用于高-Tc超导电性量子模拟器中临界温度的预测：矩阵乘积态加平均场方法
Predicting critical temperature in quantum simulators for high-$T_c$ superconductivity: the matrix product state plus mean field approach
AI总结：
本研究采用矩阵乘积态加平均场理论（MPS+MF），表征混合维度（mixD）模型，探究其实现高-Tc超导电性的潜力，为量子模拟研究高-Tc超导电性奠定基础。
AI中文摘要：
基于超冷原子晶格气体的量子模拟是研究高-Tc超导电性最具前景的平台之一，可突破经典计算机上量子多体数值计算的有限能力。尽管该领域自创立以来已取得巨大进展，但实现高-Tc超导态仍遥不可及。本研究为近期提出且已部分实现的混合维度（mixD）模型奠定了基础，这类系统具备实现极高配对能同时保持配对可观迁移率的成熟能力。我们具体研究具有各向异性隧穿的二维mixD模型的潜力，采用费米子的矩阵乘积态加平均场理论（MPS+MF），并证明这些模型可能进入高-Tc超导相。这些模拟基于对二维mixD系统子单元——一维mixD系统的全面表征，涵盖当前实验相关的系统尺寸范围，还建立了实用的经验法则，用于确定有限尺寸效应何时会阻碍用一维mixD系统构建二维系统。
英文摘要：
Quantum simulation based on ultra cold atomic lattice gases is one of the most promising platforms to investigate high-$T_c$ superconductivity beyond the limited capabilities of quantum many body numerics on classical computers. Yet, despite enormous progress since the field's inception, realizing a high-$T_c$ superconducting state still remains out of reach. The present work lays the groundwork to purpose the recently proposed, and already partly realized, mixed-dimensional (mixD) models, towards this end. These systems offer the proven capability to realize very high pairing energies while retaining appreciable mobility of pairs. We specifically investigate the potential of 2D mixD-models with anisotropic tunneling, using the matrix product state plus mean field theory (MPS+MF) for fermions, and show that these models may enter a high-$T_c$ superconducting phase. These simulations in turn are based on a comprehensive characterization of the 1D mixD-systems, which are the sub-units of which the 2D system is comprized. In this, we cover the range of currently experimentally relevant system sizes, and establish practical heuristics to determine when finite\hyp size effects preclude the use of a 1D mixD-system to build the 2D ones.
