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Quantum dynamics of an Ising spin-chain in a random transverse field
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Quantum dynamics of an Ising spin-chain in a random transverse field
Xun Jia and Sudip Chakravarty?
Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095-1547
(Dated: February 6, 2008)
We consider an Ising spin-chain in a random transverse magnetic field and compute the zero
temperature wave vector and frequency dependent dynamic structure factor numerically by using
Jordan-Wigner transformation. Two types of distributions of magnetic fields are introduced. For
a rectangular distribution, a dispersing branch is observed, and disorder tends to broaden the
dispersion peak and close the excitation gap. For a binary distribution, a non-dispersing branch at
almost zero energy is obtained. We discuss the relationship of our work to the neutron scattering
measurement in LiHoF4.
Calculation of real-time dynamics of a correlated quan-
tum system with an infinite number of degrees of freedom
are few and far between. Except for isolated examples,
construction of real-time behavior from imaginary-time
correlation functions (more amenable to numerical meth-
ods) by analytic continuation is fraught with various in-
stabilities. The theoretical challenge is particularly acute
because neutron scattering experiments often provide a
rather detailed map of the frequency, ω, and the wave
vector, k, dependent dynamical structure factor, S(k, ω).
The second motivation comes from the desire to study
the dynamics of a quantum phase transition involving a
zero temperature quantum critical point. In this respect,
the Ising spin chain in a transverse field1,2,3,4 constitutes
a schema from which much can be learned about quan-
tum criticality,5 both with and without disorder.
The third motivation is to examine how the coherence
of the quasiparticle excitations is modified in the presence
of quenched disorder and is triggered by a recent neutron
s
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