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Register a new userNumerically Exact Generalized Greens Function Cluster Expansions for Electron-Phonon Problems
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We generalize the family of approximate momentum average methods to formulate a numerically exact, convergent hierarchy of equations whose solution provides an efficient algorithm to compute the Greens function of a particle dressed by bosons suitable in the entire parameter regime. We use this approach to extract ground-state properties and spectral functions. Our approximation-free framework, dubbed the generalized Greens function cluster expansion (GGCE), allows access to exact numerical results in the extreme adiabatic limit, where many standard methods struggle or completely fail. We showcase the performance of the method, specializing three important models of charge-boson coupling in solids and molecular complexes: the molecular Holstein model, which describes coupling between charge density and local distortions, the Peierls model, which describes modulation of charge hopping due to intersite distortions, and a more complex Holstein+Peierls system with couplings to two different phonon modes, paradigmatic of charge-lattice interactions in organic crystals. The GGCE serves as an efficient approach that can be systematically extended to different physical scenarios, thus providing a tool to model the frequency dependence of dressed particles in realistic settings.
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We present the basic principles of exact diagonalization and (dynamical) density-matrix renormalization-group approaches to the calculation of ground state and dynamical properties in electron-phonon systems.
We identify a fundamental challenge for non-perturbative linked cluster expansions (NLCEs) resulting from the reduced symmetry on graphs, most importantly the breaking of translational symmetry, when targeting the properties of excited states. A generalized notion of cluster additivity is introduced, which is used to formulate an optimized scheme of graph-based continuous unitary transformations (gCUTs) allowing to solve and to physically understand this fundamental challenge. Most importantly, it demands to go beyond the paradigm of using the exact eigenvectors on graphs.
We investigate the performance of Greens function coupled cluster singles and doubles (CCSD) method as a solver for Greens function embedding methods. To develop an efficient CC solver, we construct the one-particle Greens function from the coupled cluster (CC) wave function based on a non-hermitian Lanczos algorithm. The major advantage of this method is that its scaling does not depend on the number of frequency points. We have tested the applicability of the CC Greens function solver in the weakly to strongly correlated regimes by employing it for a half-filled 1D Hubbard model projected onto a single site impurity problem and a half-filled 2D Hubbard model projected onto a 4-site impurity problem. For the 1D Hubbard model, for all interaction strengths, we observe an excellent agreement with the full configuration interaction (FCI) technique, both for the self-energy and spectral function. For the 2D Hubbard, we have employed an open-shell version of the current implementation and observed some discrepancies from FCI in the strongly correlated regime. Finally, on an example of a small ammonia cluster, we analyze the performance of the Greens function CCSD solver within the self-energy embedding theory (SEET) with Hartee-Fock (HF) and Greens function second order (GF2) for the treatment of the environment.
We study the interplay of interactions and topology in a pseudo-spin Weyl system, obtained from a minimally modified Hubbard model, using the numerically exact auxiliary-field quantum Monte Carlo method complemented by mean-field theory. We find that the pseudo-spin plays a key role in the pairing mechanism, and its effect is reflected in the structure of the pairing amplitude. An attractive on-site interaction leads to pairing between quasiparticles carrying opposite spin and opposite topological charge, resulting in the formation of real-spin singlet pairs that are a mixture of pseudo-spin singlet and pseudo-spin triplet. Our results provide a detailed characterization of the exotic pairing behavior in this system, and represent an important step towards a more complete understanding of superconductivity in the context of topological band structures, which will help guide searches for topological superconductivity in real materials and ultracold atoms.
We develop a numerical linked cluster expansion (NLCE) method that can be applied directly to inhomogeneous systems, for example Hamiltonians with disorder and dynamics initiated from inhomogeneous initial states. We demonstrate the method by calculating dynamics for single-spin expectations and spin correlations in two-dimensional spin models on a square lattice, starting from a checkerboard state. We show that NLCE can give moderate to dramatic improvement over an exact diagonalization of comparable computational cost, and that the advantage in computational resources grows exponentially as the size of the clusters included grows. Although the method applies to any type of NLCE, our explicit benchmarks use the rectangle expansion. Besides showing the capability to treat inhomogeneous systems, these benchmarks demonstrate the rectangle expansions utility out of equilibrium.
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