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Dynamical Quantum Phase Transitions: Role of Topological Nodes in Wave Function Overlaps
Zhoushen Huang1, Alexander V Balatsky1,2
1Institute for Materials Science, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Physical Review Letters
|September 3, 2016
Summary
Dynamical quantum phase transitions (DQPTs) in multiband systems are robustly linked to topologically protected nodes in wave function overlap. These nodes are crucial for understanding the vanishing Loschmidt echo at critical times.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Topological Matter
Background:
- Sudden quantum quenches can drive Bloch bands between topological phases.
- Dynamical quantum phase transitions (DQPTs) are associated with the vanishing Loschmidt echo at critical times.
- Previous analytical studies were limited to two-band models, obscuring the topology-DQPT relationship in complex systems.
Purpose of the Study:
- To elucidate the relationship between topology and DQPTs in general multiband quantum systems.
- To identify the fundamental requirements for robust DQPTs beyond two-band models.
Main Methods:
- Investigated the role of wave function overlap nodes between initial and postquench energy eigenstates.
- Analyzed topological protection of these nodes based on distinct topological indices.
- Utilized a three-band generalized Hofstadter model in one and two spatial dimensions for demonstration.
Main Results:
- Established that robust DQPTs in multiband systems necessitate nodes in the wave function overlap.
- Demonstrated that these nodes are topologically protected when participating wave functions possess distinct topological indices.
- Provided detailed theoretical evidence for these findings in 1D and 2D systems.
Conclusions:
- The existence of topologically protected nodes in wave function overlap is a key indicator of robust DQPTs in multiband systems.
- This finding extends the understanding of DQPTs beyond simplified two-band models.
- The study paves the way for exploring experimental signatures of these phenomena.
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