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Title: Time-dependent real-space renormalization-group approach: application to an adiabatic random quantum Ising model
Authors: Mason, Peter
Zagoskin, Alexandre M.
Betouras, Joseph J.
Issue Date: 2018
Publisher: © IOP Publishing
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, [in press].
Abstract: 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.
Description: This paper is closed access until 12 months after the date of publication.
Sponsor: The work was supported by EPSRC through the grant EP/M006581/1.
Version: Accepted for publication
DOI: 10.1088/1751-8121/aaf489
URI: https://dspace.lboro.ac.uk/2134/36299
Publisher Link: https://doi.org/10.1088/1751-8121/aaf489
ISSN: 1751-8113
Appears in Collections:Closed Access (Physics)

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