近日，以色列特拉维夫大学Gertian Roose团队实现了测量费米子高斯投影纠缠对态的叠加以获得晶格规范理论本征态。相关论文于2025年11月11日发表在《高能物理杂志》上。

格点费米子投影纠缠对态（GFPEPS）及其高斯版本（GGFPEPS）是一种新型格点规范理论试探态，融合了蒙特卡洛方法和张量网络领域的思想。对于此类态的可观测量计算，本质上归结为对规范场构型的蒙特卡洛积分，其概率由描述物质场的费米子张量网络收缩决定。关键优势在于该概率分布具有正定实数特性，从而规避了符号问题。

当底层PEPS本身为高斯型时，张量网络收缩可高效完成，此时该试探态已通过数值实验验证有效。研究组提出将高斯PEPS的叠加态进行格点化，并证明当叠加项数量有限时，可观测量仍可高效计算。他们论证这种构造恰好对应强相互作用规范场论真空上的束缚态情形，因此该试探态特别适用于此类物理场景。作为推论，研究组进一步给出了规范场论基态的精确格点PEPS表示形式。

附：英文原文

Title: Gauging a superposition of fermionic Gaussian projected entangled pair states to get lattice gauge theory eigenstates

Author: Roose, Gertian, Zohar, Erez

Issue&Volume: 2025-11-11

Abstract: Gauged fermionic projected entangled pair states (GFPEPS) and their Gaussian counterpart (GGFPEPS) are a novel type of lattice gauge theory Ansatz state that combine ideas from the Monte Carlo and tensor network communities. In particular, computation of observables for such states boils down to a Monte Carlo integration over possible gauge field configurations that have probabilities dictated by a fermionic tensor network contraction that accounts for the matter in that background configuration. Crucially, this probability distribution is positive definite and real so that there is no sign problem.

When the underlying PEPS is Gaussian, tensor network contraction can be done efficiently, and in this scenario the Ansatz has been tested well numerically. In this work we propose to gauge superpositions of Gaussian PEPS and demonstrate that one can still efficiently compute observables when few Gaussians are in the superposition. As we will argue, the latter is exactly the case for bound states on top of the strongly interacting LGT vacuum, which makes this Ansatz particularly suitable for that scenario.

As a corollary, we will provide an exact representation of the LGT ground state as a gauged PEPS.

DOI: 10.1007/JHEP11(2025)052

Source: https://link.springer.com/article/10.1007/JHEP11(2025)052