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Context: In the realm of quantum chemistry, the accurate prediction of electronic structure and properties of nanostructures remains a formidable challenge. Density functional theory (DFT) and density matrix renormalization group (DMRG) have emerged as two powerful computational methods for addressing electronic correlation effects in diverse molecular systems. We compare ground-state energies ( e 0 ), density profiles ( n ), and average entanglement entropies ( S ¯ ) in metals, insulators and at the transition from metal to insulator, in homogeneous, superlattices, and harmonically confined chains described by the fermionic one-dimensional Hubbard model. While for the homogeneous systems, there is a clear hierarchy between the deviations, D % (S ¯) < D % (e 0) < D ¯ % (n) , and all the deviations decrease with the chain size; for superlattices and harmonic confinement, the relation among the deviations is less trivial and strongly dependent on the superlattice structure and the confinement strength considered. For the superlattices, in general, increasing the number of impurities in the unit cell represents lower precision in the DFT calculations. For the confined chains, DFT performs better for metallic phases, while the highest deviations appear for the Mott and band-insulator phases. This work provides a comprehensive comparative analysis of these methodologies, shedding light on their respective strengths, limitations, and applications. Methods: The DFT calculations were performed using the standard Kohn-Sham scheme within the BALDA approach. It integrated the numerical Bethe-Ansatz (BA) solution of the Hubbard model as the homogeneous density functional within a local-density approximation (LDA) for the exchange-correlation energy. The DMRG algorithms were implemented using the ITensor library, which is based on the matrix product states (MPS) ansatz. The calculations were performed until the energy reaches convergence of at least 10 - 8 . [ABSTRACT FROM AUTHOR]

All-electron electronic structure methods based on the linear combination of atomic orbitals method with Gaussian basis set discretization offer a well established, compact representation that forms much of the foundation of modern correlated quantum chemistry calculations - on both classical and quantum computers. Despite their ability to describe essential physics with relatively few basis functions, these representations can suffer from a quartic growth of the number of integrals. Recent results have shown that, for some quantum and classical algorithms, moving to representations with diagonal two-body operators can result in dramatically lower asymptotic costs, even if the number of functions required increases significantly. We introduce a way to interpolate between the two regimes in a systematic and controllable manner, such that the number of functions is minimized while maintaining a block-diagonal structure of the two-body operator and desirable properties of an original, primitive basis. Techniques are analyzed for leveraging the structure of this new representation on quantum computers. Empirical results for hydrogen chains suggest a scaling improvement from O(N 4.5) in molecular orbital representations to O(N 2.6) in our representation for quantum evolution in a fault-tolerant setting, and exhibit a constant factor crossover at 15 to 20 atoms. Moreover, we test these methods using modern density matrix renormalization group methods classically, and achieve excellent accuracy with respect to the complete basis set limit with a speedup of 1-2 orders of magnitude with respect to using the primitive or Gaussian basis sets alone. These results suggest our representation provides significant cost reductions while maintaining accuracy relative to molecular orbital or strictly diagonal approaches for modest-sized systems in both classical and quantum computation for correlated systems.

In this paper, we investigate the convergence properties of density matrix renormalisation group (DMRG) calculations for vertical electronic excitations performed on three bimolecular complexes motivated by Szalay's recent benchmark results [JCTC. 2020;16:7]. Besides the high-level coupled-cluster reference spectrum, the extrapolated truncation-free DMRG results are compared against several alternative solutions based on multireference configuration interaction and coupled-cluster theories. By taking advantage of the error cancellation effects, which are inherent in the state-averaged computational scheme, we demonstrate that the extrapolated solution based on only low bond-dimensional DMRG data could already provide quantitative predictions even for large active spaces. We also show that orbital optimisation improves further the accuracy of the DMRG results which systematically approach the excitation energies of coupled cluster single-double-triple at similar computational costs. [ABSTRACT FROM AUTHOR]

One of the most powerful and popular quantum entanglement-based computation methods for the simulation of one-dimensional and quasi-two-dimensional strongly correlated materials is the Density Matrix Renormalization Group (DMRG) technique. A lower quantum entanglement between the system’s degrees of freedom will result in a higher accuracy of the method. However, quantum entanglement between two complementary subsystems of a closed system depends on how the degrees of freedom have been distributed between them, and therefore, it is not in general invariant under arbitrary unitary transformations. Entanglement is invariant only under those unitary transformations which do not mix the degrees of freedom associated with the two subsystems. Consequently, a fundamental question is that if it is possible to construct, algorithmically, unitary transformations which minimize entanglement between degrees of freedom of the system and therefore maximize the DMRG technique? A general solution to this problem is highly nontrivial in general. In this paper, we study interacting fermionic models and by considering single-particle unitary transformations only. We define a novel and efficient method to find the optimal single-particle unitary transformations. In this framework, we show that using our algorithm, the accuracy of the DMRG method at a given bond dimension is increased and the ground-state energy is decreased and approaches to its exact value. Our method paves the way toward finding more general (many-particle) optimized unitary transformations and helps us to better understand the behavior of fermions in strongly correlated materials.

In this paper, the spin ladder consisting of two antiferromagnetic Heisenberg legs is investigated by means of the density matrix renormalization group method with its matrix product state form. The energy density and bipartite entanglement measured by concurrence are calculated, the effects of interleg couplings and open boundary condition on entanglement distributions are discussed in detail when the interleg couplings are ferro- and antiferromagnetic, respectively. We found that the entanglements are mainly distributed in legs and diagonals when the interleg couplings are ferromagnetic and in rungs when the couplings are antiferromagnetic. Furthermore, the intraleg entanglements are more affected by the dimerization caused by open boundary than interleg ones. Specifically, that dimerization will be weakened by the interleg couplings, and the entanglements are distributed more uniformly. [ABSTRACT FROM AUTHOR]

The simulations of spectroscopy and quantum dynamics are of vital importance to the understanding of the electronic processes in complex systems, including the radiative/radiationless electronic relaxation relevant for optical emission, charge/energy transfer in molecular aggregates related to carrier mobility in organic materials, as well as photovoltaic and thermoelectric conversion, light‐harvesting and spin transport, and so forth. In recent years, time‐dependent density matrix renormalization group (TD‐DMRG) has emerged as a general, numerically accurate and efficient method for high‐dimensional full‐quantum dynamics. This review will cover the fundamental algorithms of TD‐DMRG in the modern framework of matrix product states (MPS) and matrix product operators (MPO), including the basic algebra with respect to MPS and MPO, the novel time evolution schemes to propagate MPS, and the automated MPO construction algorithm to encode generic Hamiltonian. Most importantly, the proposed method can handle the mixed state density matrix at finite temperature, enabling quantum statistical description for molecular aggregates. We demonstrate the performance of TD‐DMRG by benchmarking with the current state‐of‐the‐art methods for simulating quantum dynamics of the spin‐boson model and the Frenkel–Holstein(–Peierls) model. As applications of TD‐DMRG to real‐world problems, we present theoretical investigations of carrier mobility and spectral function of rubrene crystal, and the radiationless decay rate of azulene with an anharmonic potential energy surface. This article is categorized under:Theoretical and Physical Chemistry > Statistical MechanicsTheoretical and Physical Chemistry > Reaction Dynamics and KineticsSoftware > Simulation Methods [ABSTRACT FROM AUTHOR]

Phenalenyl (C 13 H 9 ) is an open-shell spin-1/2 nanographene. Using scanning tunneling microscopy (STM) inelastic electron tunneling spectroscopy (IETS), covalently bonded phenalenyl dimers have been shown to feature conductance steps associated with singlet-triplet excitations of a spin-1/2 dimer with antiferromagnetic exchange. Here, we address the possibility of tuning the magnitude of the exchange interactions by varying the dihedral angle between the two molecules within a dimer. Theoretical methods ranging from density functional theory calculations to many-body model Hamiltonians solved within different levels of approximation are used to explain STM-IETS measurements of phenalenyl dimers on a hexagonal boron nitride (h-BN)/Rh(111) surface, which exhibit signatures of twisting. By means of first-principles calculations, we also propose strategies to induce sizable twist angles in surface-adsorbed phenalenyl dimers via functional groups, including a photoswitchable scheme. This work paves the way toward tuning magnetic couplings in carbon-based spin chains and two-dimensional lattices.

The cluster mean-field with density matrix renormalization (CMFT + DMRG) method which combines the simplicity of the mean-field theory and the numerical power of the density-matrix renormalization group method is applied to understand the quantum phases of the one-dimensional Boseâ€"Hubbard models. We show that the CMFT + DMRG method is an effective numerical technique with moderate computational resources to determine relevant order parameters and correlation functions of large one-dimensional systems. We apply the CMFT + DMRG for the Bose Hubbard and extended Bose Hubbard models to account for the superfluid, Mott insulator, and density wave phases in these models. Our results are in good agreement with the known phase diagram of these models, demonstrating the efficacy of this method. [ABSTRACT FROM AUTHOR]

In this work, the cross derivative of the Gibbs free energy, initially proposed for phase transitions in classical spin models (Chen et al 2020 Phys. Rev. B 101 165123), is extended for quantum systems. We take the spin-1 XXZ chain with anisotropies as an example to demonstrate its effectiveness and convenience for the Gaussian-type quantum phase transitions therein. These higher-order transitions are very challenging to determine by conventional methods. From the cross derivative with respect to the two anisotropic strengths, a single valley structure is observed clearly in each system size. The finite-size extrapolation of the valley depth shows a perfect logarithmic divergence, signaling the onset of a phase transition. Meanwhile, the critical point and the critical exponent for the correlation length are obtained by a power-law fitting of the valley location in each size. The results are well consistent with the best estimations in the literature. Its application to other quantum systems with continuous phase transitions is also discussed briefly.

MnGen−/0/+ (n = 1–3) clusters have complicated geometric and electronic structures. In this work, we explored the isomers and electronic states of MnGen−/0/+ (n = 1–3) clusters by using density functional theory, CASPT2, and DMRG‐CASPT2 methods. The DMRG‐CASPT2 method with active spaces up to 23 orbitals could provide accurate relative energies of the low‐lying states. The results showed that the electronic states of MnGen−/0/+ (n = 1–3) have strong multireference wave functions. The hybrid PBE0 functional was sufficient to calculate the relative energies of the electronic states of manganese‐doped germanium clusters. The leading configurations, bond distances, bond orders, harmonic vibrational frequencies, relative energies, and electron detachment energies of the relevant electronic states of MnGen−/0/+ (n = 1–3) were reported. The computational results in this work showed that the DMRG‐CASPT2 method with large active spaces can be employed to study the structures and properties of transitional metal‐containing clusters with strong electron correlation effects. [ABSTRACT FROM AUTHOR]

The tensor train (TT) approximation of electronic wave functions lies at the core of the quantum chemistry density matrix renormalization group (QC-DMRG) method, a recent stateof- the-art method for numerically solving the N-electron Schr\"odinger equation. It is well known that the accuracy of TT approximations is governed by the decay of the associated singular values, which in turn strongly depends on the ordering of the one-body basis. Here we find that the singular values s1 ≥ s2≥...≥ sd of tensors representing ground states of noninteracting Hamiltonians possess a surprising inversion symmetry, s1sd = s2sd-1= s3sd-2 = ..., thus reducing the tail behavior to the leading singular value and a single hidden invariant, which moreover depends explicitly on the ordering of the basis. For correlated wave functions, we find that the tail is upper bounded by a suitable superposition of the invariants. Optimizing the invariants or their superposition thus provides a new ordering scheme for QC-DMRG. Numerical tests on simple examples, i.e., linear combinations of a few Slater determinants, show that the new scheme reduces the tail of the singular values by several orders of magnitude over existing methods, including the widely used Fiedler order. [ABSTRACT FROM AUTHOR]

We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion U ′ and Hund exchange J. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN 4 centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, U ′ changes the relative position of the peaks in the density of states, particularly on the iron d z 2 orbital, which is expected to affect the binding of ligands greatly. [ABSTRACT FROM AUTHOR]

We review a controlled numerical approach to quantum impurity problems in realistic geometries, consisting of exactly mapping the complete lattice Hamiltonian onto an equivalent one dimensional system through a unitary transformation. The resulting dimensional and entanglement reduction allows one to study the quantum many-body problem on arbitrary d-dimensional lattices using the density matrix renormalization group (DMRG) method. The real-space resolution allows one to position the impurities at the boundary or bulk of the sample and to study screening effects due to edge or surface modes. We describe how to generalize this approach to multi-impurity problems, discuss applications and possible extensions.

Density functional theory (DFT) and an advanced ab initio technique based on density matrix renormalization group (DMRG‐CASPT2) were employed to investigate a reactive N‐bridged high‐valent diiron‐oxo species involved in H‐abstraction reactions. We studied in detail two important doublet states, the ground state with two iron(IV) centers and a mixed valence FeV‐FeIV excited state. We found that the latter state is low‐lying. Furthermore, its electronic structure and spin density imply that it has significantly higher H‐abstraction reactivity than the ground state. This low‐lying excited state might be the reason behind the high oxidation reactivity of this diiron‐oxo species towards methane. [ABSTRACT FROM AUTHOR]

We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion U ′ and Hund exchange J. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN 4 centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, U ′ changes the relative position of the peaks in the density of states, particularly on the iron d z 2 orbital, which is expected to affect the binding of ligands greatly.

All-electron electronic structure methods based on the linear combination of atomic orbitals method with Gaussian basis set discretization offer a well established, compact representation that forms much of the foundation of modern correlated quantum chemistry calculations—on both classical and quantum computers. Despite their ability to describe essential physics with relatively few basis functions, these representations can suffer from a quartic growth of the number of integrals. Recent results have shown that, for some quantum and classical algorithms, moving to representations with diagonal two-body operators can result in dramatically lower asymptotic costs, even if the number of functions required increases significantly. We introduce a way to interpolate between the two regimes in a systematic and controllable manner, such that the number of functions is minimized while maintaining a block-diagonal structure of the two-body operator and desirable properties of an original, primitive basis. Techniques are analyzed for leveraging the structure of this new representation on quantum computers. Empirical results for hydrogen chains suggest a scaling improvement from O ( N ^4.5 ) in molecular orbital representations to O ( N ^2.6 ) in our representation for quantum evolution in a fault-tolerant setting, and exhibit a constant factor crossover at 15 to 20 atoms. Moreover, we test these methods using modern density matrix renormalization group methods classically, and achieve excellent accuracy with respect to the complete basis set limit with a speedup of 1–2 orders of magnitude with respect to using the primitive or Gaussian basis sets alone. These results suggest our representation provides significant cost reductions while maintaining accuracy relative to molecular orbital or strictly diagonal approaches for modest-sized systems in both classical and quantum computation for correlated systems.

The effect of spatially modulated interaction on quantum phase transition in one-dimensional interacting spinless fermion system is theoretically investigated by exact diagonalization and density matrix renormalization group method. Our calculations show that the periodically modulated interaction can drive the spinless fermion system into topological charge density wave state. The topological state is encoded by quasiparticle end states and the fractional quantized e /2 end charges, and characterized by Berry phase and Chern number. The quasiparticle energy spectra as a function of modulated interaction period appears a stunning fractal-like structure. For the quasi-periodic case, the topological phase transition can also occur. In a word, the spatially modulated interaction can be a new elegant avenue towards realizing to interacting topological phases.

We implement an efficient numerical method to calculate response functions of complex impurities based on the Density Matrix Renormalization Group (DMRG) and use it as the impurity-solver of the Dynamical Mean Field Theory (DMFT). This method uses the correction vector to obtain precise Green's functions on the real frequency axis at zero temperature. By using a self-consistent bath configuration with very low entanglement, we take full advantage of the DMRG to calculate dynamical response functions paving the way to treat large effective impurities such as those corresponding to multi-orbital interacting models and multi-site or multi-momenta clusters. This method leads to reliable calculations of non-local self energies at arbitrary dopings and interactions and at any energy scale.

Graphical abstract Highlights • Ionic-covalent singlet excited-state inversion is computed for C 14 H 16. • A conical intersection between B u states confirms B u - as a dark intermediate. • All excited states do not trivially converge to separate ionic/covalent gaps. • An A g + intermediate is realizable only for non-planar polyene geometries. Abstract Spectroscopy of all- trans linear polyenes is characterized by a one-photon electronic transition to a bright S 2 state and two-photon transition to a lower-lying dark S 1 state. We apply ab initio quantum chemistry to distinguish additional diffuse dark singlet states. Building on a systematic implementation of CASSCF and DMRGSCF coupled to strongly-contracted NEVPT2, we report the excitation energies for a series of polyenes from butadiene to C 16 H 18 at optimized S 0 , S 1 and S 2 geometries. Ionic/covalent state inversion within each manifold is identified at seven conjugated double bonds, making the B u - a dark intermediate state at its optimized geometry and the A g + the S 3 state at the S 0 optimized geometry. The relevance of these results to the function of carotenoids in photosynthetic light harvesting is discussed. [ABSTRACT FROM AUTHOR]

In this paper, the numerical solution of multidimensional hyperbolic problems is discussed with the quantized tensor train (QTT)-approximation methods. Three schemes are proposed. First, an improved implicit time iteration scheme is presented by using the two-site density matrix renormalization group (DMRG) algorithm to solve a linear system at each time step. Second, the time is considered as an independent dimension, and a discretization of the whole differential equation is introduced with all spatial and time dimensions connected in one big global linear system. Then the problem is solved in the QTT-format. The third scheme is to solve the global system by splitting the global time interval into several subintervals. The numerical experiments, with these three schemes applied to the wave equation, show that the complexity of the first scheme is linear while that of the second and third schemes is log-linear in both time and spatial grid points. [ABSTRACT FROM AUTHOR]

Abstract: The structures and spin‐state energetics of two di‐iron(II) complexes based on thiadiazole and oxadiazole ligands in different crystals were studied by using density functional theory and second‐order perturbation theory based on the density matrix renormalization group approach (DMRG‐CASPT2). When taking into account all different contributions to the relative energy, our theoretical approach is capable of providing results that are in excellent agreement with established experimental data. In all cases, we correctly describe the ground state of the complexes as well as predict their spin‐crossover behavior. A comparison between the two complexes in the gas phase and in different crystals shows how the structures change by moving from the gas phase to different crystals and reveals a large impact of the crystal stabilization on the relative spin‐state energy. This theoretical work also demonstrates the applicability of the DMRG‐CASPT2 approach to quantitatively study the spin‐state energetics of multinuclear transition‐metal complexes. [ABSTRACT FROM AUTHOR]