Spatial Kibble-Zurek mechanism through susceptibilities: the inhomogeneous quantum Ising model case

Abstract

We study the quantum Ising model in the transverse inhomogeneous magnetic field. Such a system can be approached numerically through exact diagonalization and analytically through the renormalization group techniques. Basic insights into its physics, however, can be obtained by adopting the Kibble-Zurek theory of non-equilibrium phase transitions to description of spatially inhomogeneous systems at equilibrium. We employ all these approaches and focus on derivatives of longitudinal and transverse magnetizations, which have extrema near the critical point. We discuss how these extrema can be used for locating the critical point and for verification of the Kibble-Zurek scaling predictions in the spatial quench.

arXiv comment14 pages, small updates, published version

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Cited by in corpus (7)

• Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries
• Critical quantum thermometry and its feasibility in spin systems
• Locating quantum critical points with Kibble-Zurek quenches
• Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians
• Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions
• Structure and scaling of Kitaev chain across a quantum critical point in real space
• Anomalous Dynamical Scaling at Topological Quantum Criticality