Quantum subspace-diagonalization methods, particularly Quantum Krylov Diagonalization (QKD), provide a promising route for computing low-energy spectra of quantum many-body Hamiltonians. However, existing quantum Krylov approaches rely on non-orthogonal Krylov bases, requiring overlap-matrix regularization that limits numerical stability and accuracy. In this work, we introduce an Orthogonal Quantum Krylov Diagonalization (OQKD) framework that reformulates the classical Lanczos recursion at the operator level, enabling an orthogonal quantum implementation of Krylov-subspace diagonalization. By expressing Lanczos vectors as polynomial transformations of the Hamiltonian, OQKD reproduces the orthogonality, tridiagonal structure, and convergence behavior of the classical Lanczos algorithm thus eliminating the need for overlap-matrix regularization. We further show that the required Lanczos polynomials can be implemented using block encoding and Generalized Quantum Signal Processing with the same asymptotic query complexity as Chebyshev-based QKD methods. Numerical simulations of the J_1–J_2 Heisenberg model confirm the classical Lanczos convergence and numerical stability of the proposed method, while the measurement-complexity scaling is established analytically. Building upon the OQKD framework, we then introduce a restarted state-preparation protocol that replaces a single high-degree polynomial transformation with a sequence of fixed low-degree transformations, maintaining an affordable block encoding success probability while retaining comparable convergence. These results establish OQKD as an orthogonal quantum analog of the classical Lanczos algorithm and identify the restarted protocol as a promising state-preparation strategy for Quantum Phase Estimation.

Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and Quantum Subspace Methods, offer practical solutions but face limitations in circuit depth and measurement overhead. In this article, we propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for the extraction of low-lying energy states. We show that, under certain conditions, our approach leads to a tridiagonal representation similar to that obtained with the Lanczos algorithm. The iterative process allows control over the trade-off between circuit depth, the number of variational parameters, and the number of measurements required to achieve the desired accuracy, making it suitable for current quantum hardware. As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.

The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges such as the lack of the Kohn–Sham scheme and the complexity of the pure N-representability conditions are still impeding its wild utilization. Fortunately, ensemble N-representability conditions derived in the natural orbital basis are known and trivial such that almost every functional of the 1-RDM is actually natural orbital functional, which does not perform well for all the correlation regimes. In this work, we propose a variational minimization scheme in the ensemble N-representable domain that is not restricted to the natural orbital representation of the 1-RDM. We show that splitting the minimization into the diagonal and off-diagonal parts of the 1-RDM can open the way toward the development of functionals of the orbital occupations, which remains a challenge for the generalization of site-occupation functional theory in chemistry. Our approach is tested on the uniform Hubbard model using the Müller and the Töws–Pastor functionals, as well as on the dihydrogen molecule using the Müller functional.

Mechanical degradation in electrode materials during successive electrochemical cycling is critical for battery lifetime and aging properties. A common strategy to mitigate electrode mechanical degradation is to suppress the volume variation induced by Li/Na intercalation/deintercalation, thereby designing strain-less electrodes. In this study, we investigate the electrochemically-induced volume variation in layered and spinel compounds used in Li-ion and Na-ion battery electrode materials through density functional theory computations. Specifically, we propose to decompose the volume variation into electronic, ionic, and structural contributions. Based on this analysis, we suggest methods to separately influence each contribution through strategies such as chemical substitution, doping, and polymorphism. Altogether, we conclude that volume variations can be controlled by designing either mechanically hard or compact electrode materials.

Quantum Chemistry and Physics have been pinpointed as killer applications for quantum computers, and quantum algorithms have been designed to solve the Schrödinger equation with the wavefunction formalism. It is yet limited to small systems, as their size is dictated by the number of qubits available. Computations on large systems rely mainly on mean-field-type approaches such as density functional theory, for which no quantum advantage has been envisioned so far. In this work, we question this a priori by proposing a counter-intuitive mapping from the non-interacting to an auxiliary interacting Hamiltonian that may provide the desired advantage.

The performance of embedding methods is directly tied to the quality of the bath orbital construction. In this paper, we develop a versatile framework, enabling the investigation of the optimal construction of the orbitals of the bath. As of today, in state-of-the-art embedding methods, the orbitals of the bath are constructed by performing a Singular Value Decomposition (SVD) on the impurity-environment part of the one-body reduced density matrix, as originally presented in Density Matrix Embedding Theory. Recently, the equivalence between the SVD protocol and the use of unitary transformation, the so-called Block-Householder transformation, has been established. We present a generalization of the Block-Householder transformation by introducing additional flexible parameters. The additional parameters are optimized such that the bath-orbitals fulfill physically motivated constraints. The efficiency of the approach is discussed and exemplified in the context of the half-filled Hubbard model in one-dimension.

In this work, we introduce an original self-consistent scheme based on the one-body reduced density matrix ($\gamma$) formalism. A significant feature of this methodology is the utilization of an optimal unitary transformation of the Hamiltonian, determined through a self-consistently determined, unitary reflection $\mathbf{R}[\gamma]$. This enables the extraction of all reduced properties of the system from a smaller, accurately solved embedding cluster, and to systematically reconstruct the reduced density matrix of the system. This process ensures that both extended and embedded systems satisfy the local virial-like relation, providing quantitative insight into the correspondence between the fragment in the extended system and its embedded analogue. The performance and convergence of the method, as well as the N-representability of the resulting correlated density matrix, are evaluated and discussed within the context of the one-dimensional Hubbard model, which provides exact results for a comprehensive comparison.

We derive recursive relations for the Schrieffer--Wolff (SW) transformation applied to the half-filled Hubbard dimer. While the standard SW transformation is set to block-diagonalize the transformed Hamiltonian solely at the first order of perturbation, we infer from recursive relations two types of modifications, variational or iterative, that approach, or even enforce for the homogeneous case, the desired block-diagonalization at infinite order of perturbation. The modified SW unitary transformations are then used to design an test quantum algorithms adapted to the noisy and fault-tolerant era. This work paves the way toward the design of alternative quantum algorithms for the general Hubbard Hamiltonian.

Quantum embedding is a divide and conquer strategy that aims at solving the electronic Schrödinger equation of sizeable molecules or extended systems. We establish in the present work a clearer and in-principle-exact connection between density matrix embedding theory (DMET) and density-functional theory (DFT) within the simple but nontrivial one-dimensional Hubbard model. For that purpose, we use our recent reformulation of single-impurity DMET as a Householder transformed density-matrix functional embedding theory (Ht-DMFET). On the basis of well-identified density-functional approximations, a self-consistent local potential functional embedding theory (LPFET) is formulated and implemented. Combining both LPFET and DMET numerical results with our formally exact density-functional embedding theory reveals that a single statically embedded impurity can in principle describe the density-driven Mott–Hubbard transition, provided that a complementary density-functional correlation potential (which is neglected in both DMET and LPFET) exhibits a derivative discontinuity (DD) at half filling. The extension of LPFET to multiple impurities (which would enable to circumvent the modeling of DDs) and its generalization to quantum chemical Hamiltonians are left for future work.

First-principles calculations are conducted to investigate the magnetic properties of the Na2IrO3 compounds. We reveal that the Na2IrO3's local structural distortions are essential for an accurate description of the magnetism of such systems. They provide a feasible explanation for the experimentally observed antiferromagnetic zigzag magnetic ground state. We demonstrate that the underlying competition between the spin-orbit coupling and the crystal-field splitting rules the crystal structure and profoundly influences the strength of the magnetic exchange interactions. We unambiguously identify that the D-4h-type distortions, due to the Jahn-Teller effect, are disclosed in an elongation along the IrO6 polyhedra's apical axis in the ac plane. On the other hand, the Jr atoms off-centering in the basal plane (perpendicular to the local D-4h elongation axis) arises owing to an inhomogeneous cationic charge distribution of Ir4+/Na+ in the transition-metal layer resulting in both effects being decisive in controlling the magnetism of Na2IrO3 together with the spin-orbit interactions.

Recently, some of the authors introduced the use of the Householder transformation as a simple and intuitive method for embedding local molecular fragments [see Sekaran et al., Phys. Rev. B 104, 035121 (2021) and Sekaran et al., Computation 10, 45 (2022)]. In this work, we present an extension of this approach to the more general case of multi-orbital fragments using the block version of the Householder transformation applied to the one-body reduced density matrix, unlocking the applicability to general quantum chemistry/condensed matter physics Hamiltonians. A step-by-step construction of the block Householder transformation is presented. Both physical and numerical areas of interest of the approach are highlighted. The specific mean-field (noninteracting) case is thoroughly detailed as it is shown that the embedding of a given N spin-orbital fragment leads to the generation of two separated sub-systems: (1) a 2N spin-orbitals "fragment+bath" cluster that exactly contains N electrons and (2) a remaining cluster's "environment" described by so-called core electrons. We illustrate the use of this transformation in different cases of embedding scheme for practical applications. We particularly focus on the extension of the previously introduced Local Potential Functional Embedding Theory and Householder-transformed Density Matrix Functional Embedding Theory to the case of multi-orbital fragments. These calculations are realized on different types of systems, such as model Hamiltonians (Hubbard rings) and ab initio molecular systems (hydrogen rings).

High purity polycrystalline Na0.5La0.5RuO3 was synthesized by a solid state method, and its properties were studied by magnetic susceptibility, heat capacity and resistivity measurements. We find it to be a tetragonal perovskite, in contrast to an earlier report, with random La/Na mixing. With a Curie-Weiss temperature of -231 K and effective moment of 2.74 uB/mol-Ru, there is no magnetic ordering down to 1.8 K. A broad hump at 1.4 K in the heat capacity, however, indicates the presence of a glassy magnetic transition, which we attribute to the influence of the random distribution of Na and La on the perovskite A sites. Comparison to CaRuO3, a structurally ordered ruthenate perovskite with similar properties, is presented. First-principle calculations indicate that the Na-La distribution determines the local magnetic exchange inter-actions between Ru ions, favoring either antiferromagnetic or ferromagnetic coupling when the local environment is Na or La rich. Thus our data and analysis suggest that mixing cations with different charges and sizes on the A site in this perovskite results in magnetic frustration through a balance of local magnetic exchange interactions.

Quantum embedding based on the (one-electron reduced) density matrix is revisited by means of the unitary Householder transformation. While being exact and equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the non-interacting case, the resulting Householder transformed density matrix functional embedding theory (Ht-DMFET) preserves, by construction, the single-particle character of the bath when electron correlation is introduced. In Ht-DMFET, the projected"impurity+bath"cluster's Hamiltonian (from which approximate local properties of the interacting lattice can be extracted) becomes an explicit functional of the density matrix. In the spirit of single-impurity DMET, we consider in this work a closed (two-electron) cluster constructed from the full-size non-interacting density matrix. When the (Householder transformed) interaction on the bath site is taken into account, per-site energies obtained for the half-filled one-dimensional Hubbard lattice match almost perfectly the exact Bethe Ansatz results in all correlation regimes. In the strongly correlated regime, the results deteriorate away from half-filling. This can be related to the electron number fluctuations in the (two-site) cluster which are not described neither in Ht-DMFET nor in regular DMET. As expected, the per-site energies dramatically improve when increasing the number of embedded impurities. Formal connections with density/density matrix functional theories have been briefly discussed and should be explored further. Work is currently in progress in this direction.

The increasing need for sustainable energy storage has rekindled interest for Na-ion batteries. Their energy density can be enhanced using anionic redox (AR), as reported in Na-deficient P2 phases. Contrary to their Li-rich counterparts with O3 stacking, these Na-deficient P2 phases show surprisingly good structural stability during AR. Understanding the fundamental relationship between O and P stacking and AR reversibility thus becomes critical. Herein, using density functional theory (DFT) analysis and modeling of O2- and P2-Na2∕3Mg1∕3Mn2∕3O2, we show that during AR, the oxygen network is stabilized through either (1) a highly reversible collective distortion, in P stacking, or (2) a disproportionation of oxygen pairs leading to voltage hysteresis, in O stacking. Using this 2-distortions model, we describe a magnetic-constrained DFT methodology to predict the critical state of charge for reversible cycling that we successfully extend to other Mn-based cathodes. This article provides fundamental understanding, powerful computational methods, and practical guidelines to design next-generation cathode materials.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

The capacity of Li‐ion cathode materials has recently been greatly improved by the feasibility to trigger both cationic and anionic redox reactions within the same material. This concept has rapidly been implemented to Na‐ion batteries to boost their energy density. The electrochemical properties of Na 3 RuO 4 with Li 3 RuO 4 are reported and compared herein. Strikingly, it is found that 3 Na can be extracted from Na 3 RuO 4 with the charge compensation mechanism enlisting first the oxidation of Ru 5+ to Ru 6+ , leading to Na 2 RuO 4 , and then the oxidation of oxygen during the rest of the charge. This drastically contrasts with the behavior of the Li counterpart since Ru never reaches that high oxidation state during lithium removal. By comparing the phase diagrams of A x RuO 4 (A being Li, Na, or K) together with density functional theory calculations, this finding is rationalized and it is demonstrated that this difference is mainly rooted in the size of the alkali cation. The bigger the alkali, the lower the coordination of Ru will be, stabilized by the same higher oxidation states. This work highlights the difference between Li and Na materials toward anionic redox and suggests the unusual coexistence of Ru 6+ and (O 2 ) n − , hence setting new challenges to theoreticians and opening opportunities for materials design.

Anionic redox in Li-rich and Na-rich transition metal oxides (A-rich-TMOs) has emerged as a new paradigm to increase the energy density of rechargeable batteries. Ever since, numerous electrodes delivering extra anionic capacity beyond the theoretical cationic capacity have been reported. Unfortunately, most often the anionic capacity achieved in charge is partly irreversible in discharge. A unified picture of anionic redox in A-rich-TMOs is designed here to identify the electronic origin of this irreversibility and to propose new directions to improve the cycling performance of the electrodes. The electron localization function is introduced as a holistic tool to unambiguously locate the oxygen lone pairs in the structure and follow their participation in the redox activity of A-rich-TMOs. The charge-transfer gap of transition metal oxides is proposed as the pertinent observable to quantify the amount of extra capacity achievable in charge and its reversibility in discharge, irrespective of the material chemical composition. From this generalized approach, we conclude that the reversibility of the anionic capacity is limited to a critical number of O holes per oxygen, hO ≤ 1/3.

Disordered rock salt cathodes showing both anionic and cationic redox are being extensively studied for their very high energy storage capacity. Mn-based disordered rock salt compounds show much higher energy efficiency compared to the Ni-based materials as a result of the different voltage hysteresis, 0.5 and 2 V, respectively. To understand the origin of this difference, we herein report the design of two model compounds, Li1.3Ni0.27Ta0.43O2 and Li1.3Mn0.4Ta0.3O2, and study their charge compensation mechanism through the uptake and removal of Li via an arsenal of analytical techniques. We show that the different voltage hysteresis with Ni or Mn substitution is due to the different reduction potential for anionic redox. We rationalized such a finding by DFT calculations and propose this phenomenon to be nested in the smaller charge transfer band gap of the Ni-based compounds compared to that of the Mn ones. Altogether, these findings provide vital guidelines for designing high-capacity disordered rock salt cathode materials based on anionic redox activity for the next generation of Li ion batteries.