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Hubig, Claudius; Bohrdt, Annabelle; Knap, Michael; Grusdt, Fabian; Cirac, J. Ignacio (2020): Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t - J model. In: Scipost Physics, Vol. 8, No. 2, 021
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Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t - J model after a single hole has been placed in the half-filled antiferromagnetic Background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.