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General method for calculating the universal conductance of strongly correlated junctions of multiple quantum wires

  • Rahmani, Armin
  • Hou, Chang-Yu
  • Feiguin, Adrian
  • Oshikawa, Masaki
  • Chamon, Claudio
  • Affleck, Ian
Published Article
Publication Date
Jan 27, 2012
Submission Date
Aug 22, 2011
DOI: 10.1103/PhysRevB.85.045120
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We develop a method to extract the universal conductance of junctions of multiple quantum wires, a property of systems connected to reservoirs, from static ground-state computations in closed finite systems. The method is based on a key relationship, derived within the framework of boundary conformal field theory, between the conductance tensor and certain ground state correlation functions. Our results provide a systematic way of studying quantum transport in the presence of strong electron-electron interactions using efficient numerical techniques such as the standard time-independent density-matrix renormalization-group method. We give a step-by-step recipe for applying the method and present several tests and benchmarks. As an application of the method, we calculate the conductance of the M fixed point of a Y junction of Luttinger liquids for several values of the Luttinger parameter $g$ and conjecture its functional dependence on $g$.

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