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Majorana fermion quantum mechanics for higher rank tensors

机译：用于更高阶张量的Majorana费米子量子力学

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We study quantum mechanical models in which the dynamical degrees of freedom are real fermionic tensors of rank 5 and higher. They are the nonrandom counterparts of the Sachdev-Ye-Kitaev (SYK) models where the Hamiltonian couples six or more fermions. For the tensors of rank 5, there is a unique O ( N ) 5 symmetric sixth-order Hamiltonian leading to a solvable large ? N limit dominated by the melonic diagrams. We solve for the complete energy spectrum of this model when N = 2 and deduce exact expressions for all the eigenvalues. The subset of states which are gauge invariant exhibits degeneracies related to the discrete symmetries of the gauged model. We also study quantum chaos properties of the tensor model and compare them with those of the q = 6 SYK model. For q > 6 , there is a rapidly growing number of O ( N ) q ? 1 invariant tensor interactions. We focus on those of them that are maximally single trace—their stranded diagrams stay connected when any set of q ? 3 colors is erased. We present a general discussion of why the tensor models with maximally single-trace interactions have large ? N limits dominated by the melonic diagrams. We solve the large ? N Schwinger-Dyson equations for the higher rank Majorana tensor models and show that they match those of the corresponding SYK models exactly. We also study other gauge invariant operators present in the tensor models.
机译：我们研究了量子力学模型，其中动力学自由度是5级或更高的真实费米子张量。它们是Sachdev-Ye-Kitaev（SYK）模型的非随机对等物，其中哈密顿量耦合了六个或更多个费米子。对于等级5的张量，存在唯一的O（N）5对称六阶哈密顿量，导致可解大？ N极限由旋律图控制。当N = 2时，我们求解该模型的完整能谱，并推导所有特征值的精确表达式。标度不变的状态子集表现出与标度模型的离散对称性有关的简并性。我们还研究了张量模型的量子混沌特性，并将其与q = 6 SYK模型的量子混沌特性进行了比较。当q> 6时，O（N）q？ 1不变张量相互作用。我们将重点放在那些最大为单迹的图上，当任何q？ 3种颜色被删除。我们现在对为什么具有最大单迹线相互作用的张量模型为何具有大的一般讨论进行讨论？ N极限由旋律图控制。我们解决了大吗？ N个Schwinger-Dyson方程用于较高阶的Majorana张量模型，并显示它们与相应的SYK模型的方程完全匹配。我们还研究了张量模型中存在的其他规范不变算子。

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