Algorithms

Well, in the previous section, we introduced the basic principles about the continuous-time quantum Monte Carlo impurity solver briefly. But, there is still a big gap between the basic principles and the real implementations. Thus in this section, we will dive into the iQIST software package, and introduce the algorithms, strategies, tricks, and optimization that have been implemented in it. Since the topics discussed in this section are irrelevant with each other, you can read them in a random manner.

The topics including in the section are as follows:

• Transition probability
• Hubbard-Holstein model
• Dynamical screening effect
• Physical observable
• Orthogonal polynomial representation
• Kernel polynomial method
• Improved estimator for the self-energy function
• Fast matrix update
• Good quantum number, subspace, and symmetry
• Krylov subspace iteration
• Newton-Leja polynomial interpolation
• Truncation approximation
• Lazy trace evaluation
• Skip listing algorithm
• Divide-and-conquer algorithm
• Sparse matrix tricks
• Delayed update algorithm
• Atomic eigenvalue solver
• Single particle basis
• Spin-orbit coupling
• Coulomb interaction matrix
• Maximum entropy method
• Stochastic analytical continuation