AI 中文总结
研究一维U(1)对称量子多体系统能隙相关问题，提出拓扑平凡扭转算符的基态期望值条件作为能隙lessness指标，可导出多指标，经解析和数值计算验证了结果的有效性。
AI 中文摘要
我们提出了一维尊重U(1)对称性的量子多体系统存在能隙的几个一般必要条件。我们表明，在热力学极限下，拓扑平凡扭转算符的基态期望值在特定有限尺寸标度下必须趋近于1。其违反可表明U(1)对称哈密顿量的能隙lessness。这种扭转算符的拓扑平凡性使我们能通过静态结构因子在实际实验中导出任意阶的无限多个其他能隙lessness指标，这是早期拓扑非平凡扭转算符无法获得的。我们还进行了解析和数值计算以测试结果的效率和一致性。
英文摘要
We propose several general necessary conditions for quantum many-body system in one dimension respecting U(1) symmetry to be gapped. We show that the ground-state expectation value of topologically trivial twisting operators must approach unity in the thermodynamic limit with a certain finite-size scaling. Equivalently, its violation can indicate gaplessness of U(1)-symmetric Hamiltonians. The topological triviality of such a twisting operator enables us to derive infinitely many other gaplessness indicators by static structure factor to any order in real experiments, which are impossible to obtain by earlier topologically nontrivial twisting operators. We also apply analytic and numerical calculations to test the efficiency and consistency of our results.
Comments6 pages, 1 figure
