Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines.

Area of Science:

• Quantum physics
• Condensed matter theory

Background:

• Anomalous dynamical phases were previously identified in the transverse-field Ising chain with long-range interactions.
• These phases exhibit unique behavior in the Loschmidt-echo return rate, characterized by anomalous cusps.

Purpose of the Study:

• To further investigate the nature of the anomalous dynamical phase.
• To analyze the behavior of Fisher-zero lines in the complex time plane.
• To provide a deeper understanding of quantum dynamics in long-range interacting systems.

Main Methods:

• Utilized the framework of infinite matrix product states.
• Calculated Fisher-zero lines in the complex time plane.
• Employed matrix product state time-evolution and transfer matrix methods.

Main Results:

• Fisher-zero lines show distinct behavior compared to regular phases, with some terminating before intersecting the imaginary axis.
• Identified smooth peaks in the Loschmidt-echo return rate preceding the anomalous cusps.
• Demonstrated the applicability of the numerical treatment to general quantum spin chains.

Conclusions:

• The study provides further insight into the anomalous phase of the long-range transverse-field Ising chain.
• The observed Fisher-zero line behavior is a key indicator of this anomalous phase.
• The presented numerical techniques are versatile for analyzing quantum spin chain dynamics.