# Quantum Lattice Model Solver ${\mathcal H}\Phi$

## TL;DR

${\mathcal H}\Phi$ is a versatile quantum lattice model solver that efficiently handles large systems, supports finite-temperature calculations, and is optimized for high-performance supercomputers, broadening the scope of quantum many-body simulations.

## Contribution

The paper introduces ${\mathcal H}\Phi$, a new software package that extends quantum lattice model solving capabilities with parallel efficiency and finite-temperature support.

## Key findings

- Successfully benchmarked on supercomputers like K computer and Sekirei.
- Supports a wide range of quantum lattice models with two-body interactions.
- Enables finite-temperature calculations using TPQ states.

## Abstract

${\mathcal H}\Phi$ [$aitch$-$phi$] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, ${\mathcal H}\Phi$ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, ${\mathcal H}\Phi$ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of ${\mathcal H}\Phi$. We also show the benchmark results of ${\mathcal H}\Phi$ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP).