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Journal Article

Matrix product states approaches to operator spreading in ergodic quantum systems


Luitz,  David J.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Hemery, K., Pollmann, F., & Luitz, D. J. (2019). Matrix product states approaches to operator spreading in ergodic quantum systems. Physical Review B, 100(10): 104303. doi:10.1103/PhysRevB.100.104303.

Cite as: https://hdl.handle.net/21.11116/0000-0006-93E4-2
We review different matrix-product-state (MPS) approaches to study the spreading of operators in generic nonintegrable quantum systems. As a common ground to all methods, we quantify this spreading by means of the Frobenius norm of the commutator of a spreading operator with a local operator, which is usually referred to as the out-of-time-order correlation (OTOC) function. We compare two approaches based on matrix-product states in the Schrodinger picture: the time-dependent block decimation (TEBD) and the time-dependent variational principle (TDVP), as well as TEBD based on matrix-product operators directly in the Heisenberg picture. The results of all methods are compared to numerically exact results using Krylov space exact time evolution. We find that for the Schrodinger picture, the TDVP algorithm performs better than the TEBD algorithm.
Moreover, the tails of the OTOC are accurately obtained both by TDVP MPS and TEBD MPO. They are in very good agreement with exact results at short times, and appear to be converged in bond dimensions even at longer times. However, the growth and saturation regimes are not well captured by either of the methods.