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arXiv · 2001.04278

From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics

Tony Jin·Alexandre Krajenbrink·Denis Bernard
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Abstract

We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process which is a stochastic model of fermions on a lattice hopping with random amplitudes. In this setting, we analytically show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear stochastic Kardar-Parisi-Zhang dynamics. Similarly to classical simple exclusion processes, we further introduce the discrete Cole-Hopf (or G\"artner) transform of the height field which satisfies a quantum version of the Stochastic Heat Equation. Finally, we investigate the limit of the height field theory in the continuum under the celebrated Kardar-Parisi-Zhang scaling and the regime of almost-commuting quantum noise.

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Tony Jin, Alexandre Krajenbrink, Denis Bernard. 2020-01-13. From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics. https://doi.org/10.1103/physrevlett.125.040603

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