface for the Bogoliubov quasi particles. We further study experimentally relevant properties of this intriguing pairing state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Theoretical Studies in Very Strongly Correlated Matter

In this Final Technical Report, a summary of research carried out by the PI and his group from 9/1/2006 to 8/31/2023, on developing new approaches to understand very strongly correlated systems is provided. Novel materials where interactions dominate the kinetic energy (due to hopping motion) of electrons, pose a major puzzle in condensed matter systems. These are located in regimes of parameters where traditional theoretical approaches fail, and new concepts and formalisms are called for. In the area of thermal or thermoelectrical transport the PI has found two new formulas for the Seebeck coefficient. These are easier to apply than the general Kubo formulas, and give interesting insights that lead to new directions in the search for better materials for energy harvesting.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Ground-state-based model reduction with unitary circuits

Here, we present a method to numerically obtain low-energy effective models based on a unitary transformation of the ground state. The algorithm finds a unitary circuit that transforms the ground state of the original model to a projected wavefunction with only the low-energy degrees of freedom. The effective model can then be derived using the unitary transformation encoded in the circuit. We test our method on the one-dimensional and two-dimensional square-lattice Hubbard model at half-filling, and obtain more accurate effective spin models than the standard perturbative approach.

Hubbard model↗
DOE OSTI2023

Machine learning the spectral function of a hole in a quantum antiferromagnet

Understanding charge motion in a background of interacting quantum spins is a fundamental problem in quantum many-body physics. The most extensively studied model for this problem is the so-called t-t'-t''-J model, where the determination of the parameter t' in the context of cuprate superconductors is challenging. Here we present a theoretical study of the spectral functions of a mobile hole in the t-t'-t''-J model using two machine-learning techniques: K-nearest neighbor regression (KNN) and a feed-forward neural network (FFNN). We employ the self-consistent Born approximation to generate a dataset of about 1.3 x 10 5 spectral functions. Here we show that, for the forward problem, both methods allow for the accurate and efficient prediction of spectral functions, allowing, e.g., rapid searches through parameter space. Furthermore, we find that for the inverse problem (inferring Hamiltonian parameters from spectra), the FFNN can, but the KNN cannot, accurately predict the model parameters using merely the density of states. Our results suggest that it may be possible to use deep-learning methods to predict materials parameters from experimentally measured spectral functions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Beyond fragmented dopant dynamics in quantum spin lattices: Robust localization and non-Gaussian diffusion

The motion of dopants in magnetic spin lattices has received tremendous attention for at least four decades due to its connection to high-temperature superconductivity. Despite these efforts, we lack a complete understanding of their behavior, especially out of the equilibrium and at nonzero temperatures. In this paper, we take a significant step towards a much deeper understanding based on state-of-the-art matrix-product-state calculations. In particular, we investigate the nonequilibrium dynamics of a dopant in two-leg 𝑡−𝐽 ladders with antiferromagnetic XXZ spin interactions. In the Ising limit, we find that the dopant is localized for all investigated nonzero temperatures due to an emergent disordered potential, with a localization length controlled by the underlying correlation length of the spin lattice, which increases exponentially with decreasing temperature. The dopant, hereby, only delocalizes asymptotically in the zero temperature limit. This greatly generalizes the localization effect discovered recently in Hilbert space fragmented models [Phys. Rev. Res. 6, 023325 (2024), SciPost Phys. Core 7, 054 (2024)]. In the presence of spin-exchange processes at rate 𝛼, the dopant diffuses with a diffusion coefficient, 𝐷 ℎ , depending nonmonotonically on 𝛼. It initially increases linearly as 𝐷 ℎ ∝ 𝛼 for 𝛼 ≪ 1 before dropping off as 𝛼 −1 for 𝛼 > 1. Moreover, we show that the underlying spin dynamics at infinite temperature behaves qualitatively the same, albeit with important quantitative differences. We substantiate these findings by showing that the dynamics features self-similar scaling behavior, which strongly deviates from the Gaussian behavior of regular diffusion, especially for weak spin exchange. Finally, we show that the diffusion coefficient 𝐷 ℎ follows an Arrhenius relation at high temperatures, whereby it is exponentially suppressed upon cooling.

Anomalous diffusion↗
DOE OSTI2022

Pairing properties of the $t$–$t$'–$t$"–$J$ model

We study the pairing properties of the two-dimensional t–t'–t"–J model, where t' and t" are second and third neighbor hoppings, at a doping level x ≈ 0.1. Recent studies of the t–t'–J model find strong pairing for t' > 0, associated with electron doping, but an absence of pairing for t'<0, associated with hole doping. This is in contrast to the cuprates, where the highest transition temperatures appear for hole doping. Model parametrizations for the cuprates estimate a t" comparable to t', which, in principle, might fix this discrepancy. However, we find that it does not; we observe a suppression of pairing for the hole-doped system (t' < 0,t" > 0), while for the electron-doped system (t' > 0,t" < 0) d-wave pairing is robust. As a result, extended hoppings appear to be insufficient to make the one-band t–t'–J model capable of describing the pairing in the hole-doped system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Root-N Krylov-space correction vectors for spectral functions with the density matrix renormalization group

In this work, we propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov-space decomposition to compute the correction vectors. Our approach entails the calculation of the root-N (N=2 is the standard square root) of the Hamiltonian propagator using Krylov-space decomposition and repeating this procedure N times to obtain the actual correction vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, whereas achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry and provide evidence that the root-N approach reaches a much improved spectral resolution compared to the conventional correction vector.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Doped moiré magnets: Renormalized flat bands and excitonic phases

Here, we explore the phase diagram of a twisted bilayer of strongly interacting electrons on a honeycomb lattice close to half filling using the slave-boson mean-field theory. Our analysis indicates that a variety of new phases can be realized as a function of chemical doping and twist angle. In particular, we find a nonmagnetic excitonic insulating phase that breaks the translational symmetry of the underlying moiré pattern. This phase results from the interplay of strong Coulomb interactions and the twist angle. In addition, we show that the features of the renormalized dispersion, such as the magic angles, depend significantly on the interactions. Our results highlight the rich physics arising in doped moiré superlattices of Mott insulators.

flat bands↗