Study on Frustrated Quantum Phase Transition Achievable by Quantum Computing

TL;DR

This paper investigates the potential for quantum computers to simulate frustrated quantum phase transitions in hexagonal lattices, comparing results with traditional methods and other lattice types.

Contribution

It introduces a new study of quantum phase transitions in hexagonal lattices using quantum Monte Carlo simulations, expanding beyond square and triangular lattices.

Findings

Impact of transverse magnetic fields on order parameters

Simulation results for various lattice sizes

Comparison with square and triangular lattice results

Abstract

Quantum computers, with parallel computing and entanglement effects, excel in cryptography analysis and big data processing. However, they are not fully developed yet, and their performance needs further evaluation. Traditional computer data, especially in simulating quantum phase transitions, are still needed for reference. Two-dimensional frustrated lattice systems can be chosen for studying quantum phase transitions. Currently, significant progress has been made in the study of frustrated square and triangular lattices using traditional computers, while research on hexagonal lattices is limited. This paper consists of four parts. The first part introduces the background of quantum computers and the concept of quantum phase transitions, with the selection of order parameters in hexagonal lattices. The second part elaborates the ideas of the quantum Monte Carlo algorithm. The third part presents numerical simulations, exploring the impact of different transverse magnetic fields on order parameters under low-temperature conditions and showcasing results for various lattice sizes. The fourth part summarizes and looks ahead, comparing the results with those of square and triangular lattices as well as relevant theoretical analyses.