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

• URL: http://arxiv.org/abs/2001.04278v1
• Date: Mon, 13 Jan 2020 14:30:36 GMT
• Title: From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics
• Authors: Tony Jin, Alexandre Krajenbrink and Denis Bernard
• Abstract summary: We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process. We show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear dynamics.
• Score: 68.8204255655161
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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