Higher-order tensors and tests of quantum mechanics

Liqun Qi, Haibin Chen, Yannan Chen

Ryo Sakai, Shinji Takeda

We apply the higher order tensor renormalization group to two and three dimensional lattice fermion systems. To deal with tensor networks including Grassmann variables, we introduce Grassmann higher order tensor renormalization group (GHOTRG). Thanks to its deterministic property, GHOTRG is perfectly free of the sign problem. To test the validity of the new algorithm, we analyze well-known systems such as the Thirring model using GHOTRG.

U. Fano, A. R. P. Rau

Ryo Sakai, Shinji Takeda, Yusuke Yoshimura

We apply the higher order tensor renormalization group to two and three dimensional relativistic fermion systems on the lattice. In order to perform a coarse-graining of tensor networks including Grassmann variables, we introduce Grassmann higher order tensor renormalization group. We test the validity of the new algorithm by comparing its results with those of exact or previous methods.

Edward S. Fry, Thomas Walther

Rathindra Nath Das, Sourav Dutta, Archana Maji

In this article we study the presence of chaos in supersymmetric(SUSY) quantum mechanics. For that purpose we present a form of 4-point out of time order correlator(OTOC) for SUSY quantum mechanical systems using tensor product formalism. We calculate the 4-point OTOC for SUSY 1D harmonic oscillator and find that the OTOC is exactly equal to that of 1D bosonic harmonic oscillator system. In similar manner using the eigenstate representation of supersymmetric systems we calculate the generalized higher order out of time order correlator. The higher order OTOC is a more sensitive measure of chaos than the usual 4-point correlator used in literature. Finally, we calculate the generalized 2N-point OTOC for SUSY 1D harmonic oscillator.