A research team from the Department of Physics, the University of Hong Kong (HKU) has developed a new algorithm to measure entanglement entropy, advancing the exploration of more comprehensive laws in quantum mechanics, a move closer towards actualisation of application of quantum materials.
This
pivotal research work has recently been published in Physical Review Letters.
Quantum
materials play a vital role in propelling human advancement. The search for
more novel quantum materials with exceptional properties has been pressing
among the scientific and technology community.
2D Moire
materials such as twisted bilayer graphene are having a far-reaching role in
the research of novel quantum states such as superconductivity which suffers no
electronic resistance. They also play a role in the development of
"quantum computers" that vastly outperforming the best supercomputers
in existence.
But
materials can only arrive at "quantum state" , i.e. when thermal
effects can no longer hinder quantum fluctuations which trigger the quantum
phase transitions between different quantum states or quantum phases, at
extremely low temperatures (near Absolute Zero, -273.15°C) or under exceptional
high pressure. Experiments testing when and how atoms and subatomic particles
of different substances "communicate and interact with each other freely
through entanglement" in quantum state are therefore prohibitively costly
and difficult to execute.
The study
is further complicated by the failure of classical LGW (Landau, Ginzburg,
Wilson) framework to describe certain quantum phase transitions, dubbed
Deconfined Quantum Critical Points (DQCP). The question then arises whether
DQCP realistic lattice models can be found to resolve the inconsistencies
between DQCP and QCP. Dedicated exploration of the topic produces copious
numerical and theoretical works with conflicting results, and a solution
remains elusive.
Mr Jiarui
ZHAO, Dr Zheng YAN, and Dr Zi Yang MENG from the Department of Physics, HKU
successfully made a momentous step towards resolving the issue through the
study of quantum entanglement, which marks the fundamental difference between
quantum and classical physics.
The
research team developed a new and more efficient quantum algorithm of the Monte
Carlo techniques adopted by scientists to measure the Renyi entanglement
entropy of objects. With this new tool, they measured the Rényi entanglement
entropy at the DQCP and found the scaling behaviour of the entropy, i.e. how
the entropy changes with the system sizes, is in sharp contrast with the
description of conventional LGW types of phase transitions.
"Our findings helped confirm a revolutionised understanding of phase transition theory by denying the possibility of a singular theory describing DQCP. The questions raised by our work will contribute to further breakthroughs in the search for a comprehensive understanding of unchartered territory," said Dr Zheng Yan.
"The finding has changed our understanding of the traditional phase transition theory and raises many intriguing questions about deconfined quantum criticality. This new tool developed by us will hopefully help the process of unlocking the enigma of quantum phase transitions that has perplexed the scientific community for two decades," said Mr Zhao Jiarui, the first author of the journal paper and a PhD student who came up with the final fixes of the algorithm.
"This
discovery will lead to a more general characterisation of the critical
behaviour of novel quantum materials, and is a move closer towards
actualisation of application of quantum materials which play a vital role in
propelling human advancement." Dr Meng Zi Yang remarked.
The models
To test
the efficiency and superior power of the algorithm and demonstrate the distinct
difference between the entanglement entropy of normal QCP between DQCP, the
research team chose two representative models -- the J1-J2 model hosting normal
O(3) QCP and the J-Q3 model hosting DQCP, as shown in Image 2.
Nonequilibrium increment algorithm
Based on
previous methods, the research team created a highly paralleled increment
algorithm. As illustrated in Image 3, to the main idea of the algorithm is to
divide the whole simulation task into many smaller tasks and uses massive CPUs
to parallelly execute the smaller tasks thus greatly decreasing the simulation
time. This improved method helped the team to simulate the two models
previously mentions with high efficiency and better data quality.
References:
- Jiarui Zhao, Yan-Cheng Wang, Zheng Yan, Meng Cheng, Zi Yang Meng. Scaling of Entanglement Entropy at Deconfined Quantum Criticality. Physical Review Letters, 2022; 128 (1) DOI: 10.1103/PhysRevLett.128.010601
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