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.

14 pages, small updates, published version

References in corpus (5)

• Many-Body Physics with Ultracold Gases
• Universal adiabatic dynamics across a quantum critical point
• Phase Transition in Space: How Far Does a Symmetry Bend Before It Breaks?
• Gradient critical phenomena in the Ising quantum chain
• Gradient critical phenomena in the Ising quantum chain: surface behaviour

Cited by in corpus (3)

• Critical quantum thermometry and its feasibility in spin systems
• Structure and scaling of Kitaev chain across a quantum critical point in real space
• Anomalous Dynamical Scaling at Topological Quantum Criticality