We present a finite-temperature extension of density matrix embedding theory (FT-DMET) for realistic crystalline systems. We describe a practical framework for constructing extended bath orbitals, solving the embedding problem, and performing DMET self-consistency at finite temperature. To reduce computational cost, we introduce strategies based on mutual-information-guided bath truncation, controlled treatment of the thermal electron number without explicit optimization, and the use of low-temperature impurity solvers and one-shot FT-DMET in the low-temperature regime. We apply this approach to periodic hydrogen chains and square lattices to characterize their finite-temperature phases. We observe the Pomeranchuk-like effect in one dimension and enhanced stability of long-range order in two dimensions.
We present a finite-temperature extension of density matrix embedding theory (FT-DMET) for realistic crystalline systems. We describe a practical framework for constructing extended bath orbitals, solving the embedding problem, and performing DMET self-consistency at finite temperature. To reduce computational cost, we introduce strategies based on mutual-information-guided bath truncation, controlled treatment of the thermal electron number without explicit optimization, and the use of low-temperature impurity solvers and one-shot FT-DMET in the low-temperature regime. We apply this approach to periodic hydrogen chains and square lattices to characterize their finite-temperature phases. We observe the Pomeranchuk-like effect in one dimension and enhanced stability of long-range order in two dimensions.
We present a finite-temperature extension of density matrix embedding theory (FT-DMET) for realistic crystalline systems. We describe a practical framework for constructing extended bath orbitals, solving the embedding problem, and performing DMET self-consistency at finite temperature. To reduce computational cost, we introduce strategies based on mutual-information-guided bath truncation, controlled treatment of the thermal electron number without explicit optimization, and the use of low-temperature impurity solvers and one-shot FT-DMET in the low-temperature regime. We apply this approach to periodic hydrogen chains and square lattices to characterize their finite-temperature phases. We observe the Pomeranchuk-like effect in one dimension and enhanced stability of long-range order in two dimensions.
We describe an efficient quantum embedding framework for realistic ab initio density matrix embedding theory (DMET) calculations in solids. We discuss in detail the choice of orbitals and mapping to a lattice, treatment of the virtual space and bath truncation, and the lattice-to-embedded integral transformation. We apply DMET in this ab initio framework to a hexagonal boron nitride monolayer, crystalline silicon, and nickel monoxide in the antiferromagnetic phase, using large embedded clusters with up to 300 embedding orbitals. We demonstrate our formulation of ab initio DMET in the computation of ground-state properties such as the total energy, equation of state, magnetic moment, and correlation functions.
This thesis describes several topics related to finite temperature studies of strongly correlated systems: finite temperature density matrix embedding theory (FT-DMET), finite temperature metal-insulator transition, and quantum algorithms including quantum imaginary time evolution (QITE), quantum Lanczos (QLanczos), and quantum minimally entangled typical thermal states (QMETTS) algorithms. While the absolute zero temperature is not reachable, studies of physical and chemical problems at finite temperatures, especially at low temperature, is essential for understanding the quantum behaviors of materials in realistic conditions. Here we define low temperature as the temperature regime where the quantum effect is not largely dissipated due to thermal fluctuation. Treatment of systems at low temperature is specially difficult compared to both high temperature - where classical approximation can be applied - and zero temperature where only the ground state is required to describe the system of interest. FT-DMET is a wavefunction-based embedding scheme which can handle finite temperature simulations of a variety of strongly correlated problems. The "high-level in low-level" framework enables FT-DMET to tackle large bulk sizes and capture the majority of the entanglement at the same time. FT-DMET formulations and implementation details for both model systems and ab initio problems are provided in Chapter 2 and Chapter 3. Metal-insulator transition is a common but important phase transition in many strongly correlated materials. The widely accepted scheme to distinguish an insulator from a metal is band structure theory based on a single-particle picture. However, insulating phases caused by disorder or strong correlation cannot be explained merely with the band structure. In Chapter 4, we demonstrate that electron locality/mobility is a more general criteria to detect metal-insulator transition. We further introduce complex polarization as the order parameter to reflect the electron locality/mobility and provide a formalism based on thermofield theory to evaluate the complex polarization at finite temperature. Quantum algorithms are designed to perform simulations on a quantum device. The infrastructure of a quantum processing unit (QPU) utilizes the superposition property of quantum bits (qubits), and thus can potentially outplay the classical simulations in computational scaling for certain problems. In Chapter 5, we introduce the QITE algorithm, which can be applied to quantum simulations of both ground state and finite temperature problems. We further introduce a subspace method, QLanczos algorithm, and a a finite temperature quantum algorithm, QMETTS, where QITE is used as a building block for the two algorithms. We demonstrate above quantum algorithms with simulations on both classical computers and quantum computers.
Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these, Density Matrix Embedding Theory (DMET) is an efficient approach that enforces self-consistency at the level of one-particle reduced density matrices (1-RDMs), facilitating applications across diverse quantum systems. However, conventional DMET is constrained by the requirement that the global 1-RDM (low-level descriptor) be an orthogonal projector, limiting flexibility in bath construction and potentially impeding accuracy in strongly correlated regimes. In this work, we introduce a generalized DMET framework in which the low-level descriptor can be an arbitrary 1-RDM and the bath construction is based on optimizing a quantitative criterion related to the maximal disentanglement between different fragments. This yields an alternative yet controllable bath space construction for generic 1-RDMs, lifting a key limitation of conventional DMET. We demonstrate its consistency with conventional DMET in appropriate limits and exploring its implications for bath construction, downfolding (impurity Hamiltonian construction), low-level solvers, and adaptive fragmentation. We expect that this more flexible framework, which leads to several new variants of DMET, can improve the robustness and accuracy of DMET.
We introduce extended density matrix embedding theory (EDMET), a static quantum embedding theory explicitly self-consistent with respect to local two-body physics. This overcomes the biggest practical and conceptual limitation of more traditional one-body embedding methods, namely the lack of screening and treatment of longer-range interactions. This algebraic zero-temperature embedding augments a local interacting cluster model with a minimal number of bosons from a description of the full system correlations via the random phase approximation, and admits an analytic approach to build a self-consistent Coulomb-exchange-correlation kernel. For extended Hubbard models with nonlocal interactions, this leads to the accurate description of phase transitions, static quantities, and dynamics. We also move towards ab initio systems via the Parriser-Parr-Pople model of conjugated coronene derivatives, finding good agreement with experimental optical gaps.
Density matrix embedding theory [G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)] and density embedding theory [I. W. Bulik, G. E. Scuseria, and J. Dukelsky, Phys. Rev. B 89, 035140 (2014)] have recently been introduced for model lattice Hamiltonians and molecular systems. In the present work, the formalism is extended to the ab initio description of infinite systems. An appropriate definition of the impurity Hamiltonian for such systems is presented and demonstrated in cases of 1, 2, and 3 dimensions, using coupled cluster theory as the impurity solver. Additionally, we discuss the challenges related to disentanglement of fragment and bath states. The current approach yields results comparable to coupled cluster calculations of infinite systems even when using a single unit cell as the fragment. The theory is formulated in the basis of Wannier functions but it does not require separate localization of unoccupied bands. The embedding scheme presented here is a promising way of employing highly accurate electronic structure methods for extended systems at a fraction of their original computational cost.