Update of $\mathcal{H}\Phi$: Newly added functions and methods in versions 2 and 3

TL;DR

This paper details the new functions and methods added to the open-source $\\mathcal{H}\Phi$ software in versions 2 and 3, enhancing capabilities for quantum many-body system calculations including spectrum, excited states, finite-temperature states, and integration with ab initio Hamiltonians.

Contribution

The paper introduces multiple new computational methods and formats in $\\mathcal{H}\Phi$ versions 2 and 3, expanding its functionality for quantum many-body simulations.

Findings

Implementation of shifted Krylov spectrum calculations

Addition of GPGPU-accelerated full diagonalization

Introduction of real-time evolution and finite-temperature methods

Abstract

$\mathcal{H}\Phi$ [$aitch$-$phi$] is an open-source software package of numerically exact and stochastic calculations for a wide range of quantum many-body systems. In this paper, we present the newly added functions and the implemented methods in vers. 2 and 3. In ver. 2, we implement spectrum calculations by the shifted Krylov method, and low-energy excited state calculations by the locally optimal blocking preconditioned conjugate gradient (LOBPCG) method. In ver. 3, we implement the full diagonalization method using ScaLAPACK and GPGPU computing via MAGMA. We also implement a real-time evolution method and the canonical thermal pure quantum (cTPQ) state method for finite-temperature calculations. The Wannier90 format for specifying the Hamiltonians is also implemented. Using the Wannier90 format, it is possible to perform the calculations for the $ab$ $initio$ low-energy effective Hamiltonians of solids obtained by the open-source software RESPACK. We also update Standard mode $\unicode{x2014}$simplified input format in $\mathcal{H}\Phi$$\unicode{x2014}$ to use these functions and methods. We explain the basics of the implemented methods and how to use them.