High Resolution Image Download MS PowerPoint Slide We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the constrained random phase approximation to construct an effective multiband Hubbard model, which is subsequently solved using tensor networks. Our work focuses on one-dimensional and quasi-one-dimensional materials, for which we employ the machinery of matrix product states. We apply this framework to the conjugated polymers trans -polyacetylene and polythiophene, as well as the quasi-one-dimensional charge-transfer insulator Sr 2 CuO 3 . The predicted band gaps show quantitative agreement with state-of-the-art computational techniques and experimental measurements. Beyond band gaps, tensor networks provide access to a wide range of physically relevant properties, including spin magnetization and various excitation energies. Their flexibility supports the implementation of complex Hamiltonians with longer-range interactions, while the bond dimension enables systematic control over accuracy. Furthermore, the computational cost scales efficiently with system size, demonstrating the framework’s scalability.
High Resolution Image Download MS PowerPoint Slide We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the constrained random phase approximation to construct an effective multiband Hubbard model, which is subsequently solved using tensor networks. Our work focuses on one-dimensional and quasi-one-dimensional materials, for which we employ the machinery of matrix product states. We apply this framework to the conjugated polymers trans -polyacetylene and polythiophene, as well as the quasi-one-dimensional charge-transfer insulator Sr 2 CuO 3 . The predicted band gaps show quantitative agreement with state-of-the-art computational techniques and experimental measurements. Beyond band gaps, tensor networks provide access to a wide range of physically relevant properties, including spin magnetization and various excitation energies. Their flexibility supports the implementation of complex Hamiltonians with longer-range interactions, while the bond dimension enables systematic control over accuracy. Furthermore, the computational cost scales efficiently with system size, demonstrating the framework’s scalability.
Predicting the properties of correlated materials and molecules often requires a many-body description that goes beyond single-particle and mean-field approximations. Tensor networks address this challenge by exploiting the entanglement structure of quantum states to construct compact, systematically improvable representations. Although developed largely for idealized model Hamiltonians, these methods are increasingly being integrated into material-specific calculations. This Perspective introduces their underlying principles and examines how network geometry, bond-dimension truncation, and approximate contraction determine the accuracy and computational reach of these approaches. We survey applications across regimes of increasing complexity, ranging from ground-state properties of quantum magnets and itinerant-fermion systems to excitation spectra, nonequilibrium dynamics, finite-temperature and open systems, and molecular electronic structure. We then examine four routes connecting these methods to real materials, including experimentally constrained models, downfolded Hamiltonians, dynamical mean-field theory with tensor network impurity solvers, and quantum embedding. Throughout, we evaluate the maturity of existing capabilities and their principal limitations, synthesizing this assessment into a practical method-selection guide. We argue that reliable materials predictions require quantifying uncertainties introduced at each stage, from constructing material-specific Hamiltonians to extracting experimentally accessible observables. Finally, we identify the algorithmic advances and reproducible computational practices needed to establish tensor networks as a routine tool for predictive materials science and quantum chemistry.
We study quasi-one-dimensional strongly correlated materials using a multi-step approach based on density functional theory, downfolding techniques, and tensor-network simulations. The downfolding procedure yields effective multiband Hubbard models that capture the competition between electron hopping and local Coulomb interactions relevant to the system's low-energy properties. The resulting multiband Hubbard models are solved using matrix product states. Applied to Sr2CuO3, SrBaCuO3, and Ba2CuO3, this purely one-dimensional treatment yields no long-range magnetic order, in contrast to the magnetic ordering observed experimentally. To account for this behavior, we extend the multi-step approach by incorporating interchain couplings through a self-consistent mean-field scheme. This combined approach stabilizes finite staggered magnetizations, providing a consistent description of magnetic order in agreement with experiment. For Sr2CuO3.5 and SrCuO2, we also tested an approach proposed for ladder materials, however, we find that these materials are not well suited for this approach due to the small magnitude of the intraladder hopping parameters.
The Hubbard model is a simple but profound theoretical tool for understanding the physics underlying strongly correlated systems. This phenomenology includes, but is not limited to, metal-insulating transitions, charge and spin order (charge density/spin density waves), superconducting phases, non-Fermi liquid physics, among others. Examining one dimensional physical models described by the Hubbard Hamiltonian can teach us much about the related physics of higher dimensional systems. Applying advanced numerical computational techniques such as density matrix numerical renormalization group (DMRG) to one-dimensional manypbody model Hamiltonians allows for the calculation of ground state energies and dynamical spectral functions with extremely high precision and accuracy. This thesis explores the application of DMRG numerical techniques to one-dimensional physical systems described by Hamiltonians beyond the conventional Hubbard model, and the nuanced physical effects observed for these systems across various regimes and phases. A Wannier Hubbard chain composed of non-orthogonal overlapping atomic orbitals was transformed to an orthogonal atomic basis using a non-unitary Lowdin transformation. The calculation of energies, dynamical spectral functions and the photoemission spectrum for this Wannier Hubbard chain revealed phases not previously observed for Hubbard chains at half-filling. Additional analysis and calculations were performed for a CuO chain described by the Luther-Emery Hamiltonian that epitomizes charge-transfer physics. The motivation for studying this CuO chain was previous literature on transition metal oxides (TMOs) and the mapping of multiband Hamiltonians to single band models in certain energy regimes. Finally, we performed computational analysis for a spin-3/2 generalized Hubbard chain. By spanning the full phase space of our spin-3/2 Hubbard chain in terms of chemical potential μ and external magnetic field h we observed non-typical Cooper pairing states and novel phases for different symmetries of our Hamiltonian.--Author's abstract
The accurate first-principles description of strongly correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving compressed many-body Hamiltonians that maintain the essential physics of strongly correlated materials. The solution of these material-specific models is still exponentially difficult to generate on classical computers, but quantum algorithms allow for a significant speed-up in obtaining the ground states of these compressed Hamiltonians. Here, we demonstrate that using quantum algorithms to obtain the properties of downfolded Hamiltonians can indeed yield high-fidelity solutions. By combining ab initio downfolding and variational quantum eigensolvers, we correctly predict the antiferromagnetic state of one-dimensional cuprate Ca2CuO3, the excitonic ground state of monolayer WTe2, and the charge-ordered state of correlated metal SrVO3. Numerical simulations using a classical tensor network implementation of variational quantum eigensolvers allow us to simulate large models with up to 54 qubits and encompassing up to four bands in the correlated subspace, which is indicative of the complexity that our framework can address. Through these methods we demonstrate the potential of classical preoptimization and downfolding techniques for enabling efficient materials simulation using quantum algorithms.
In this Thesis, we develop and apply an accurate method to determine the ground-state properties of strongly-correlated electrons in the framework of lattice model Hamiltonians. In lattice density-functional theory (LDFT) the basic variable is the one-particle density matrix γ. From a generalized HK theorem, the ground state energy Egs[γgs] = minγ E[γ] is obtained by minimizing the energy-functional E[γ] over all the physical or representable γ. The energy functional can be divided into two contributions: the kinetic-energy functional T [γ], which linear dependence on γ is exactly known, and the correlation-energy functional W [γ], which dependence on γ is not explicitly known. Finding accurate approximations for W [γ] constitutes the actual challenge of this thesis. Part of this work is based on previous studies which derive an approximation of W [γ] for the Hubbard Hamiltonian based on scaling hypothesis and an exact analytical results for the Hubbard dimer. However, this approach is limited to spin independent and homogeneous systems. In order to extend the scope of LDFT, we have developed three different approaches to derive W [γ] in order to study broken symmetry problems. First we extend the previous scaling functional to system having charge transfer. By a systematic study of the dependence of W [γ] on the charge distribution we find similar scaling properties as for the homogeneous case. An extension to the Hubbard model on bipartite lattices is then derived and applied to finite and infinite systems with repulsive and attractive interactions. The high accuracy of this functional is demonstrated. Nevertheless, this approach is difficult to transfer to more complex systems, since the calculation of W [γ] applies to the system as a whole. To overcome this problem, we derive another approximation based on local scaling properties. This functional is formulated on-site so that it can be applied to any ordered or disordered Hamiltonian with on-site interaction. As applications we study the metal-insulator transition in the ionic Hubbard model in oneand two-dimensions, as well as the one-dimensional Hubbard chain with first and second nearest neighbor hoppings. Finally, we develop a numerical approach of W [γ], on the basis on exact diagonalizations of an effective many-body Hamiltonian corresponding to a cluster surrounded by an effective medium. This effective Hamiltonian depends on the density matrix γ and allows to derive approximation to W [γ] which improve systematically with increasing cluster size. The formulation is spin-dependent and allows a straightforward generalization to multi-orbital correlated systems such spd-Hamiltonians. In addition it take into account the effects of short-range charge and spin fluctuations in the functional. The accuracy of the method is demonstrated for the Hubbard model by comparison with the Bethe-Ansatz solution (1D) and quantum Monte Carlo simulations (2D). Finally, an outlook or relevant future developments of the theory is provided.
Tensor networks (TNs) and the breadth of algorithms acting on them have seen astounding success in simulating quantum many-body systems in the strongly interacting regime with both accuracy and efficiency. In the context of quantum chemistry, Steven White’s density matrix renormalization group (DMRG) continues to take center stage as the TN method of choice, seeing countless theoretical and computational breakthroughs in recent decades yet remaining fettered by a few persistent shortcomings, notably, a lack of size-extensivity and quasi-exactness . Here, we present a simple yet versatile framework for circumventing these issues: the bootstrap embedded density matrix renormalization group (BE-DMRG), and numerically validate its size-extensive and quasi-exact ground-state properties for a test bed of strongly correlated molecular systems (linear H - chains; quasi-linear E - polyacetylene; 2D and 3D H -lattices; 2D arene flakes ). Spanning a breadth of system sizes (10 to 200 orbitals) and entanglement topologies (linear to highly nonlinear), we demonstrate the robustness of the BE-DMRG for problems far beyond the reach of conventional DMRG implementations. Furthermore, by detailing BE-DMRG convergence behavior with respect to exact diagonalization, we find the rate of convergence with bond dimension to be significantly faster than, yet just as reliable as, that of conventional DMRG. Ultimately, we find that the embedded DMRG might serve as a natural extension of White’s original formulation to higher dimensions without the need for higher-order tensor networks. The coupling of tensor network theories to the framework of quantum embedding, more broadly, may become an incomparably powerful tool for the study of strongly correlated molecules and materials.