Direct free energy evaluation of classical and quantum many-body systems via field-theoretic simulation.
Direct free energy evaluation of classical and quantum many-body systems via field-theoretic simulation.
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通过场论模拟直接估算经典和量子多体系统的自由能。
DOI：
10.1073/pnas.2201804119
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发表时间：
2022-05-03
影响因子：
11.1
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中科院分区：
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分子模拟中自由能的准确评估对许多科学领域都很重要，包括流体和固体相平衡，生物分子凝聚物和量子相变等。不幸的是，自由能估计是繁琐的，计算昂贵的分子模型的自由度表示在粒子坐标。我们表明，作为一个经典或量子场论的模型的替代表示提供了一个化学势算子，可以平均产生一个直接和低成本的吉布斯自由能的估计。平均是使用“场论”计算机模拟，采用波动场，而不是粒子。经典和量子体系的分子模拟中的自由能评估是计算密集型的，并且需要复杂的算法。这是因为自由能取决于可接近相空间的体积，这个量与多体问题的坐标表示中的积分测度密不可分。相反，同样的问题表示为场论（辅助场或相干态）孤立的粒子数作为一个简单的参数在哈密顿量或作用泛函，并使识别的化学势场算子。我们发现，这一功能导致一个“直接”的方法的自由能评价，其中粒子模型转换为场论和适当的场算子平均使用场论模拟进行复杂的Langevin采样。这些平均值提供了一个即时的估计亥姆霍兹自由能的正则系综和熵的微正则系综。该方法被示出为一个经典的聚合物溶液，嵌段共聚物熔体表现出液晶和固体中间相，和相互作用玻色子的量子流体。
The accurate evaluation of free energies within molecular simulations is important to many scientific fields, including fluid and solid phase equilibria, biomolecular condensates, and quantum phase transitions, among others. Unfortunately, free energy estimation is tedious and computationally expensive for molecular models whose degrees of freedom are expressed in particle coordinates. We show that alternative representations of a model as a classical or quantum field theory provide access to a chemical potential operator that can be averaged to yield a direct and low-cost estimate of the Gibbs free energy. The averaging is performed using a “field-theoretic” computer simulation that employs fluctuating fields rather than particles. Free energy evaluation in molecular simulations of both classical and quantum systems is computationally intensive and requires sophisticated algorithms. This is because free energy depends on the volume of accessible phase space, a quantity that is inextricably linked to the integration measure in a coordinate representation of a many-body problem. In contrast, the same problem expressed as a field theory (auxiliary field or coherent states) isolates the particle number as a simple parameter in the Hamiltonian or action functional and enables the identification of a chemical potential field operator. We show that this feature leads a “direct” method of free energy evaluation, in which a particle model is converted to a field theory and appropriate field operators are averaged using a field-theoretic simulation conducted with complex Langevin sampling. These averages provide an immediate estimate of the Helmholtz free energy in the canonical ensemble and the entropy in the microcanonical ensemble. The method is illustrated for a classical polymer solution, a block copolymer melt exhibiting liquid crystalline and solid mesophases, and a quantum fluid of interacting bosons.