Path dependent scaling of geometric phase near a quantum multi-critical point

Abstract

We study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by applying a rotation in all spins about z-axis by an angle $\eta$. Although the geometric phase itself vanishes at the multi-critical point, the derivative with respect to the anisotropy parameter of the model shows peaks at different points on the ferromagnetic side close to it where the energy gap is a local minimum; we call these points `quasi-critical'. The value of the derivative at any quasi-critical point scales with the system size in a power-law fashion with the exponent varying continuously with the parameter $\alpha$ that defines a path, upto a critical value $\alpha ={\alpha }_c=2$. For $\alpha >{\alpha }_c$, or on the paramagnetic side no such peak is observed. Numerically obtained results are in perfect agreement with analytical predictions.

5 pages, 6 figures

References in corpus (12)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Geometric phases and criticality in spin chain systems
• Ground state fidelity from tensor network representations
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Observation of the ground-state-geometric phase in a Heisenberg XY model
• Oscillating fidelity susceptibility near a quantum multicritical point
• Geometric phases and quantum phase transitions
• Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching
• Geometric phases and criticality in spin systems
• Geometric Phase and Quantum Phase Transition in the Lipkin-Meshkov-Glick model

Cited by in corpus (5)

• Geometry of quantum phase transitions
• Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
• Geometric phase and multipartite entanglement of Rydberg atom chains