arXiv subjects

Seher Karakuzu

Publications and source records attributed to Seher Karakuzu.

10 recordsLinked to original sources

arXiv2023

A flexible class of exact Hubbard-Stratonovich transformations

We consider a class of Hubbard-Stratonovich transformations suitable for treating Hubbard interactions in the context of quantum Monte Carlo simulations. A tunable parameter $p$ allows us to continuously vary from a discrete Ising auxiliary field ($p=\infty$) to a compact auxiliary field that couples to electrons sinusoidally ($p=0$). In tests on the single-band Hubbard model, we find that the severity of the sign problem decreases systematically with increasing $p$. Selecting $p$ finite, however, enables continuous sampling methods like the Langevin or Hamiltonian Monte Carlo methods. We explore the tradeoffs between various simulation methods through numerical benchmarks.

cond-mat.str-el↗

arXiv2023

Magnetism and Metallicity in Moiré Transition Metal Dichalcogenides

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript we analyze the moiré Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal-insulator phase diagram for the full range of magnetic fields up to the fully spin polarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments.

cond-mat.str-el↗

arXiv2022

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.

cond-mat.str-el↗

arXiv2022

Stripe correlations in the two-dimensional Hubbard-Holstein model

Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon ($e$-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped singleband Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters like the next-nearest-neighbor hopping $t^\prime$ or phonon energy $Ω$. Our results help elucidate how the $e$-ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high-$T_\mathrm{c}$ cuprates.

cond-mat.str-el↗

arXiv2022

Intertwined spin, charge and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit

The high-temperature superconducting cuprates are governed by intertwined striped magnetic and charge orders in addition to superconductivity. Remarkably similar behavior has also been seen in numerical calculations for the Hubbard model describing the copper-oxygen layers in these materials. Finite cluster methods typically find that spin and charge stripe order dominates, while embedded quantum cluster methods, which access the thermodynamic limit, often conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in an embedded cluster calculation for the Hubbard model. This discovery demonstrates that striped states survive in the thermodynamic limit and allows us to study their influence on the model's superconducting properties, where we find evidence for pair-density-wave correlations intertwined with the stripe correlations.

cond-mat.str-el↗

arXiv2021

Superconductivity in the bilayer Hubbard model: Are two Fermi surfaces better than one?

Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping $t_\perp$, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Liftshiz transition and even when it becomes incipient. Here, we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust $s_\pm$ pairing correlations in the large $t_\perp$ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased $T_c$. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.

cond-mat.str-el↗

arXiv2020

The overdoped end of the cuprate phase diagram

Studying the disappearance of superconductivity at the end of the overdoped region of the cuprate phase diagram offers a different approach for investigating the interaction which is responsible for pairing in these materials. In the underdoped region this question is complicated by the presence of charge and stripe ordered phases as well as the pseudogap. In the overdoped region the situation appears simpler with only a normal phase, a superconducting phase and impurity scattering. Here, for the overdoped region, we report the results of a combined dynamic cluster approximation (DCA) and a weak Born impurity scattering calculation for a $t-t'-U$ Hubbard model. We find that a decrease in the $d$-wave pairing strength of the two-particle scattering vertex is closely coupled to changes in the momentum and frequency structure of the magnetic spin fluctuations as the system is overdoped. Treating the impurity scattering within a disordered BCS $d$-wave approximation, we see how the combined effects of the decreasing $d$-wave pairing strength and weak impurity scattering lead to the end of the $T_c$ dome.

cond-mat.supr-con↗

arXiv2018

Solution of the "sign problem" for the half filled Hubbard-Holstein model

We show that, by an appropriate choice of auxiliary fields and exact integration of the phonon degrees of freedom, it is possible to define a 'sign-free' path integral for the so called Hubbard-Holstein model at half-filling. We use a statistical method, based on an accelerated and efficient Langevin dynamics, for evaluating all relevant correlation functions of the model. Preliminary calculations at $U/t=4$ and $U/t=1$, for $ω_0/t=1$, indicate a quite extended region around $U \simeq {g^2 \over ω_0}$ without either antiferromagnetic or charge-density-wave orders, separating two quantum critical points at zero temperature. The elimination of the sign problem in a model without explicit particle-hole symmetry may open new perspectives for strongly correlated models, even away from the purely attractive or particle-hole symmetric cases.

cond-mat.str-el↗

arXiv2018

Study of the superconducting order parameter in the negative-$U$ 2D-Hubbard model by grand-canonical twist-averaged boundary conditions

By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the $s$-wave superconducting order parameter and the pairing correlations for the negative-$U$ Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs is much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of $|U|/t$ and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behaviour of the superconducting phase, by means of a suitably chosen Jastrow factor including long-range density-density correlations.

cond-mat.str-el↗

arXiv2017

Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model

By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional Hubbard-Holstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping $t$, the on-site electron-electron interaction $U$, the phonon energy $ω_0$, and the electron-phonon coupling $g$. At half filling, the ground state is an antiferromagnetic insulator for $U \gtrsim 2g^2/ω_0$, while it is a charge-density-wave (or bi-polaronic) insulator for $U \lesssim 2g^2/ω_0$. In addition to these phases, we find a superconducting phase that intrudes between them. For $ω_0/t=1$, superconductivity emerges when both $U/t$ and $2g^2/tω_0$ are small; then, by increasing the value of the phonon energy $ω_0$, it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case.

cond-mat.str-el↗