Researchers from the University of Innsbruck, including Michael Kaicher, Joseph Vovrosh, Alexandre Dauphin, and Simon B. Jäger, have developed a new method for simulating quantum systems that could have significant implications for the energy industry, particularly in the development of quantum technologies for energy applications. Their work, published in the journal Physical Review Letters, introduces a new approach to studying the dynamics of spin-1/2 systems, which are fundamental to understanding many physical phenomena.
The researchers have developed a new type of fermionic mean-field theory, which they call parity-violating fermionic mean-field theory (PV-FMFT). This theory is based on parity-violating fermionic Gaussian states (PV-FGS) and provides a numerically efficient way to study the real- and imaginary-time evolution of spin-1/2 Hamiltonians with arbitrary geometries and interactions. The new theory extends previous formulations of parity-preserving fermionic mean-field theory (PP-FMFT) by including fermionic displacement operators in the variational Ansatz.
One of the key advantages of PV-FMFT is that it can be applied to general spin-1/2 Hamiltonians, describe quenches from arbitrary initial spin-1/2 product states, and compute local and non-local observables in a straightforward manner. The computational cost of PV-FMFT is also modest, scaling as O(N^3) in the worst case for a system of N spins or fermionic modes. The researchers demonstrated that PV-FMFT can exactly capture the imaginary- and real-time dynamics of non-interacting spin-1/2 Hamiltonians.
The researchers also studied the post-quench dynamics of the one- and two-dimensional Ising model in the presence of longitudinal and transversal fields using PV-FMFT. They computed the single-site magnetization and correlation functions and compared them against results from other state-of-the-art numerical approaches. In two-dimensional spin systems, they showed that the employed spin-to-fermion mapping can break rotational symmetry within the PV-FMFT description, and they discussed the resulting consequences for the calculated correlation functions.
The researchers suggest that PV-FMFT could be used as a benchmark for other numerical techniques and quantum simulators, and they outline both its capabilities and its limitations. The new method could have significant implications for the energy industry, particularly in the development of quantum technologies for energy applications, such as quantum sensors and quantum communication systems. The ability to simulate and understand the dynamics of spin-1/2 systems is fundamental to the development of these technologies, and the new method developed by the researchers from the University of Innsbruck could provide a powerful tool for advancing this field.
Source: Physical Review Letters
This article is based on research available at arXiv.