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Quantum impurity in a Luttinger liquid: Universal conductance with entanglement renormalization

Lo, Ya-Lin and Hsieh, Yun-Da and Hou, Chang-Yu and Chen, Pochung and Kao, Ying-Jer (2014) Quantum impurity in a Luttinger liquid: Universal conductance with entanglement renormalization. Physical Review B, 90 (23). Art. No. 235124. ISSN 1098-0121.

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We study numerically the universal conductance of Luttinger-liquid wire with a single impurity via the multiscale entanglement renormalization ansatz (MERA). The scale-invariant MERA provides an efficient way to extract scaling operators and scaling dimensions for both the bulk and the boundary conformal field theories. By utilizing the key relationship between the conductance tensor and ground-state correlation function, the universal conductance can be evaluated within the framework of the boundary MERA. We construct the boundary MERA to compute the correlation functions and scaling dimensions for the Kane-Fisher fixed points by modeling the single impurity as a junction (weak link) of two interacting wires. We show that the universal behavior of the junction can be easily identified within the MERA and argue that the boundary MERA framework has tremendous potential to classify the fixed points in general multiwire junctions.

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Additional Information:© 2014 American Physical Society. Received 3 March 2014; revised manuscript received 18 November 2014; published 15 December 2014. We acknowledge the inspiring discussions with G. Evenbly, G. Vidal,M. Oshikawa, and M. Cazalilla. C.-Y. Hou acknowledges the support from DARPA-QuEST program, Packard foundation, and IQIM. The support from Ministry of Science and Technology in Taiwan through Grants No. 100-2112-M-002-013-MY3, No. 100-2923-M-004-002 -MY3, No. 102-2112-M-002-003-MY3, No. 101-2112-M-007-010-MY3, as well as the support fromNational Taiwan University Grant No. 101R891004, are acknowledged. The MERA computation is based on the Universal Tensor Network Library (Uni10).
Group:Institute for Quantum Information and Matter, IQIM
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Ministry of Science and Technology (Taipei)100-2112-M- 002-013-MY3
Ministry of Science and Technology (Taipei)100-2923-M-004-002 -MY3
Ministry of Science and Technology (Taipei)102- 2112-M-002-003-MY3
Ministry of Science and Technology (Taipei)101-2112-M-007-010-MY3
National Taiwan University101R891004
Classification Code:PACS number(s): 05.10.Cc, 02.70.−c, 05.60.Gg, 05.50.+q
Record Number:CaltechAUTHORS:20150115-095052317
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Official Citation:Lo, Y.-L., Hsieh, Y.-D., Hou, C.-Y., Chen, P., & Kao, Y.-J. (2014). Quantum impurity in a Luttinger liquid: Universal conductance with entanglement renormalization. Physical Review B, 90(23), 235124.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53764
Deposited By: Jason Perez
Deposited On:15 Jan 2015 20:03
Last Modified:27 Mar 2017 19:43

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