Many-body Techniques Research Articles

Luttinger liquid tensor network: Sine versus tangent dispersion of massless Dirac fermions

To apply the powerful many-body techniques of tensor networks to massless Dirac fermions, one wants to discretize the p·σ Hamiltonian and construct a matrix-product-operator (MPO) representation. We compare two alternative discretization schemes, one with a sine dispersion, the other with a tangent dispersion, applied to a one-dimensional Luttinger liquid with Hubbard interaction. Both types of lattice fermions allow for an exact MPO representation of low bond dimension, so they are efficiently computable, but only the tangent dispersion gives a power law decay of the propagator in agreement with the continuum limit: The sine dispersion is gapped by the interactions, evidenced by an exponentially decaying propagator. Our construction of a tensor network with an unpaired Dirac cone works around the fermion-doubling obstruction by exploiting the fact that the Hamiltonian of tangent fermions permits a generalized eigenproblem. Published by the American Physical Society 2024

First-principles calculation of Hubbard U for Terbium metal under high pressure

Using density functional theory (DFT) and linear response approaches, we compute the on-site Hubbard interaction U of elemental Terbium (Tb) metal in the pressure range ∼ 0–65 GPa. The resulting first-principles U values with experimental crystal structures enable us to examine the magnetic properties of Tb using a DFT+U method. The lowest-energy magnetic states in our calculations for different high-pressure Tb phases—including hcp, α-Sm, and dhcp—are found to be compatible with the corresponding magnetic ordering vectors reported in experiments. The result shows that the inclusion of Hubbard U substantially improves the accuracy and efficiency in modeling correlated rare-earth materials. Our study also provides the necessary U information for other quantum many-body techniques to study Tb under extreme pressure conditions.

Local and Nonlocal Electronic Correlations at the Metal-Insulator Transition in the Two-Dimensional Hubbard Model.

Elucidating the physics of the single-orbital Hubbard model in its intermediate-coupling regime is a key missing ingredient to our understanding of metal-insulator transitions in real materials. Using recent nonperturbative many-body techniques that are able to interpolate between the spin-fluctuation-dominated Slater regime at weak coupling and the Mott insulator at strong coupling, we obtain the momentum-resolved spectral function in the intermediate regime and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations in the formation of an insulating state. This allows us to identify the Slater and Heisenberg regimes in the phase diagram, which are separated by a crossover region of competing spatial and local electronic correlations. We identify the crossover regime by investigating the behavior of the local magnetic moment, shedding light on the formation of the insulating state at intermediate couplings.

Non-collinear magnetism driven by a hidden multipolar order in PrO2

Standard microscopic approach to magnetic orders is based on assuming a Heisenberg form for inter-atomic exchange interactions. These interactions are considered as the driving force for the ordering transition with magnetic moments serving as the primary order parameter. Any higher-rank multipoles appearing simultaneously with such magnetic order are typically treated as auxiliary order parameters rather than a principal cause of the transition. In this study, we show that these traditional assumptions are violated in the case of PrO2. Evaluating a full set of Pr-Pr superexchange interactions from a first-principles many-body technique we find that its unusual non-collinear 2k magnetic structure stems from high-rank multipolar interactions, and that the corresponding contribution of the Heisenberg interactions is negligible. The observed magnetic order in PrO2 is thus auxiliary to high-rank “hidden” multipoles. Within this picture we consistently account for previously unexplained experimental observations like the magnitude of exchange splitting and the evolution of magnetic structure in external field. Our findings challenge the standard paradigm of observable magnetic moments being the driving force for magnetic transitions.

Competition between Solvent···Solvent and Solvent···Solute Interactions in the Microhydration of the Tetrafluoroborate Anion, BF4-(H2O)n=1,2,3,4.

This study systematically examines the interactions of the tetrafluoroborate anion (BF4-) with up to four water molecules (BF4-(H2O)n=1,2,3,4). Full geometry optimizations and subsequent harmonic vibrational frequency computations are performed using a variety of density functional theory (DFT) methods (B3LYP, B3LYP-D3BJ, and M06-2X) and the MP2 ab initio method with a triple-ζ correlation consistent basis set augmented with diffuse functions on all non-hydrogen atoms (cc-pVTZ for H and aug-cc-pVTZ for B, O, and F; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the CCSD(T) ab initio method and the haTZ basis set for the mono- and dihydrate (n = 1, 2) structures. The 2-body:Many-body (2b:Mb) technique, in which CCSD(T) computations capture the 1- and 2-body contributions to the interactions and MP2 computations recover all higher-order contributions, was used to extend these demanding computations to the tri- and tetrahydrate (n = 3, 4) systems. Four, five, and eight new stationary points have been identified for the di-, tri-, and tetrahydrate systems, respectively. The global minimum of the monohydrate adopts a symmetric double ionic hydrogen bond motif with C2v symmetry and an electronic dissociation energy of 13.17 kcal mol-1 at the CCSD(T)/haTZ level of theory. This strong solvent···solute interaction, however, competes with solute···solute interactions in the lowest-energy BF4-(H2O)n=2,3,4 minima that are not seen in the other di-, tri-, or tetrahydrate minima. The latter interactions help increase the 2b:Mb dissociation energies to more than 26, 41, and 51 kcal mol-1 for n = 2, 3, and 4, respectively. Structures that form hydrogen bonds between the solvating water molecules also exhibit the largest shifts in the harmonic OH stretching frequencies for the waters of hydration. These shifts can exceed -280 cm-1 relative to an isolated H2O molecule at the 2b:Mb/haTZ level of theory.

Quantum Monte Carlo calculations in configuration space with three-nucleon forces

Neutron matter, through its connection to neutron stars as well as systems like cold atom gases, is one of the most interesting yet computationally accessible systems in nuclear physics. The Configuration-Interaction Monte Carlo (CIMC) method is a stochastic many-body technique allowing to tackle strongly coupled systems. In contrast to other Quantum Monte Carlo methods employed in nuclear physics, the CIMC method can be formulated directly in momentum space allowing for an efficient use of non-local interactions. In this work we extend CIMC method to include three-nucleon interactions through the normal-ordered two-body approximation. We present results for the equation of state of neutron matter in line with other many-body calculations that employ low resolution chiral interactions, and provide predictions for the momentum distribution and the static structure factor.

PyQMC: An all-Python real-space quantum Monte Carlo module in PySCF.

We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for a simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.

Slater transition methods for core-level electron binding energies.

Methods for computing core-level ionization energies using self-consistent field (SCF) calculations are evaluated and benchmarked. These include a "full core hole" (or "ΔSCF") approach that fully accounts for orbital relaxation upon ionization, but also methods based on Slater's transition concept in which the binding energy is estimated from an orbital energy level that is obtained from a fractional-occupancy SCF calculation. A generalization that uses two different fractional-occupancy SCF calculations is also considered. The best of the Slater-type methods afford mean errors of 0.3-0.4eV with respect to experiment for a dataset of K-shell ionization energies, a level of accuracy that is competitive with more expensive many-body techniques. An empirical shifting procedure with one adjustable parameter reduces the average error below 0.2eV. This shifted Slater transition method is a simple and practical way to compute core-level binding energies using only initial-state Kohn-Sham eigenvalues. It requires no more computational effort than ΔSCF and may be especially useful for simulating transient x-ray experiments where core-level spectroscopy is used to probe an excited electronic state, for which the ΔSCF approach requires a tedious state-by-state calculation of the spectrum. As an example, we use Slater-type methods to model x-ray emission spectroscopy.

Accumulative reservoir construction: Bridging continuously relaxed and periodically refreshed extended reservoirs

The simulation of open many-body quantum systems is challenging, requiring methods to both handle exponentially large Hilbert spaces and represent the influence of (infinite) particle and energy reservoirs. These two requirements are at odds with each other: Larger collections of modes can increase the fidelity of the reservoir representation but come at a substantial computational cost when included in numerical many-body techniques. An increasingly utilized and natural approach to control the growth of the reservoir is to cast a finite set of reservoir modes themselves as an open quantum system. There are, though, many routes to do so. Here, we introduce an accumulative reservoir construction -- an ARC -- that employs a series of partial refreshes of the extended reservoirs. Through this series, the representation accumulates the character of an infinite reservoir. This provides a unified framework for both continuous (Lindblad) relaxation and a recently introduced periodically refresh approach (i.e., discrete resets of the reservoir modes to equilibrium). In the context of quantum transport, we show that the phase space for physical behavior separates into discrete and continuous relaxation regimes with the boundary between them set by natural, physical timescales. Both of these regimes "turnover" into regions of over- and under-damped coherence in a way reminiscent of Kramers' crossover. We examine how the range of behavior impacts errors and the computational cost, including within tensor networks. These results provide the first comparison of distinct extended reservoir approaches, showing that they have different scaling of error versus cost (with a bridging ARC regime decaying fastest). Exploiting the enhanced scaling, though, will be challenging, as it comes with a substantial increase in (operator space) entanglement entropy.

Equilibrium and out-of-equilibrium realistic phonon self-energy free from overscreening

In model Hamiltonians, like Fr\"ohlich's, the electron-phonon interaction is assumed to be screened from the beginning. The same occurs when this interaction is obtained by using the state-of-the-art density functional perturbation theory as starting point. In this work I formally demonstrate that these approaches are affected by a severe overscreening error. By using an out-of-equilibrium many-body technique I discuss how to merge the many-body approach with density functional perturbation theory in order to correct the overscreening error. A symmetric statically screened phonon self-energy is obtained by downfolding the exact Baym-Kadanoff equations. The statically screened approximation proposed here is shown to have the same long-range spatial limit of the exact self-energy and to respect the fluctuation-dissipation theorem. The doubly screened approximation, commonly used in the literature, is shown, instead, to be overscreened, to violate several many-body properties and to have a wrong spatial long-range decay. The accuracy of the proposed approximation is tested against the exact solution of an extended model Fr\"ohlich Hamiltonian and it is applied to a paradigmatic material: ${\mathrm{MgB}}_{2}$. I find that the present treatment enhances the linewidths by $57%$ with respect to what has been previously reported for the anomalous ${E}_{2g}$ mode. I further discover that the ${A}_{2u}$ mode is also anomalous (its strong coupling being completely quenched by the overscreened expression). The present results deeply question methods based on state-of-the-art approaches and impact a wide range of fields such as thermal conductivity, phononic instabilities, and nonequilibrium lattice dynamics.

Quantification of electron correlation for approximate quantum calculations.

State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater-Jastrow wave functions.

First-principles study of the structural and electronic properties of BN-ring doped graphene

Since advanced silicon-based device components are moderately chemically tunable, doped graphene has emerged as a promising candidate to replace this semiconducting material in flexible miniaturized electronic devices. Indeed, heteroatom codoping (i.e., with boron and/or nitrogen) is an appealing strategy to tune both its structural and electronic properties, possibly inducing a band gap in graphene. However, presently synthesized BN-doped carbon-based materials are randomly doped, leading their electronic properties not to be reproducible. Using first-principles techniques, the present study investigates the periodic doping of graphene with borazine-like rings in order to search for an entirely new class of BNC hybrid 2D materials exhibiting high stabilities and optimized band gaps for optoelectronic applications. Ab initio calculations show that BN-ring doped graphene displays cohesive energies comparable with benchmark ideal periodic BNC systems (such as ${\mathrm{BC}}_{3}$ and ${\mathrm{BC}}_{2}\mathrm{N}$) with a decreasing linear trend toward high concentrations of BN rings. Band gaps of BN-ring doped graphene systems are calculated using many-body perturbation techniques and are found to be sensitive to the doping pattern and to be considerably larger for high concentration of BN rings exhibiting the same orientation. These predictions suggest that BN-ring doped graphene materials could be interesting candidates for the next generation of optoelectronic devices and open new opportunities for their synthesis using chemical bottom-up approaches.

Many-body analysis and spectroscopic characterization of diazene oligomers: A theoretical study

The present study reports the many-body analysis and spectroscopic characterization of linear and cyclic diazene oligomers in gas and water solvent states. The oligomers of diazene from monomer to pentamer have been considered for the study. The spectroscopic studies such as geometrical parameters, infrared spectra, electronic absorption spectra, and natural transition orbitals (NTOs) were reported. Many-body analysis techniques have been implemented to study the interactions among the diazene oligomers. These calculations have been performed using exchange and correlation functional (B3LYP) and 6–311++G (d,p) basis set. The geometrical parameters and infrared modes of monomer diazene in the gas state are well-matched with the available experimental determinations at this level of theory. A significant change in vibrational modes of linear and cyclic diazene oligomers has been observed in the gas phase-to-water solvent state. The time-dependent density functional theory (TD-DFT) has been used to calculate the electronic absorption spectra of diazene oligomers. The Wavelength of electronic transitions, oscillator strength, and HOMO to LUMO gap has been reported. Many-body analysis shows that two-, three-, four-, and five-body energies have a remarkable contribution to the binding energy in addition to relaxation energies. All these calculations have been performed using Gaussian 16 program package.

Fermionic interpretation of the quantum phase transition in XXZ magnets

Quantum phase transitions in quantum magnets constitute an important field that has attracted great interests. Although a variety of analytic and numerical methods have been introduced in this direction, faithful fermionic descriptions are still desired because they can transform the spin models to a form tractable by conventional many-body techniques, yielding more transparent physical pictures. We generalize the Chern-Simons fermionization approach and apply it to the XXZ quantum magnets. After fermionzation, the Ising interaction of the XXZ spin model leads to a fermion-fermion interaction. We show that the additional fermion-fermion interaction generates an interesting phase transition between two fermionic ordered states, i.e., the Chern-Simons superconductor and the Chern-Simons exciton insulator. We also demonstrate that this transition in the fermionic language essentially describes the quantum phase transition between the planar and out-of-plane N\'eel orders in the spin picture. The fermionic mean-field theory further leads to a nonlinear $\ensuremath{\sigma}$ model that describes the quantum phase transition, which is further supported by our density matrix renormalization group calculations in the original spin model. Our work introduces a fermionic interpretation of quantum phase transitions and advances the existing knowledge of quantum magnets.

Nonlocal correlation effects in fermionic many-body systems: Overcoming the noncausality problem

Motivated by the intriguing physics of quasi-two-dimensional fermionic systems, such as high-temperature superconducting oxides, layered transition metal chalcogenides, or surface or interface systems, the development of many-body computational methods geared at including both local and nonlocal electronic correlations has become a rapidly evolving field. It has been realized, however, that the success of such methods can be hampered by the emergence of noncausal features in the effective or observable quantities involved. Here, we present an approach wherein local many-body techniques such as dynamical mean-field theory (DMFT) are extended to nonlocal correlations and interactions, which preserves causality and has a physically intuitive interpretation. Our strategy has implications for the general class of DMFT-inspired many-body methods and can be adapted to cluster, dual boson, or dual fermion techniques with minimal effort.

Coexisting charge density wave and ferromagnetic instabilities in monolayer InSe

Recently fabricated InSe monolayers exhibit remarkable characteristics that indicate the potential of this material to host a number of many-body phenomena. In this work, we systematically describe collective electronic effects in hole-doped InSe monolayers using advanced many-body techniques. To this end, we derive a realistic electronic-structure model from first principles that takes into account the most important characteristics of this material, including a flat band with prominent van Hove singularities in the electronic spectrum, strong electron–phonon coupling, and weakly screened long-ranged Coulomb interactions. We calculate the temperature-dependent phase diagram as a function of band filling and observe that this system is in a regime with coexisting charge density wave and ferromagnetic instabilities that are driven by strong electronic Coulomb correlations. This regime can be achieved at realistic doping levels and high enough temperatures, and can be verified experimentally. We find that the electron–phonon interaction does not play a crucial role in these effects, effectively suppressing the local Coulomb interaction without changing the qualitative physical picture.

Magnetic correlations in infinite-layer nickelates: An experimental and theoretical multimethod study

We report a comprehensive study of magnetic correlations in ${\mathrm{LaNiO}}_{2}$, a parent compound of the recently discovered family of infinite-layer (IL) nickelate superconductors, using multiple experimental and theoretical methods. Our specific heat, muon-spin rotation ($\ensuremath{\mu}\mathrm{SR}$), and magnetic susceptibility measurements on polycrystalline ${\mathrm{LaNiO}}_{2}$ show that long-range magnetic order remains absent down to 2 K. Nevertheless, we detect residual entropy in the low-temperature specific heat, which is compatible with a model fit that includes paramagnon excitations. The $\ensuremath{\mu}\mathrm{SR}$ and low-field static and dynamic magnetic susceptibility measurements indicate the presence of short-range magnetic correlations and glassy spin dynamics, which we attribute to local oxygen nonstoichiometry in the average infinite-layer crystal structure. This glassy behavior can be suppressed in strong external fields, allowing us to extract the intrinsic paramagnetic susceptibility. Remarkably, we find that the intrinsic susceptibility shows non-Curie-Weiss behavior at high temperatures, in analogy to doped cuprates that possess robust nonlocal spin fluctuations. The distinct temperature dependence of the intrinsic susceptibility of ${\mathrm{LaNiO}}_{2}$ can be theoretically understood by a multimethod study of the single-band Hubbard model in which we apply complementary cutting-edge quantum many-body techniques (dynamical mean-field theory, cellular dynamical mean-field theory, and the dynamical vertex approximation) to investigate the influence of both short- and long-ranged correlations. Our results suggest a profound analogy between the magnetic correlations in parent (undoped) IL nickelates and doped cuprates.

Dynamical mean-field theory study of a ferromagnetic CrI3 monolayer

We have employed one of the well-known many-body techniques, density functional theory plus dynamical mean-field theory (DFT + DMFT), to investigate the electronic structure of ferromagnetic monolayer CrI3 as a function of temperature and hole-doping concentration. The computed magnetic susceptibility follows the Curie's law, indicating that the ferromagnetism of monolayer CrI3 originates from localized magnetic moments of Cr atoms rather than Stoner-type itinerant ones. The DFT + DMFT calculations show a different coherent temperature for each spin component, demonstrating apparent strong spin-dependent electronic correlation effects in monolayer CrI3. Furthermore, we have explored the doping-dependent electronic structure of monolayer CrI3 and found that its electronic and magnetic properties are easily tunable by the hole-doping.

First-principles modelling for time-resolved ARPES under different pump–probe conditions

First-principles methods for time-resolved angular resolved photoelectron spectroscopy play a pivotal role in providing interpretation and microscopic understanding of the complex experimental data and in exploring novel observables or observation conditions that may be achieved in future experiments. Here we describe an efficient, reliable and scalable first-principles method for tr-ARPES based on time-dependent density functional theory including propagation and surface effects usually discarded in the widely used many-body techniques based on computing the non-equilibrium spectral function and discuss its application to a variety of pump–probe conditions. We identify four conditions, depending on the length of the probe relative to the excitation in the materials on the one hand and on the overlap between pump and probe on the other hand. Within this paradigm different examples of observables of time-resolved ARPES are discussed in view of the newly developed and highly accurate time-resolved experimental spectroscopies.

Theoretical study of the electronic structure of hafnium (Hf,Z=72) and rutherfordium (Rf,Z=104) atoms and their ions: Energy levels and hyperfine-structure constants

Energy levels, magnetic dipole, and electric quadrupole hyperfine structure of the superheavy element rutherfordium (Rf, $Z$=104) and its first three ions are calculated using a combination of the configuration interaction, coupled-cluster single-doubles, and many-body perturbation theory techniques. The results are to be used in future interpretations of the measurements in terms of nuclear magnetic dipole and electric quadrupole momenta. To have a guide on the accuracy of the study, we perform similar calculations for hafnium (Hf, $Z$=72) and its ions. Hf is a lighter analog of Rf with a similar electronic structure. Good agreement with the experiment for Hf and with available previous calculations of the energy levels of Rf is demonstrated.