自旋玻色子模型的广义多极子展开：环境纠缠和有偏二态系统
A generalized multi-polaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system
摘要：
本文对自旋玻色子模型的多体基态展开了一个系统的变分相干态展开，其中一个量子二能级系统耦合到一个谐振子连续体。在这种技术的核心能量约束合理化的极化子（与经典的期望值一致的浴状态的位移）和反极化子（由于量子隧道效应的反位移）。我们提出了一个全面的研究的基态两能级系统的人口和相干性作为隧道振幅，耗散强度和偏置的函数（类似于定义的两态系统的双阱势的不对称性）。不同的环境模式之间的纠缠进行了研究，通过寻找一个给定的环境模式和所有其他模式之间的二分纠缠熵的光谱签名。我们观察到这种熵的行为急剧变化，增加耗散，表明环境状态的纠缠性质。此外，熵在强耗散下在大的能量范围内传播，这证明了表征底层近藤态的宽纠缠窗口。最后，精确的数值重整化群计算和精确的Bethe Anastomic模型的解决方案的比较表明，我们的变分优化多极子扩展的快速收敛，这表明它也应该是一个有用的工具，耗散模型的更大的复杂性，相关的量子物理和化学的众多系统的兴趣。
英文摘要：
We develop a systematic variational coherent state expansion for the many-body ground state of the spin-boson model, in which a quantum two-level system is coupled to a continuum of harmonic oscillators. Energetic constraints at the heart of this technique are rationalized in terms of polarons (displacements of the bath states in agreement with classical expectations) and antipolarons (counter-displacements due to quantum tunneling effects). We present a comprehensive study of the ground state two-level system population and coherence as a function of tunneling amplitude, dissipation strength, and bias (akin to asymmetry of the double well potential defining the two-state system). The entanglement among the different environmental modes is investigated by looking at spectroscopic signatures of the bipartite entanglement entropy between a given environmental mode and all the other modes. We observe a drastic change in behavior of this entropy for increasing dissipation, indicative of the entangled nature of the environmental states. In addition, the entropy spreads over a large energy range at strong dissipation, a testimony to the wide entanglement window characterizing the underlying Kondo state. Finally, comparisons to accurate numerical renormalization group calculations and to the exact Bethe Ansatz solution of the model demonstrate the rapid convergence of our variationally-optimized multi-polaron expansion, suggesting that it should also be a useful tool for dissipative models of greater complexity, as relevant for numerous systems of interest in quantum physics and chemistry.
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