aiqbench analysis
This research advances the theoretical toolkit for quantum many-body physics by refining martingale methods within tensor networks to compute spectral gaps more efficiently than previous techniques. The study provides a numerically motivated approach that not only outperforms existing benchmarks but also simplifies proofs regarding the gapped nature of Matrix Product State parent Hamiltonians. These improvements are significant for researchers tackling fundamental problems in quantum simulation and condensed matter theory where gap estimation is critical.
Lower Bounds on Spectral Gaps of Parent Hamiltonians via Tensor Networks
arXiv:2607.19078v1 Announce Type: new Abstract: Proving spectral gaps above the ground space is a central problem in quantum many-body physics. Yet, finding lower bounds on the gap is notoriously difficult. We revisit the martingale method, originally developed by Fannes, Nachtergaele, and Werner [Fannes '92, Nachtergaele '96] to prove the existence of spectral gaps of parent Hamiltonians of Matrix Product States (MPS), and provide improvements to the different steps of the method. Most importantly, we devise a new technique which allows to compute the key quantity in the martingale method -- the overlap of local ground spaces -- exactly and efficiently. This enables a clear improvement of the method, allowing it to outperform other existing techniques to lower bound gaps, which we demonstrate by benchmarking on several models. Remarkably, our -- numerically motivated -- approach at the same time also yields a significantly simplified proof of the fact that parent Hamiltonians of any (well-behaved) MPS are always gapped.
Abstract:Proving spectral gaps above the ground space is a central problem in quantum many-body physics. Yet, finding lower bounds on the gap is notoriously difficult. We revisit the martingale method, originally developed by Fannes, Nachtergaele, and Werner [Fannes '92, Nachtergaele '96] to prove the existence of spectral gaps of parent Hamiltonians of Matrix Product States (MPS), and provide improvements to the different steps of the method. Most importantly, we devise a new technique which allows to compute the key quantity in the martingale method -- the overlap of local ground spaces -- exactly and efficiently. This enables a clear improvement of the method, allowing it to outperform other existing techniques to lower bound gaps, which we demonstrate by benchmarking on several models. Remarkably, our -- numerically motivated -- approach at the same time also yields a significantly simplified proof of the fact that parent Hamiltonians of any (well-behaved) MPS are always gapped.
Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)
arXiv:2607.19078 [quant-ph]
(or arXiv:2607.19078v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2607.19078 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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