The three site interacting spin chain in staggered field: Fidelity vs Loschmidt echo

Abstract

We study the the ground state fidelity and the ground state Loschmidt echo of a three site interacting XX chain in presence of a staggered field which exhibits special types of quantum phase transitions due to change in the topology of the Fermi surface, apart from quantum phase transitions from gapped to gapless phases. We find that on one hand, the fidelity is able to detect only the boundaries separating the gapped from the gapless phase; it is completely insensitive to the phase transition from two Fermi points region to four Fermi points region lying within this gapless phase. On the other hand, Loschmidt echo shows a dip only at a special point in the entire phase diagram and hence fails to detect any quantum phase transition associated with the present model. We provide appropriate arguments in support of this anomalous behavior.

7 pages, 4 Figures, Accepted in Phys. Rev. E

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• Out-of-time-order correlations and Floquet dynamical quantum phase transition
• Decoherence from spin environments: Loschmidt echo and quasiparticle excitations
• Dynamical crossover behavior in the relaxation of quenched quantum many-body systems
• Fidelity susceptibility and Loschmidt echo for generic paths in a three spin interacting transverse Ising model
• Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions
• Exactly Solvable 1D Quantum Models with Gamma Matrices
• Separation of the Kibble-Zurek Mechanism from Quantum Criticality
• Nonlocal pseudospin dynamics in a quantum Ising chain
• Dynamical Phase Transitions in Periodically Driving 1D Ising Model