Arxiv Selection May 2019

May 1-May 7 Ahmet Keles, May 8-May 14 Haiping Hu, May 15-May 21 Bhaskar Mukherjee, May 22- May 28 Biao Huang

May. 22

arXiv:1905.07694

Periodic Table of SYK and supersymmetric SYK

Fadi Sun, Jinwu Ye

Comments: One Table, 3 Figures, 22 pages

Subjects: Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)

We develop a systematic and unified random matrix theory to classify Sachdev-Ye-Kitaev (SYK) and supersymmetric (SUSY) SYK models and also work out the structure of the energy levels in one periodic table. The SYK with even q- and SUSY SYK with odd q-body interaction, N even or odd number of Majorana fermions are put on the same footing in the minimal Hilbert space, N(mod8) and q(mod4) double Bott periodicity are identified. Exact diagonalizations are performed to study both the bulk energy level statistics and hard edge behaviours. A new moment ratio of the smallest positive eigenvalue is introduced to determine hard edge index efficiently. Excellent agreements between the ED results and the symmetry classifications are demonstrated. Our complete and systematic methods can be transformed to map out more complicated periodic tables of SYK models with more degree of freedoms, tensor models and symmetry protected topological phases. Possible classification of charge neutral quantum black holes are hinted.

arXiv:1905.07989

Classification of Topological Excitations in Quadratic Bosonic Systems

Zixian Zhou, Liang-Liang Wan, Zhi-Fang Xu

Subjects: Quantum Gases (cond-mat.quant-gas)

We investigate the classification of topological excitations in quadratic bosonic systems with an excitation band gap. Time-reversal, charge-conjugation, and parity symmetries in bosonic systems are introduced to realize a ten-fold symmetry classification. We find a specific decomposition of the quadratic bosonic Hamiltonian and use it to prove that each quadratic bosonic system is homotopic to a direct sum of two single-particle subsystems. The classification table of topological excitations is thus derived via inheriting from that of Atland-Zirnbauer classes and unique topological phases of bosons are predicted. Finally, concrete bosonic models are proposed to demonstrate the peculiarity of bosonic topological excitations.