Variational wavefunction for Mott insulator at finite $U$ using ancilla qubits

Boran Zhou, Hui-Ke Jin, Ya-Hui Zhang
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Abstract

The Mott regime with finite $U$ offers a promising platform for exploring novel phases of matter, such as quantum spin liquids (QSL) that exhibit fractionalization and emergent gauge field. Here, we provide a new class wavefunction, dubbed ancilla wavefunction, to capture both charge and spin (gauge) fluctuations in QSLs at finite $U$. The ancilla wavefunction can unify the Fermi liquid and Mott insulator phases with a single variation parameter $\Phi$ tuning the charge gap. As $\Phi \rightarrow\infty$, the wavefunction reduces to the Gutzwiller projected state, while at $\Phi=U/2$, it is effectively equivalent to applying an inverse Schrieffer-Wolff transformation to the Gutzwiller projected state. This wavefunction can be numerically simulated in the matrix product state representation, and its performance is supported by numerical results for both one- and two-dimensional Hubbard models. Besides, we propose the possibility of a narrow regime of fractional Fermi liquid phase between the usual Fermi liquid and the Mott insulator phases close to the metal insulator transition -- a scenario typically overlooked by the conventional slave rotor theory. Our ancilla wavefunction offers a novel conceptual framework and a powerful numerical tool for understanding Mott physics.
利用安吉拉量子比特计算有限 U$ 时莫特绝缘体的变分波函数
有限 $U$ 的莫特体系为探索物质的新阶段提供了一个前景广阔的平台,例如量子自旋液体 (QSL),它表现出分数化和新兴量规场。在这里,我们提供了一种新的类波函数(称为 ancilla 波函数),用于捕捉有限 U$ 时 QSL 中的电荷和自旋(规)波动。ancilla波函数可以用一个调整电荷间隙的变化参数$\Phi$来统一费米液体和莫特绝缘体相。当 $\Phi \rightarrow\infty$ 时,波函数还原为古茨维勒投影态,而在 $\Phi=U/2$ 时,它实际上等同于对古茨维勒投影态进行反施里弗-沃尔夫变换。这种波函数可以用矩阵乘积状态表示法进行数值模拟,其性能得到了一维和二维哈巴德模型的数值结果的支持。此外,我们还提出了在通常的费米液体相与莫特绝缘体相之间存在一个接近金属绝缘体转变的狭小的分数费米液体相的可能性--传统的从转子理论通常会忽略这种情况。我们的辅助波函数为理解莫特物理学提供了新颖的概念框架和强大的数值工具。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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