Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions

Abstract

We clarify the long-standing controversy concerning the behavior of the ground state fidelity in the vicinity of a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type in one-dimensional systems. Contrary to the prediction based on the Gaussian approximation of the Luttinger liquid approach, it is shown that the fidelity susceptibility does not diverge at the transition, but has a cusp-like peak ${\chi }_c-\chi (\lambda )\sim \sqrt{|{\lambda }_c-\lambda |}$, where $\lambda$ is a parameter driving the transition, and ${\chi }_c$ is the peak value at the transition point $\lambda ={\lambda }_c$. Numerical claims of the logarithmic divergence of fidelity susceptibility with the system size (or temperature) are explained by logarithmic corrections due to marginal operators, which is supported by numerical calculations for large systems.

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• Generalized fidelity susceptibility at phase transitions
• Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models
• Fidelity susceptibility as a diagnostic of the commensurate-incommensurate transition: A revisit of the programmable Rydberg chain
• Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
• Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
• Ground-state phase diagram of a spin-1/2 frustrated XXZ ladder
• ${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry
• Emergent phases in a compass chain with multisite interactions
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Conditional global entanglement in a Kosterlitz-Thouless quantum phase transition
• Long-Range Order and Quantum Criticality in Antiferromagnetic Chains with Long-Range Staggered Interactions