不解决符号问题而解决费米子问题：求解二维量子点的相似变换传播子破缺波函数
Solving fermion problems without solving the sign problem: symmetry-breaking wave functions from similarity-transformed propagators for solving 2D quantum dots
摘要：
众所周知，在多费米子系统的路径积分Monte Carlo计算中，使用原始二阶传播子会导致符号问题。在这项工作中，我们表明，通过使用相似变换的Fokker-Planck传播子，它是可能的，以解决一个大的量子点的基态，多达100个极化电子，而不解决的符号问题。这些相似变换的传播子自然地产生先前在量子点和量子霍尔效应的研究中使用的旋转破环基态波函数。然而，这个推导表明，电子应该位于{ \it最小化}玻色子基态波函数的位置，而不是位于{ \it最大化}势能的位置。通过使用这些作为初始波函数在具有二阶和四阶传播子的基态路径积分蒙特卡罗计算中可以获得能量的进一步改进。
英文摘要：
It is well known that the use of the primitive second-order propagator in Path Integral Monte Carlo calculations of many-fermion systems leads to the sign problem. In this work, we show that by using the similarity-transformed Fokker-Planck propagator, it is possible to solve for the ground state of a large quantum dot, with up to 100 polarized electrons, without solving the sign problem. These similarity-transformed propagators naturally produce rotational symmetry-breaking ground state wave functions previously used in the study of quantum dots and quantum Hall effects. However, instead of localizing the electrons at positions which {\it minimize} the potential energy, this derivation shows that they should be located at positions which {\it maximize} the bosonic ground state wave function. Further improvements in the energy can be obtained by using these as initial wave functions in a Ground State Path-Integral Monte Carlo calculation with second and fourth-order propagators.
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