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 expansion's utility out of equilibrium.
We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into equivalence classes essentially governed by hypergraph isomorphism. Concretely, a reduced König representation of the hypergraphs is used to make the equivalence relation accessible by graph isomorphism. During this procedure we determine the embedding factor for each equivalence class, which is used in the final resummation in order to obtain the final res…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the limiting factor for these calculations. Here, we show that a partial diagonalization of the largest clusters in the expansion using the Lanczos algorithm can be as useful as full diagonalization for the method while mitigating some of the time and memory issues. As a test case, we consider a frustrated Heisenberg model on the checkerboard lattice and find that …
Imperfections in correlated materials can alter their ground state as well as finite-temperature properties in significant ways. Here, we develop a method based on numerical linked-cluster expansions for calculating exact finite-temperature properties of disordered lattice models directly in the thermodynamic limit. We show that a continuous distribution for disordered parameters can be achieved using a set of carefully chosen discrete modes in the distribution, which allows for the averaging of properties over all disorder realizations. We benchmark our results for thermodynamic properties of…
We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely recta…
We demonstrate that numerical linked cluster expansions (NLCE) yield a powerful approach to calculate time-dependent correlation functions for quantum many-body systems in one dimension. As a paradigmatic example, we study the dynamics of the spin current in the spin-1/2 XXZ chain for different values of anisotropy, as well as in the presence of an integrability-breaking next-nearest neighbor interaction. For short to intermediate time scales, we unveil that NLCE yields a convergence towards the thermodynamic limit already for small cluster sizes, which is much faster than in direct calculatio…
The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as many-body localization or the effect of disorder on Mott metal-insulator transitions. Here, we utilize the numerical linked-cluster expansion technique, extended to treat disordered quantum lattice models, and study exact thermodynamic properties of the disordered Fermi-Hubbard model on the square and cubic geometries. We consider box distributions for the disor…
Numerical Block Diagonalization and Linked-Cluster Expansion for Deriving Effective Hamiltonians: Applications to Spin Excitations
RIKEN Center for Emergent Matter Science（理化学研究所物质结构研究中心）；School of Physical and Chemical Sciences, Queen Mary University of London（伦敦大学玛丽女王学院物理与化学科学学院）
