Cluster Dynamical Mean-field Theory Research Articles

Quenched Pair Breaking by Interlayer Correlations as a Key to Superconductivity in La_{3}Ni_{2}O_{7}.

The recent discovery of superconductivity in La_{3}Ni_{2}O_{7} with T_{c}≃80 K under high pressure opens up a new route to high-T_{c} superconductivity. This material realizes a bilayer square lattice model featuring a strong interlayer hybridization unlike many unconventional superconductors. A key question in this regard concerns how electronic correlations driven by the interlayer hybridization affect the low-energy electronic structure and the concomitant superconductivity. Here, we demonstrate using a cluster dynamical mean-field theory that the interlayer electronic correlations (IECs) induce a Lifshitz transition resulting in a change of Fermi surface topology. By solving an appropriate gap equation, we further show that the leading pairing instability, s± wave, is enhanced by the IECs. The underlying mechanism is the quenching of a strong ferromagnetic channel, resulting from the Lifshitz transition driven by the IECs. Based on this picture, we provide a possible reason of why superconductivity emerges only under high pressure.

Single-site DFT+DMFT for vanadium dioxide using bond-centered orbitals

We present a combined density-functional theory and single-site dynamical mean-field theory (DMFT) study of vanadium dioxide (VO2) using an unconventional set of bond-centered orbitals as the basis of the correlated subspace. VO2 is a prototypical material undergoing a metal-insulator transition (MIT), hosting both intriguing physical phenomena and the potential for industrial applications. With our choice of correlated subspace basis, we investigate the interplay of structural dimerization and electronic correlations in VO2 in a computationally cheaper way compared to other state-of-the-art methods, such as cluster DMFT. Our approach allows us to treat the rutile and M1 monoclinic VO2 phases on an equal footing and to vary the dimerizing distortion continuously, exploring the energetics of the transition between the two phases. The choice of basis presented in this work hence offers a complementary view on the long-standing discussion of the MIT in VO2 and suggests possible future extensions to other similar materials hosting molecular-orbital-like states. Published by the American Physical Society 2024

CDMFT+HFD: An extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model

We examine the phase diagram of the extended Hubbard model on a square lattice, for both attractive and repulsive nearest-neighbor interactions, using CDMFT+HFD, a combination of Cluster Dynamical Mean Field theory (CDMFT) and a Hartree-Fock mean-field decoupling of the inter-cluster extended interaction. For attractive non-local interactions, this model exhibits a region of phase separation near half-filling, in the vicinity of which we find islands of d-wave superconductivity, decaying rapidly as a function of doping, with disconnected regions of extended s-wave order at smaller (higher) electron densities. On the other hand, when the extended interaction is repulsive, a Mott insulating state at half-filling is destabilized by hole doping, in the strong-coupling limit, in favor of d-wave superconductivity. At the particle-hole invariant chemical potential, we find a first-order phase transition from antiferromagnetism (AF) to d-wave superconductivity as a function of the attractive nearest-neighbor interaction, along with a deviation of the density from the half-filled limit. A repulsive extended interaction instead favors charge-density wave (CDW) order at half-filling.

Restoring translational symmetry in periodic all-orbital dynamical mean-field theory simulations.

Dynamical mean-field theory (DMFT) and its cluster extensions provide an efficient Green's function formalism to simulate spectral properties of periodic systems at the quantum many-body level. However, traditional cluster DMFT breaks translational invariance in solid-state materials, and the best strategy to capture non-local correlation effects within cluster DMFT remains elusive. In this work, we investigate the use of overlapping atom-centered impurity fragments in recently-developed ab initio all-orbital DMFT, where all local orbitals within the impurity are treated with high-level quantum chemistry impurity solvers. We demonstrate how the translational symmetry of the lattice self-energy can be restored by designing symmetry-adapted embedding problems, which results in an improved description of spectral functions in two-dimensional boron nitride monolayers and graphene at the levels of many-body perturbation theory (GW) and coupled-cluster theory. Furthermore, we study the convergence of self-energy and density of states as the embedding size is systematically expanded in one-shot and self-consistent DMFT calculations.

Pyqcm: An open-source Python library for quantum cluster methods

Pyqcm is a Python/C++ library that implements a few quantum cluster methods with an exact diagonalization impurity solver. Quantum cluster methods are used in the study of strongly correlated electrons to provide an approximate solution to Hubbard-like models. The methods covered by this library are Cluster Perturbation Theory (CPT), the Variational Cluster Approach (VCA) and Cellular (or Cluster) Dynamical Mean Field Theory (CDMFT). The impurity solver (the technique used to compute the cluster’s interacting Green function) is exact diagonalization from sparse matrices, using the Lanczos algorithm and variants thereof. The core library is written in C++ for performance, but the interface is in Python, for ease of use and inter-operability with the numerical Python ecosystem. The library is distributed under the GPL license.

Codebase release 2.2 for Pyqcm

Pyqcm is a Python/C++ library that implements a few quantum cluster methods with an exact diagonalization impurity solver. Quantum cluster methods are used in the study of strongly correlated electrons to provide an approximate solution to Hubbard-like models. The methods covered by this library are Cluster Perturbation Theory (CPT), the Variational Cluster Approach (VCA) and Cellular (or Cluster) Dynamical Mean Field Theory (CDMFT). The impurity solver (the technique used to compute the cluster’s interacting Green function) is exact diagonalization from sparse matrices, using the Lanczos algorithm and variants thereof. The core library is written in C++ for performance, but the interface is in Python, for ease of use and inter-operability with the numerical Python ecosystem. The library is distributed under the GPL license.

Dynamical variational Monte Carlo as a quantum impurity solver: Application to cluster dynamical mean field theory

Dynamical variational Monte Carlo as a quantum impurity solver: Application to cluster dynamical mean field theory

Photoinduced charge dynamics in 1T−TaS2

Nonequilibrium cluster dynamical mean-field theory simulations of a realistic multilayer structure are used to study the charge carrier dynamics induced by a laser pulse in 1$T$-TaS${}_{2}$. The solution is propagated up to picosecond timescales and shows that long-lived charge excitations only exist in the surface state of a specific structure, while the disturbance of bonding states in the bilayers that make up the bulk of the structure explain the almost instantaneous appearance of in-gap states reported in recent experiments.

Superconductivity in the twisted bilayer transition metal dichalcogenide WSe2 : A quantum cluster study

The observation of flat energy bands in transition metal dichalcogenide bilayers such as twisted ${\mathrm{WSe}}_{2}$ makes those materials interesting prospects for reproducing the behavior observed in graphene-based systems. We use an effective Hubbard model providing a description of twisted ${\mathrm{WSe}}_{2}$ to explore the presence of superconductivity, which was previously reported in experiments. Using both the variational cluster approximation and cluster dynamical mean-field theory, we predict the existence of chiral superconductivity of type $d\ifmmode\pm\else\textpm\fi{}id$ that can be tuned by the twist angle and by the application of a perpendicular displacement field in both electron- and hole-doped systems.

Prediction of anomalies in the velocity of sound for the pseudogap of hole-doped cuprates

We predict sound anomalies at the doping $\delta_{p}$ where the pseudogap ends in the normal state of hole-doped cuprates. Our prediction is based on the two-dimensional compressible Hubbard model using cluster dynamical mean-field theory. We find sharp anomalies (dips) in the velocity of sound as a function of doping and interaction. These dips are a signature of supercritical phenomena, stemming from an electronic transition without symmetry breaking below the superconducting dome. If experimentally verified, these signatures may help to solve the fundamental question of the nature of the pseudogap -- pinpointing its origin as due to Mott physics and resulting short-range correlations.

Mechanism of superconductivity in the Hubbard model at intermediate interaction strength

We study the fluctuations responsible for pairing in the d-wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum- and frequency-dependent fluctuations generate the d-wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity in both the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin fluctuation theory.

Chiral $p$-wave superconductivity in twisted bilayer graphene from dynamical mean field theory

We apply cluster dynamical mean field theory with an exact-diagonalization impurity solver to a Hubbard model for magic-angle twisted bilayer graphene, built on the tight-binding model proposed by Kang and Vafek [1], which applies to the magic angle 1.30^\circ1.30∘. We find that triplet superconductivity with p+ip symmetry is stabilized by CDMFT, as well as a subdominant singlet d+id state. A minimum of the order parameter exists close to quarter-filling and three-quarter filling, as observed in experiments.

Spin texture in a bilayer high-temperature cuprate superconductor

We investigate the possibility of spin texture in the bilayer cuprate superconductor $\rm Bi_2Sr_2CaCu_2O_{8+\delta}$ using cluster dynamical mean field theory (CDMFT). The one-band Hubbard model with a small interlayer hopping and a Rashba spin-orbit coupling is used to describe the material. The $d$-wave order parameter is not much affected by the presence of the Rashba coupling, but a small triplet component appears. We find a spin texture circulating in the same direction around $\mathbf{k}=(0,0)$ and $\mathbf{k}=(\pi,\pi)$ and stable against the superconducting phase. The amplitude of the spin structure, however, is strongly affected by the pseudogap phenomenon, more so than the spectral function itself.

Information-theoretic measures of superconductivity in a two-dimensional doped Mott insulator

A key open issue in condensed-matter physics is how quantum and classical correlations emerge in an unconventional superconductor from the underlying normal state. We study this problem in a doped Mott insulator with information-theory tools on the two-dimensional (2D) Hubbard model at finite temperature with cluster dynamical mean-field theory. We find that the local entropy detects the superconducting state and that the difference in the local entropy between the superconducting and normal states follows the same difference in the potential energy. We find that the thermodynamic entropy is suppressed in the superconducting state and monotonically decreases with decreasing doping. The maximum in entropy found in the normal state above the overdoped region of the superconducting dome is obliterated by superconductivity. The total mutual information, which quantifies quantum and classical correlations, is amplified in the superconducting state of the doped Mott insulator for all doping levels and shows a broad peak versus doping, as a result of competing quantum and classical effects.

Pole structure of the electronic self-energy with coexistence of charge order and superconductivity

We compare the pole structure of the electronic Green's function obtained by Cluster Dynamical Mean Field Theory to the results from the fractionalized Pair Density Wave idea. In the superconducting phase, we can consider the system in a state with coexistence of Superconducting and Charge order. Writing the Green's function in a way analogous to the previously proposed "hidden-fermions" model from S. Sakai et al (2016) leads to a similar pole structure for the self-energy. The fractionalization of the Pair Density Wave order also describes the pseudogap phase as a superposition of superconducting and charge order fluctuations. Considering a phenomenological lifetime for the particle-particle and particle-hole pairs leads to an electronic spectral function that matches the numerical results.

Possible insulator-pseudogap crossover in the attractive Hubbard model on the Lieb lattice

We study the attractive Hubbard model in the Lieb lattice to understand the normal state above the superconducting critical temperature in a flat band system. We use cluster dynamical mean-field theory to compute the two-particle susceptibilities with full quantum fluctuations included in the cluster. At interaction strengths lower than the hopping amplitude, we find that the normal state on the flat band is an insulator. The insulating behavior stems from the localization properties of the flat band. A flat-band enhanced pseudogap with a depleted spectral function arises at larger interactions.

Spin density wave order in interacting type-I and type-II Weyl semimetals

Weyl semimetals, featuring massless linearly dispersing chiral fermions in three dimensions, provide an excellent platform for studying the interplay of electronic interactions and topology, and exploring new correlated states of matter. Here, we examine the effect of a local repulsive interaction on an inversion-symmetry breaking Weyl semimetal model, using cluster dynamical mean field theory and variational cluster approximation methods. Our analysis reveals a continuous transition from the gapless Weyl semimetal phase to a gapped spin density wave ordered phase at a critical value of the interaction, which is determined by the band structure parameters. Further, we introduce a finite tilt in the linear dispersion and examine the corresponding behavior for a type-II Weyl semimetal model, where the critical interaction strength is found to be significantly diminished, indicating a greater susceptibility towards interactions. The behavior of different physical quantities, such as the double occupancy, the spectral function and the Berry curvature associated with the Weyl nodes are obtained in both the semimetallic and the magnetically ordered states. Finally, we provide an interaction-induced phase diagram for the Weyl semimetal model, as a function of the tilt parameter.

Charge- and pair-density-wave orders in the one-band Hubbard model from dynamical mean field theory

We study the charge-density-wave order and its competition with superconductivity in the one-band Hubbard model for high-$T_c$ superconducting cuprates. We use cluster dynamical mean field theory (CDMFT) at $T=0$. The one-band Hubbard model only contains copper atoms, and a physical charge-density-wave with charge excesses located on the oxygen atoms manifests itself as a bond-density-wave (BDW) within this context. It arises purely out of local correlation effects and also leads to a $s'$-wave pair-density-wave in the presence of $d$-wave superconductivity. The $d$-wave BDW is suppressed on increasing $U$ and is favored on increasing the magnitude of the second-neighbor hopping $t'$. Further, the $d$-wave BDW order is weakened when in competition with superconductivity, as seen in experiments. Additionally it behaves quite differently on varying $U$ in the superconducting state compared to the normal state.

Mott transition of fermions in anisotropic ruby lattice

<sec>In this work, the Hubbard model is adopted to describe fermions with on-site repulsive interaction and the nearest-neighbor hopping in anisotropic ruby lattice. The combination of cluster dynamical mean field theory and continuous-time quantum Monte Carlo algorithm is used to solve the theoretical model.</sec> <sec>It is widely accepted that the density of states and the double occupancy are two important quantities for determining the phase transition of two-dimensional strongly correlated system. Therefore, based on the self-consistent calculation, using the maximum entropy method to calculate the single particle density of states and double occupancy of fermions in anisotropic ruby lattice. Here in this work, there are 6 sites in a cluster.</sec> <sec>The influences of temperature, interaction and anisotropic parameter on metal-insulator phase transition of fermions in anisotropic ruby lattice are discussed based on the calculations of single particle density of state and double occupancy. Finally, the metal-Mott insulator phase diagram which shows the competition between temperature and on-site repulsive interaction in the phase transition of fermions in anisotropic ruby lattice is presented. The results shows that the system is in metallic state for the regime of weak interaction and low temperature, and the Mott insulator appears in the regime of strong interaction and high temperature. The metallic state and Mott insulating one are separated by the second-order transition line in the phase diagram.</sec>

Real-space cluster dynamical mean-field theory: Center-focused extrapolation on the one- and two particle-levels

We revisit the cellular dynamical mean-field theory (CDMFT) for the single-band Hubbard model on the square lattice at half filling, reaching real-space cluster sizes of up to 9×9 sites. Using benchmarks against direct lattice diagrammatic Monte Carlo at high temperature, we show that the self-energy obtained from a cluster center-focused extrapolation converges faster with the cluster size than the periodization schemes previously introduced in the literature. The same benchmark also shows that the cluster spin susceptibility can be extrapolated to the exact result at large cluster size, even though its spatial extension is larger than the cluster size.6 MoreReceived 11 March 2020Revised 14 July 2020Accepted 27 August 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033476Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsStrongly correlated systemsTechniquesDynamical mean field theoryHubbard modelCondensed Matter, Materials & Applied Physics