From Stochastic Spin Chains to Quantum Kardar-Parisi-Zhang Dynamics
Tony Jin1,2, Alexandre Krajenbrink2,3,4, Denis Bernard2
1DQMP, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva, Switzerland.
Physical Review Letters
|August 16, 2020
Summary
We present an asymmetric quantum exclusion process for fermions. This model
Area of Science:
- Statistical mechanics
- Quantum physics
- Condensed matter theory
Background:
- The quantum symmetric simple exclusion process models fermion behavior on lattices.
- Understanding stochastic dynamics in quantum systems is crucial for many-body physics.
Purpose of the Study:
- To introduce and analyze the asymmetric extension of the quantum symmetric simple exclusion process.
- To explore the emergent dynamics and mathematical properties of this quantum model.
Main Methods:
- Analytical methods to derive the height field from the fermion current.
- Introduction of a discrete Cole-Hopf transform for the height field.
- Investigation of continuum limits under Kardar-Parisi-Zhang scaling and quantum noise regimes.
Main Results:
- The time-integrated fermion current defines a height field exhibiting quantum nonlinear stochastic Kardar-Parisi-Zhang dynamics.
- A quantum version of the stochastic heat equation is satisfied by the transformed height field.
- Analysis of the continuum limit under specific scaling and noise conditions.
Conclusions:
- The asymmetric quantum simple exclusion process offers a new framework for studying quantum stochastic dynamics.
- Emergent Kardar-Parisi-Zhang and stochastic heat equation behaviors are demonstrated in a quantum fermionic system.
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