Exponential damping induced by random and realistic perturbations

Physical review. E, vol. 101, pp. 062133

Abstract

Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that if the perturbation exhibits a random-matrix structure in the eigenbasis of the unperturbed Hamiltonian, then this perturbation effectively leads to an exponential damping of the original dynamics. Employing a combination of dynamical quantum typicality and numerical linked cluster expansions, we demonstrate that our theoretical findings for random matrices can, in some cases, be relevant for the dynamics of realistic quantum many-body models as well. Specifically, we study the decay of current autocorrelation functions in spin-1/2 ladder systems, where the rungs of the ladder are treated as a perturbation to the otherwise uncoupled legs. We find a convincing agreement between the exact dynamics and the lowest-order prediction over a wide range of interchain couplings.

Authors 7

1. Jonas Richter

   Osnabrück University

   Affiliation as printed

   Department of Physics, University of Osnabrück, D-49069 Osnabrück, Germany

2. Fengping Jin

   Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany

3. Lars Knipschild

   Osnabrück University

   Affiliation as printed

   Department of Physics, University of Osnabrück, D-49069 Osnabrück, Germany

4. Hans A. De Raedt

   University of Groningen · Zernike Institute for Advanced Materials

   Affiliation as printed

   Zernike Institute for Advanced Materials, University of Groningen, NL-9747AG Groningen, The Netherlands

5. Kristel F. L. Michielsen Aachen

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany

   RWTH Aachen University, D-52056 Aachen, Germany

6. Jochen Gemmer

   Osnabrück University

   Affiliation as printed

   Department of Physics, University of Osnabrück, D-49069 Osnabrück, Germany

7. Robin Steinigeweg

   Osnabrück University

   Affiliation as printed

   Department of Physics, University of Osnabrück, D-49069 Osnabrück, Germany