Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain

Abstract

We study the fidelity susceptibility of quantum antiferromagnetic Ising chain with a long-range power law interaction $1/r^{\alpha }$ using the large-scale density matrix renormalization group method. We find that the critical adiabatic dimension $\mu =2$ and the critical exponent of the correlation length $\nu =1$ for arbitrary $\alpha >0$, indicating all quantum phase transitions are second-order Ising transitions. In addition, we numerically determine the complete phase diagram for $0<\alpha \le 3$ from the data collapse of the fidelity susceptibility and show that the critical point $h_c$ changes monotonously with respect to $\alpha$. This work will shed light on the nature of phase transitions in the quantum long-range antiferromagnetic Ising chain from a quantum information perspective.

5 pages, 5 figures

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• Fidelity Susceptibility in the Quantum Rabi Model
• Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain
• Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Transverse-field $XY$ spin chain with the competing long-range interactions: Multi-criticality around the $XX$-symmetric point
• Long-Range Order and Quantum Criticality in Antiferromagnetic Chains with Long-Range Staggered Interactions