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arXiv 2106.09197cond-mat.quant-gascond-mat.stat-mech
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光晶格中玻色气体具有本征非厄米结构的有限温度平均场论

Finite temperature mean-field theory with intrinsic non-hermitian structures for Bose gases in optical lattices

Liang He, Su Yi

摘要:

我们揭示了一个与平均场论相关的发散问题,该理论适用于光晶格中的玻色气体,该晶格是由广泛使用的跳跃项的直接平均场解耦构造的,其中相应的平均场哈密顿量通常假设一旦考虑了平均场超流序参量的空间依赖性,则没有较低的能量约束。通过系统的泛函积分方法,我们解决了这个问题,通过建立一个一般的有限温度平均场论,可以处理任何可能的空间依赖的序参量,而不会导致发散的问题。有趣的是,我们发现该理论通常假设一种固有的非埃尔米特结构,这种结构源于系统跳跃矩阵的不确定性。在此理论范围内,我们开发了一种有效的方法,用于调查在有限温度下的系统的物理,系统的性能可以通过直接调查的有效势函数的鞍点的序参量计算。我们通过研究光晶格中玻色气体的有限温度超流跃迁来说明我们的方法。由于有限温度平均场论是相当普遍的,这种方法可以直接应用于研究具有复杂空间结构相的相关系统的有限温度性质。

英文摘要:

We reveal a divergent issue associated with the mean-field theory for Bose gases in optical lattices constructed by the widely used straightforward mean-field decoupling of the hopping term, where the corresponding mean-field Hamiltonian generally assumes no lower energy bound once the spatial dependence of the mean-field superfluid order parameter is taken into account. Via a systematic functional integral approach, we solve this issue by establishing a general finite temperature mean-field theory that can treat any possible spatial dependence of the order parameter without causing the divergent issue. Interestingly, we find the theory generally assumes an intrinsic non-hermitian structure that originates from the indefiniteness of the hopping matrix of the system. Within this theory, we develop an efficient approach for investigating the physics of the system at finite temperature, where properties of the system can be calculated via straightforward investigation on the saddle points of an effective potential function for the order parameter. We illustrate our approach by investigating the finite temperature superfluid transition of Bose gases in optical lattices. Since the underlying finite temperature mean-field theory is quite general, this approach can be straightforwardly applied to investigate the finite temperature properties of related systems with phases possessing complex spatial structures.

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