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

  title={Spatial Kibble–Zurek mechanism through susceptibilities: the inhomogeneous quantum Ising model case},
  author={Mateusz K. Łącki and Bogdan Damski},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  • M. Łącki, B. Damski
  • Published 31 July 2017
  • Physics
  • Journal of Statistical Mechanics: Theory and Experiment
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 insight 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… 
6 Citations

Figures from this paper

Locating quantum critical points with Kibble-Zurek quenches

We describe a scheme for finding quantum critical points based on studies of a non-equilibrium susceptibility during continues quenches taking the system from one phase to another. We assume that two

Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians

We introduce a phenomenological theory for many-body control of critical phenomena by engineering causally-induced gaps for quantum Hamiltonian systems. The core mechanisms are controlling

Critical quantum thermometry and its feasibility in spin systems

In this work, we study temperature sensing with finite-sized strongly correlated systems exhibiting quantum phase transitions. We use the quantum Fisher information (QFI) approach to quantify the

On the size of boundary effects in the Ising chain

We discuss the length at which boundaries affect the magnetization of the quantum Ising chain with free ends. For this purpose we introduce two characteristic length scales describing the size of the

Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions

Driving a homogeneous system across a quantum phase transition in a quench-time $\tau_Q$ generates excitations on wavelengths longer than the Kibble-Zurek (KZ) length

Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries

Spontaneous breaking of continuous time translation symmetry into a discrete one is related to time crystal formation. While the phenomenon is not possible in the ground state of a time-independent



Dynamics of an inhomogeneous quantum phase transition

We argue that, in a second-order quantum phase transition driven by an inhomogeneous quench, the density of quasi-particle excitations is suppressed when velocity at which a critical point propagates

Gradient critical phenomena in the Ising quantum chain

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

Nonlinear quenches of power-law confining traps in quantum critical systems

We describe the coherent quantum evolution of a quantum many-body system with a time-dependent power-law confining potential. The amplitude of the inhomogeneous potential is driven in time along a

Nonequilibrium dynamic critical scaling of the quantum Ising chain.

Qualitatively athermal features of the scaling functions of the one-dimensional transverse-field Ising chain are found, and it is shown that they should be robustly observable within present cold atom experiments.

Universal adiabatic dynamics in the vicinity of a quantum critical point

We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second-order quantum phase transition. It is shown that despite the conventional

Critical quench dynamics in confined systems.

Under this protocol, general scaling laws for the density of excitations created during the nonadiabatic sweep of the confining potential are derived and it is found that the mean excitation density follows an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential.

Inhomogeneous quasi-adiabatic driving of quantum critical dynamics in weakly disordered spin chains

We introduce an inhomogeneous protocol to drive a weakly disordered quantum spin chain quasi-adiabatically across a quantum phase transition and minimize the residual energy of the final state. The

Adiabatic-impulse approximation for avoided level crossings: From phase-transition dynamics to Landau-Zener evolutions and back again

We show that a simple approximation based on concepts underlying the Kibble-Zurek theory of second order phase-transition dynamics can be used to treat avoided level crossing problems. The approach

Universal scaling for a quantum discontinuity critical point and quantum quenches

We study slow variation (both spatial as well as temporal) of a parameter of a system in the vicinity of discontinuous quantum phase transitions, in particular, a discontinuity critical point (DCP)

Adiabatic dynamics of an inhomogeneous quantum phase transition: the case of a z>1 dynamical exponent

We consider an inhomogeneous quantum phase transition across a multicritical point of the XY quantum spin chain. This is an example of a Lifshitz transition with a dynamical exponent z=2. Just like