论文标题
可集成的两个站点sachdev-ye-kitaev模型的复制对称性破坏
Replica Symmetry Breaking for the Integrable Two-Site Sachdev-Ye-Kitaev Model
论文作者
论文摘要
我们分析了一个两体的非智物两位点sachdev-ye-kitaev模型，其中一个位点复合物的耦合与另一个位点结合。该模型在站点之间没有明确的耦合，显示了无限数量的相变数，这是分区函数以Matsubara频率分配到产品中的结果。我们以两种不同的方式计算淬灭的自由能，首先是从单粒子能量来计算的，其次是求解Schwinger-Dyson方程。第一个计算可以完全根据一个站点模型完成。当Matsubara频率进入耦合矩阵的光谱支持时，共轭复制品进入。第二个计算是基于两个站点分区函数的复制技巧。两种方法都给出相同的结果。自由弗里米昂分区函数可以作为耦合矩阵的矩阵模型重新塑造。在较小的细节中，该模型是描述QCD的手性相变的随机矩阵模型，两体模型的顺序参数对应于QCD的手性冷凝物。与相应的四体模型相比，我们能够确定自由能的哪些特征是由于四体模型的混乱性。两种模型的高温相都是熵的，在这两种情况下都是由光谱密度决定的。四体Syk模型具有低温相，其自由能几乎与温度无关，即使实际频谱没有表现出空白，也会向理论的有效缝隙发出有效的空白。但是，两体Syk模型的低温自由能并不平坦，实际上它振荡至任意低温。这表明，两体模型的熵并不总是正面的，这一点不太理想的特征，这很可能是非热性的结果。
We analyze a two-body nonhermitian two-site Sachdev-Ye-Kitaev model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of phase transitions which is a consequence of the partition function factorizing into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways, first in terms of the single-particle energies, and second by solving the Schwinger-Dyson equations. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases is determined by the spectral density. The four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. However the low-temperature free energy of the two-body SYK model is not flat, in fact it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive, which most likely is a consequence of the nonhermiticity.
