New Method Enhances Simulation of Quantum Systems with Long-Range Interactions

A new method for simulating one-dimensional quantum systems with long-range interactions has been introduced by researchers Rakesh Achutha, Donghoon Kim, Yusuke Kimura, and Tomotaka Kuwahara. Their paper, titled "Efficient Simulation of 1D Long-Range Interacting Systems at Any Temperature," was submitted to arXiv on September 4, 2024.

The authors developed an algorithm that operates efficiently across all temperatures, utilizing a quasi-polynomial runtime for inverse temperatures up to ( \beta = \text{poly} (\ln(n)) ). Central to their approach is the Density Matrix Renormalization Group (DMRG) algorithm, which traditionally lacks guaranteed efficiency. The researchers introduced a new truncation scheme for the matrix product operator of quantum Gibbs states, allowing for controlled error management.

Additionally, the method enables the simulation of time evolution in systems with long-range interactions, achieving greater precision than previously established bounds, specifically the Lieb-Robinson bound. This advancement could have significant implications for the study of quantum systems, enhancing the ability to model complex interactions in quantum physics.

The full paper can be accessed at arXiv:2409.02819.