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Localization transition in one dimension using Wegner flow equations

Quito, Victor L. and Titum, Paraj and Pekker, David and Refael, Gil (2016) Localization transition in one dimension using Wegner flow equations. Physical Review B, 94 (10). Art. No. 104202. ISSN 2469-9950. doi:10.1103/PhysRevB.94.104202.

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The flow-equation method was proposed by Wegner as a technique for studying interacting systems in one dimension. Here, we apply this method to a disordered one-dimensional model with power-law decaying hoppings. This model presents a transition as function of the decaying exponent α. We derive the flow equations and the evolution of single-particle operators. The flow equation reveals the delocalized nature of the states for α<12. Additionally, in the regime α>12, we present a strong-bond renormalization group structure based on iterating the three-site clusters, where we solve the flow equations perturbatively. This renormalization group approach allows us to probe the critical point (α=1). This method correctly reproduces the critical level-spacing statistics and the fractal dimensionality of the eigenfunctions.

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Additional Information:© 2016 American Physical Society. Received 17 June 2016; revised manuscript received 31 August 2016; published 19 September 2016. The authors would like to acknowledge useful discussions with S. Kehrein, S. Gopalakrishnan, E. Miranda, and D. Huse. P.T. and G.R. are grateful for support from NSF through Grant No. DMR-1410435, as well as the Institute of Quantum Information and Matter, an NSF Frontier center funded by the Gordon and Betty Moore Foundation, and the Packard Foundation. V.L.Q. acknowledges financial support from FAPESP, through Grants No. 2012/17082-7 and No. 2009/17531-3.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)2012/17082-7
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)2009/17531-3
Issue or Number:10
Record Number:CaltechAUTHORS:20160928-115939815
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Official Citation:Localization transition in one dimension using Wegner flow equations Victor L. Quito, Paraj Titum, David Pekker, and Gil Refael Phys. Rev. B 94, 104202 (2016)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:70640
Deposited By: Tony Diaz
Deposited On:28 Sep 2016 19:06
Last Modified:11 Nov 2021 04:32

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