论文标题
副本对称溶液的稳定性在非对齐的Bose-Hubbard模型中的稳定性
Stability of the replica-symmetric solution in the off-diagonally-disordered Bose-Hubbard model
论文作者
论文摘要
我们研究了由玻色 - 假汉密尔顿（Bose-Hubbard Hamiltonian）用随机隧道振幅描述的相互作用玻色子的无序系统。我们得出了该模型复制对称解的稳定性条件。遵循de almeida和thouless的方案，我们通过构建相应的Hessian矩阵并检查其阳性半finitiententes，确定该溶液是否对应于最小自由能。因此，我们通过基于其预期的对称性来假设特征向量的集合来找到特征值，并要求特征值是非负数的。我们以数值评估频谱，并识别产生始终非负值的特征值的矩阵块。因此，我们发现来自脱钩子空间的特征值的子集足以将其视为稳定标准。我们还确定了系统中存在的相的稳定性，发现无序相是稳定的，玻璃相不稳定，而超流相相位既稳定又不稳定。
We study a disordered system of interacting bosons described by the Bose-Hubbard Hamiltonian with random tunneling amplitudes. We derive the condition for the stability of the replica-symmetric solution for this model. Following the scheme of de Almeida and Thouless, we determine if the solution corresponds to the minimum of free energy by building the respective Hessian matrix and checking its positive semidefiniteness. Thus, we find the eigenvalues by postulating the set of eigenvectors based on their expected symmetry, and require the eigenvalues to be non-negative. We evaluate the spectrum numerically and identify matrix blocks that give rise to eigenvalues that are always non-negative. Thus, we find a subset of eigenvalues coming from decoupled subspaces that is sufficient to be checked as the stability criterion. We also determine the stability of the phases present in the system, finding that the disordered phase is stable, the glass phase is unstable, while the superfluid phase has both stable and unstable parts.
