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Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks.

Phillip Helms¹, Garnet Kin-Lic Chan¹

¹Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

Physical Review Letters

|October 16, 2020

Summary

We used 2D tensor networks to study a classical system

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Area of Science:

Statistical Mechanics
Condensed Matter Physics
Computational Physics

Background:

Dynamical observables in classical nonequilibrium systems are challenging to analyze.
Large deviation functions provide insights into rare events and system behavior.
The 2D asymmetric simple exclusion process is a fundamental model for transport phenomena.

Purpose of the Study:

To apply 2D tensor network methods for calculating large deviation functions.
To investigate the dynamical phase behavior of the 2D asymmetric simple exclusion process.
To identify and characterize phase transitions in this nonequilibrium system.

Main Methods:

Utilizing 2D tensor networks to compute large deviation functions.
Analyzing the dynamics of the asymmetric simple exclusion process in two dimensions.
Mapping out phase diagrams and critical exponents.

Main Results:

Successfully obtained large deviation functions for dynamical observables.
Identified a novel dynamical phase transition from a jammed to a flowing phase.
Characterized the distinct properties of the jammed and flowing phases.

Conclusions:

2D tensor networks are powerful tools for nonequilibrium statistical mechanics.
The asymmetric simple exclusion process exhibits rich dynamical phase behavior.
The study provides a framework for analyzing complex nonequilibrium phenomena.