Three-site interacting spin chain in a staggered field: fidelity versus Loschmidt echo

Area of Science:

• Condensed matter physics
• Quantum magnetism
• Many-body systems

Background:

• Interacting XX spin chains are fundamental models in quantum magnetism.
• Quantum phase transitions (QPTs) are driven by changes in system parameters, altering ground states.
• Topological properties of the Fermi surface can lead to distinct QPTs.

Purpose of the Study:

• Investigate ground state fidelity and Loschmidt echo as probes for QPTs in a three-site XX chain with a staggered field.
• Characterize QPTs associated with both gapped-gapless transitions and Fermi surface topology changes.
• Understand the limitations of fidelity and Loschmidt echo in detecting different types of QPTs.

Main Methods:

• Analysis of ground state fidelity.
• Calculation of the ground state Loschmidt echo.
• Examination of a three-site interacting XX chain model.
• Inclusion of a staggered external field.
• Study of Fermi surface topology variations.

Main Results:

• Ground state fidelity successfully identifies boundaries between gapped and gapless phases.
• Fidelity is insensitive to the topological phase transition within the gapless phase (two to four Fermi points).
• The Loschmidt echo exhibits a dip at only one specific point, failing to detect other QPTs.

Conclusions:

• Fidelity and Loschmidt echo exhibit anomalous behavior in detecting QPTs in this model.
• The sensitivity of these measures depends on the nature of the quantum phase transition.
• Further theoretical arguments are provided to explain these observed behaviors.