Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model

Abstract

We study the reduced fidelity susceptibility ${\chi }_r$ for an $M$-body subsystem of an $N$-body Lipkin-Meshkov-Glick model with $\tau =M/N$ fixed. The reduced fidelity susceptibility can be viewed as the response of subsystem to a certain parameter. In noncritical region, the inner correlation of the system is weak, and ${\chi }_r$ behaves similar with the global fidelity susceptibility ${\chi }_g$, the ratio $\eta ={\chi }_r/{\chi }_g$ depends on $\tau$ but not $N$. However, at the critical point, the inner correlation tends to be divergent, then we find ${\chi }_r$ approaches ${\chi }_g$ with the increasing the $N$, and $\eta =1$ in the thermodynamic limit. The analytical predictions are perfect agreement with the numerical results.

6 pages, 3 figures

References in corpus (20)

• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Entanglement in a second order quantum phase transition
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Quantum fidelity and quantum phase transitions in matrix product states
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Ground-state fidelity in one-dimensional gapless model
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Fidelity Between Partial States as Signature of Quantum Phase Transitions
• Reduced fidelity susceptibility and its finite-size scaling behaviors
• Reduced fidelity in topological quantum phase transitions
• Multiparticle Entanglement in the Lipkin-Meshkov-Glick Model
• Phase diagram of a Bose-Fermi mixture in a one-dimensional optical lattice in terms of fidelity and entanglement

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