全息玻色-哈伯德模型
Towards a Holographic Bose-Hubbard Model
摘要：
我们提出了大N玻色-哈伯德模型的全息构造。该模型是基于麦克斯韦场耦合到带电标量场上的AdS 2硬壁。我们实现了玻色-哈伯德模型的瓣状相结构，发现在大库仑排斥极限下，该模型允许莫特绝缘体基态存在。在莫特绝缘体阶段，玻色子被定位在每个位置上。在零跳变时，我们发现不同填充物的Mott绝缘相之间的跃迁对应于一阶能级交叉相变。在有限跳变时，我们发现了Mott相和非均匀相之间的全息相变。然后我们分析了莫特绝缘体相和非均匀相周围的场的扰动。我们发现几乎为零模式的非均匀相。
英文摘要：
We present a holographic construction of the large-N Bose-Hubbard model. The model is based on Maxwell fields coupled to charged scalar fields on the AdS2 hard wall. We realize the lobe-shaped phase structure of the Bose-Hubbard model and find that the model admits Mott insulator ground states in the limit of large Coulomb repulsion. In the Mott insulator phases, the bosons are localized on each site. At zero hopping we find that the transitions between Mott insulating phases with different fillings correspond to first order level-crossing phase transitions. At finite hopping we find a holographic phase transition between the Mott phase and a non-homogeneous phase. We then analyze the perturbations of fields around both the Mott insulator phase and inhomogeneous phase. We find almost zero modes in the non-homogeneous phase.
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