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Time-dependent real-space renormalization-group approach: application to an adiabatic random quantum Ising model

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journal contribution
posted on 2018-12-03, 13:54 authored by Peter Mason, Alexandre ZagoskinAlexandre Zagoskin, Joseph BetourasJoseph Betouras
We develop a time-dependent real-space renormalization-group approach which can be applied to Hamiltonians with time-dependent random terms. To illustrate the renormalization-group analysis, we focus on the quantum Ising Hamiltonian with random site- and time-dependent (adiabatic) transverse-field and nearest-neighbour exchange couplings. We demonstrate how the method works in detail, by calculating the off-critical flows and recovering the ground state properties of the Hamiltonian such as magnetization and correlation functions. The adiabatic time allows us to traverse the parameter space, remaining near-to the ground state which is broadened if the rate of change of the Hamiltonian is finite. The quantum critical point, or points, depend on time through the time-dependence of the parameters of the Hamiltonian. We, furthermore, make connections with Kibble-Zurek dynamics and provide a scaling argument for the density of defects as we adiabatically pass through the critical point of the system.

Funding

The work was supported by EPSRC through the grant EP/M006581/1.

History

School

  • Science

Department

  • Physics

Citation

MASON, P., ZAGOSKIN, A.M. and BETOURAS, J.J., 2018. Time-dependent real-space renormalization-group approach: application to an adiabatic random quantum Ising model. Journal of Physics A: Mathematical and Theoretical, 52: 045004.

Publisher

© IOP Publishing

Version

  • AM (Accepted Manuscript)

Publisher statement

This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/aaf489.

Publication date

2019-01-07

ISSN

1751-8113

eISSN

1751-8121

Language

  • en

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