arXiv subjects

Lucas K. Wagner

Publications and source records attributed to Lucas K. Wagner.

At least 19 recordsLinked to original sources

arXiv2026

Effects of the surface on double surface Fermi arcs in a realistic tight-binding model of Na$_3$Bi (100)

Na$_3$Bi is a topological Dirac semimetal (TDSM) that can support double surface Fermi arcs (DSFAs), which are important for its material classification and their potential use in spintronic devices. However, it is unclear how the surfaces affect realistic Na$_3$Bi (100) systems. To investigate the effects of diverse surfaces on DSFAs, we consider first principles derived tight-binding models of two Na$_3$Bi (100) terminations. On the stoichiometric termination, we find DSFAs as expected. On the non-stoichiometric structure there are DSFAs on one termination and two loops that retain many of the properties of DSFAs. Thus, the local properties such as spin momentum locking and hybridization with the Dirac points appear to be more robust than their global connectivity. That is, the surface can reshape the arc fingerprint without destroying the arc-like physics.

cond-mat.mtrl-sci↗

arXiv2026

Quantum Monte Carlo assessment of embedding for for strongly correlated defects: interplay between mean-field starting point and interactions

Point defects are of interest for many applications, from quantum sensing to modifying bulk properties of materials. Because of their localized orbitals, the electronic states are often strongly correlated, which has led to a proliferation of quantum embedding techniques to treat this correlation. In these techniques, most of the one-body states are treated with a weakly correlated theory such as density functional theory, and certain one-body states are singled out as an active space to be treated using an effective interaction. We assess these techniques for iron and chromium defects in aluminum nitride using quantum Monte Carlo (QMC) calculations on identical Hamiltonians. For these systems, we find the dominant errors in the embedding arise from the one-body crystal-field splitting in the d orbitals inherited from density functional theory (DFT), rather than double counting corrections, with the screened interactions also affected by the DFT orbitals. Strikingly, the best double counting recipe is opposite in these two cases. Because excitation energies can agree while the underlying wave functions do not, diagnosing these errors requires detailed information about the many-body wave functions, which QMC provides.

cond-mat.str-el↗

arXiv2026

Excited state optimization for strongly correlated quantum defects using ensemble variational Monte Carlo

Using the recently introduced ensemble variational Monte Carlo (VMC), we study optimized wave functions for strongly correlated point defects, including nitrogen-vacancy and silicon-vacancy centers in diamond and substitutional iron and chromium impurities in aluminum nitride. We study the effects of fully optimized determinant expansion parameters, orbitals, and Jastrow correlation factors on these systems. We find that orbitals from the hybrid functional PBE0 are much better (have lower objective functional) than semilocal PBE, which results in changes in the excitation energies up to 0.5 eV. Further improvements can be made by directly optimizing the objective functional, resulting in changes in excitation energies up to 0.2 eV. The most important parameter varies from defect to defect, reinforcing the necessity of optimizing all parameters to obtain accurate excited states in strongly correlated defects.

cond-mat.str-el↗

arXiv2025

Particle-hole asymmetric phases in doped twisted bilayer graphene

Despite much theoretical work, developing a comprehensive ab initio model for twisted bilayer graphene (TBG) has proven challenging due to the inherent trade-off between accurately describing the band structure and incorporating the interactions within the Hamiltonian, particularly given the topological obstruction -- so-called fragile topology -- to the description of the model in terms of localized symmetric Wannier functions within the flat band manifold. Here, we circumvent this obstruction by using an extended 8-orbital model, for which localized Wannier orbitals have been formulated by Carr et al. [1]. We constructed an extended multi-orbital Hubbard model, and performed Hartree-Fock (HF) calculations to explore its phase diagram across commensurate fillings from -3 to 3. We found several nearly-degenerate insulating states at charge neutrality, all of which exhibit orbital orders. Crucially, TBG near magic angle is known to be particle-hole asymmetric, which is naturally captured by the single-particle band structure of our model and is reflected in the distinction between the symmetry broken states obtained at electron and hole dopings away from the charge neutral point. At filling -1 and +2, quantum anomalous hall states are obtained, while for the rest of the integer fillings away from charge neutrality, we found the system to realize metallic states with various orbital, valley and spin orderings. We also observed that most of the Hartree--Fock ground states exhibit a generalized valley Hund's-like rule, resulting in valley polarization. Importantly, we show that the incorporation of the intra-valley and inter-valley exchange interactions is crucial to properly stabilize the ordered symmetry-broken states. In agreement with experiments, we find significant particle-hole asymmetry, which underscores the importance of using particle-hole asymmetric models.

cond-mat.str-el↗

arXiv2025

Expressivity of determinantal ansatzes for neural network wave functions

Neural network wave functions have shown promise as a way to achieve high accuracy on the many-body quantum problem. These wave functions most commonly use a determinant or sum of determinants to antisymmetrize many-body orbitals which are described by a neural network. In many cases, the wave function is projected onto a fixed-spin state. Such a treatment is allowed for spin-independent operators; however, it cannot be applied to spin-dependent problems, such as Hamiltonians containing spin-orbit interactions. We show that for spin-independent Hamiltonians, a strict upper bound property is obeyed between a traditional Hartree-Fock like determinant, full spinor wave function, the full determinant wave function, and a generalized spinor wave function. The relationship between a spinor wave function and the full determinant arises because the full determinant wave function is the spinor wave function projected onto a fixed-spin, after which antisymmetry is implicitly restored in the spin-independent case. For spin-dependent Hamiltonians, the full determinant wave function is not applicable, because it is not antisymmetric. Numerical experiments on the H$_3$ molecule and two-dimensional homogeneous electron gas confirm the bounds.

cond-mat.str-el↗

arXiv2025

Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer

Fixed-node diffusion quantum Monte Carlo (FN-DMC) is a widely-trusted many-body method for solving the Schrödinger equation, known for its reliable predictions of material and molecular properties. Furthermore, its excellent scalability with system complexity and near-perfect utilization of computational power makes FN-DMC ideally positioned to leverage new advances in computing to address increasingly complex scientific problems. Even though the method is widely used as a computational gold standard, reproducibility across the numerous FN-DMC code implementations has yet to be demonstrated. This difficulty stems from the diverse array of DMC algorithms and trial wave functions, compounded by the method's inherent stochastic nature. This study represents a community-wide effort to assess the reproducibility of the method, affirming that: Yes, FN-DMC is reproducible (when handled with care). Using the water-methane dimer as the canonical test case, we compare results from eleven different FN-DMC codes and show that the approximations to treat the non-locality of pseudopotentials are the primary source of the discrepancies between them. In particular, we demonstrate that, for the same choice of determinantal component in the trial wave function, reliable and reproducible predictions can be achieved by employing the T-move (TM), the determinant locality approximation (DLA), or the determinant T-move (DTM) schemes, while the older locality approximation (LA) leads to considerable variability in results. These findings demonstrate that, with appropriate choices of algorithmic details, fixed-node DMC is reproducible across diverse community codes-highlighting the maturity and robustness of the method as a tool for open and reliable computational science.

physics.comp-ph↗

arXiv2025

Graphene-hBN interlayer interactions from quantum Monte Carlo

The interaction between graphene and hexagonal boron nitride (hBN) plays a pivotal role in determining the electronic and structural properties of graphene-based devices. In this work, we employ quantum Monte Carlo (QMC) to study the interlayer interactions and stacking-fault energy (SFE) between graphene and hBN. We generated QMC energies for several rigid bilayer stacking configurations and fitted these data to the Kolmogorov-Crespi type interlayer potential (ILP) model. Our QMC-derived potential offers a more reliable alternative to conventional density functional theory methods, which are prone to errors in predicting properties in van der Waals materials. This study enables highly accurate predictions of structural and electronic properties in graphene hBN heterostructures. The resulting ILP-QMC potential is made available for further use in simulating complex systems, such as twisted bilayer graphene (TBG) on hBN.

cond-mat.mtrl-sci↗

arXiv2025

Renormalized density matrix downfolding: A rigorous framework in learning emergent models from ab initio many-body calculations

We present a generalized framework, renormalized density matrix downfolding (RDMD), to derive systematically improvable, highly accurate, and nonperturbative effective models from ab initio calculations. This framework moves beyond the common role of ab initio calculations as calculating the parameters of a proposed Hamiltonian. Instead, RDMD provides the capability to decide whether a given effective Hilbert space can be identified from the ab initio data and assess the relative quality of ansatz Hamiltonians. Any method of ab initio solution can be used as a data source, and as the ab initio solutions improve, the resultant model also improves. We demonstrate the framework in an application to the downfolding of a hydrogen chain to a spin model, in which we find the interatomic separations for which a nonperturbative mapping can be made even in the strong coupling regime where standard methods fail, and compute a renormalized spin model Hamiltonian that quantitatively reproduces the ab initio dynamics.

cond-mat.str-el↗

arXiv2024

Capturing spin fluctuations in CaCuO$_2$: $\textit{Ab initio}$ QMC calculations with multi-determinant wave functions

We present an advanced $\textit{ab initio}$ quantum Monte Carlo (QMC) calculation of the ground state of undoped CaCuO$_2$. We extend the traditional single-determinant Slater-Jastrow approach to include multi-determinant wave functions, inhomogeneous Jastrow factors, and orbital optimization. Our results demonstrate not only an improvement in the variational bound of the ground state energy -- 2.3 eV per formula unit lower than previous state of the art techniques -- but also confirm the presence of spin fluctuations in multi-determinant wave functions in a strongly correlated cuprate system, which is integral to understanding high-$T_c$ superconductivity. This is the first demonstration of capturing spin fluctuations in QMC wave functions on a cuprate, establishing the groundwork for new studies on doped cuprates in the superconducting state, where spin fluctuations require more accurate characterization.

cond-mat.str-el↗

arXiv2024

Downfolding from Ab Initio to Interacting Model Hamiltonians: Comprehensive Analysis and Benchmarking of the DFT+cRPA Approach

Model Hamiltonians are regularly derived from first-principles data to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited state energies and wavefunctions using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double counting correction diminishes the quality. Background screening to the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians

cond-mat.str-el↗

arXiv2023

Ensemble variational Monte Carlo for optimization of correlated excited state wave functions

Variational Monte Carlo methods have recently been applied to the calculation of excited states; however, it is still an open question what objective function is most effective. A promising approach is to optimize excited states using a penalty to minimize overlap with lower eigenstates, which has the drawback that states must be computed one at a time. We derive a general framework for constructing objective functions with minima at the the lowest $N$ eigenstates of a many-body Hamiltonian. The objective function uses a weighted average of the energies and an overlap penalty, which must satisfy several conditions. We show this objective function has a minimum at the exact eigenstates for a finite penalty, and provide a few strategies to minimize the objective function. The method is demonstrated using ab initio variational Monte Carlo to calculate the degenerate first excited state of a CO molecule.

physics.comp-ph↗

arXiv2023

Registry-dependent potential energy and lattice corrugation of twisted bilayer graphene from quantum Monte Carlo

An uncertainty in studying twisted bilayer graphene (TBG) is the minimum energy geometry, which strongly affects the electronic structure. The minimum energy geometry is determined by the potential energy surface, which is dominated by van der Waals (vdW) interactions. In this work, large-scale diffusion quantum Monte Carlo (QMC) simulations are performed to evaluate the energy of bilayer graphene at various interlayer distances for four stacking registries. An accurate registry-dependent potential is fit to the QMC data and is used to describe interlayer interactions in the geometry of near-magic-angle TBG. The band structure for the optimized geometry is evaluated using the accurate local-environment tight-binding model. We find that compared to QMC, DFT-based vdW interactions can result in errors in the corrugation magnitude by a factor of 2 or more near the magic angle. The error in corrugation then propagates to the flat bands in twisted bilayer graphene, where the error in corrugation can affect the bandwidth by about 30\% and can change the nature and degeneracy of the flat bands.

cond-mat.mes-hall↗

arXiv2022

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 simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.

cond-mat.mtrl-sci↗

arXiv2022

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 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, the authors 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 the evaluation of 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 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.

physics.chem-ph↗

arXiv2022

Revisiting the Dark Matter Interpretation of Excess Rates in Semiconductors

In light of recent results from low-threshold dark matter detectors, we revisit the possibility of a common dark matter origin for multiple excesses across numerous direct detection experiments, with a focus on the excess rates in semiconductor detectors. We explore the interpretation of the low-threshold calorimetric excess rates above 40 eV in the silicon SuperCDMS Cryogenic Phonon Detector and above 100 eV in the germanium EDELWEISS Surface detector as arising from a common but unknown origin, and demonstrate a compatible fit for the observed energy spectra in both experiments, which follow a power law of index $α= 3.43^{+0.11}_{-0.06}$. Despite the intriguing scaling of the normalization of these two excess rates with approximately the square of the mass number $A^2$, we argue that the possibility of common origin by dark matter scattering via nuclear recoils is strongly disfavored, even allowing for exotic condensed matter effects in an as-yet unmeasured kinematic regime, due to the unphysically-large dark matter velocity required to give comparable rates in the different energy ranges of the silicon and germanium excesses. We also investigate the possibility of inelastic nuclear scattering by cosmic ray neutrons, solar neutrinos, and photons as the origin, and quantitatively disfavor all three based on known fluxes of particles.

hep-ph↗

arXiv2021

Excited states in variational Monte Carlo using a penalty method

The authors present a technique using variational Monte Carlo to solve for excited states of electronic systems. The technique is based on enforcing orthogonality to lower energy states, which results in a simple variational principle for the excited states. Energy optimization is then used to solve for the excited states. This technique is applied to the well-characterized benzene molecule, in which $\sim$10,000 parameters are optimized for the first 12 excited states. Agreement within approximately 0.2 eV is obtained with higher scaling coupled cluster methods; small disagreements with experiment are likely due to vibrational effects.

physics.chem-ph↗

arXiv2021

An accurate tight binding model for twisted bilayer graphene describes topological flat bands without geometric relaxation

A major hurdle in understanding the phase diagram of twisted bilayer graphene (TBLG) are the roles of lattice relaxation and electronic structure on isolated band flattening near magic twist angles. In this work, the authors develop an accurate local environment tight binding model (LETB) fit to tight binding parameters computed from $ab\ initio$ density functional theory (DFT) calculations across many atomic configurations. With the accurate parameterization, it is found that the magic angle shifts to slightly lower angles than often quoted, from around 1.05$^\circ$ to around 0.99$^\circ$, and that isolated flat bands appear for rigidly rotated graphene layers, with enhancement of the flat bands when the layers are allowed to distort. Study of the orbital localization supports the emergence of fragile topology in the isolated flat bands without the need for lattice relaxation.

cond-mat.mes-hall↗

arXiv2021

Identifying materials with charge-spin physics using charge-spin susceptibility computed from first principles

The authors present a quantity termed charge-spin susceptibility, which measures the charge response to spin degrees of freedom in strongly correlated materials. This quantity is simple to evaluate using both standard density functional theory and many-body electronic structure techniques, enabling comparison between different levels of theory. A benchmark on 28 layered magnetic materials shows that large values of charge-spin susceptibility correlate with unconventional ground states such as disordered magnets and unconventional superconductivity.

cond-mat.supr-con↗