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Published on: May 30, 2014
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Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems
Yikang Zhang1, Thomas Barthel1
1Department of Physics, Duke University, Durham, North Carolina 27708, USA.
Physical Review Letters
|September 30, 2022
Summary
Steady states of quantum many-body systems with finite-range interactions exhibit exponentially decaying Green's functions. Fermionic systems are noncritical, while bosonic systems can be critical in higher dimensions, revealing insights into quantum phase transitions.
Area of Science:
- Quantum Many-Body Physics
- Open Quantum Systems
- Statistical Mechanics
Background:
- Investigating steady states of open quantum systems is crucial for understanding their long-term behavior.
- Lindblad master equations describe the dynamics of open quantum systems.
Purpose of the Study:
- To analyze the steady states of translation-invariant, quasifree, and quadratic open quantum many-body systems.
- To determine conditions for criticality and phase transitions in these systems.
Main Methods:
- Analysis of Lindblad master equations with quadratic Hamiltonians and linear/quadratic Lindblad operators.
- Characterization of steady states using Green's functions and correlation functions.
Main Results:
- Steady states of 1D systems with finite-range interactions possess exponentially decaying Green's functions.
- Fermionic systems are noncritical in any dimension; bosonic systems can be critical in D>1.
- All gapped Liouvillians in quadratic systems belong to the same phase without additional symmetry constraints.
Conclusions:
- The nature of steady states depends on system dimensionality, particle statistics, and interaction range.
- Understanding criticality and phase transitions in open quantum systems is essential for their characterization.
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