Gradient critical phenomena in the Ising quantum chain

Abstract

We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling theory for the density profiles induced by the gradient perturbation which involves a characteristic length given by the width of the interface region. The scaling predictions are tested in the framework of the mean-field Ginzburg-Landau theory. Then we consider the Ising quantum chain in a linearly varying transverse field which corresponds to the extreme anisotropic limit of a classical two-dimensional Ising model. The quantum Hamiltonian can be diagonalized exactly in the scaling limit where the eigenvalue problem is the same as for the quantum harmonic oscillator. The energy density, the magnetization profile and the two-point correlation function are studied either analytically or by exact numerical calculations. Their scaling behaviour are in agreement with the predictions of the scaling theory.

15 pages, 6 figures, submited to J. Phys. A

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• Signature of Quantum Criticality in the Density Profiles of Cold Atom Systems
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• Quantum phase transition in space in a ferromagnetic spin-1 Bose-Einstein condensate
• Inhomogeneous quasi-adiabatic driving of quantum critical dynamics in weakly disordered spin chains
• Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of z > 1 dynamical exponent
• Gradient critical phenomena in the Ising quantum chain: surface behaviour
• Locating quantum critical points with Kibble-Zurek quenches
• Smoothly-varying hopping rates in driven flow with exclusion
• Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians
• The geometry of percolation fronts in two-dimensional lattices with spatially varying densities
• Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap
• Monte Carlo Study of an Inhomogeneous Blume-Capel Model
• Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions
• Universal scaling in quenches across a discontinuity critical point
• One-dimensional Bose gas driven by a slow time-dependent harmonic trap
• Spatial Kibble-Zurek mechanism through susceptibilities: the inhomogeneous quantum Ising model case
• Universal scaling effects of a temperature gradient at first-order transitions
• Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions
• Defect production in quench from current-carrying non-equilibrium state
• Critical dynamics in trapped particle systems
• Anomalous Dynamical Scaling at Topological Quantum Criticality