Junctions of multiple quantum wires with different Luttinger parameters

Hou, Chang-Yu; Rahmani, Armin; Feiguin, Adrian; Chamon, Claudio

doi:10.1103/physrevb.86.075451

Cited by 37 publications

(88 citation statements)

References 68 publications

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“…The resulting asymmetry in the S-matrix and the conductance matrix may grow in the process of renormalization. Such a scenario is implied in the work 20 . In order to compare our results with those in 20 , we now discuss a possible anisotropy in the conductance tensor.…”

Section: Fully Anisotropic Y-junctionmentioning

confidence: 99%

“…This minimal modification enables us to elucidate the differences between our conclusions and those in 20 . We show that the set of RG equations for the most general asymmetric chiral case can be easily derived in our formalism, and allows us to discuss the robustness of our results obtained for the partially asymmetric case (g 1 = g 2 ) with respect to further asymmetry.…”

Section: Introductionmentioning

confidence: 99%

“…[20] for the scaling dimensions of the leading irrelevant boundary operators, ∆ χ . This becomes clear after the identification of our α χ with their 2 − 2∆ χ , and after putting their g 1 = g 2 ; g 3 equal to our K; K 3 .…”

Section: Stability Of Fixed Pointsmentioning

confidence: 99%

“…As we will show below, we do not find a fixed point with the characteristics of D, but in contrast we find two new fixed points, not discussed in Refs. [10,20].…”

Section: Introductionmentioning

confidence: 99%

“…It should be compared to the sequence N ,Ā, χ ± ,Ā, A, shown in Fig. 5(e) in 20 . We notice two differences here: one is related to the fact that Hou et al 20 do not include the M point in their analysis, therefore they do not show the combination of several stable FPs, e.g.…”

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confidence: 99%

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Chiral Y junction of Luttinger liquid wires at strong coupling: Fermionic representation

Aristov

Wölfle

2013

Phys. Rev. B

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We calculate the conductances of a three-terminal junction set-up of spinless Luttinger liquid wires threaded by a magnetic flux, allowing for different interaction strength g3 = g in the third wire. We employ the fermionic representation in the scattering state picture, allowing for a direct calculation of the linear response conductances, without the need of introducing contact resistances at the connection points to the outer ideal leads. The matrix of conductances is parametrized by three variables. For these we derive coupled renormalization group (RG) equations, by summing up infinite classes of contributions in perturbation theory. The resulting general structure of the RG equations may be employed to describe junctions with an arbitrary number of wires and arbitrary interaction strength in each wire. The fixed point structure of these equations (for the chiral Yjunction) is analyzed in detail. For repulsive interaction (g, g3 > 0) there is only one stable fixed point, corresponding to the complete separation of the wires. For attractive interaction (g < 0 and/or g3 < 0) four fixed points are found, the stability of which depends on the interaction strength. We confirm our previous weak-coupling result of lines of fixed points for special values of the interaction parameters reaching into the strong coupling domain. We find new fixed points not discussed before, even at the symmetric line g = g3, at variance with the results of Oshikawa et al. The pair tunneling phenomenon conjectured by the latter authors is not found by us.

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Section: Fully Anisotropic Y-junctionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Stability Of Fixed Pointsmentioning

confidence: 99%

“…As we will show below, we do not find a fixed point with the characteristics of D, but in contrast we find two new fixed points, not discussed in Refs. [10,20].…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Chiral Y junction of Luttinger liquid wires at strong coupling: Fermionic representation

Aristov

Wölfle

2013

Phys. Rev. B

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Ambiguity in renormalization of the conductance of an X-junction between quantum wires with a Luttinger-type interaction

Aristov

Niyazov

2015

Theor Math Phys

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We study four-lead junction of semi-infinite wires by using fermionic representation in the scattering state formalism. The model of spinless fermions with short-range Luttinger liquid type interaction is used. We find the renormalization group (RG) equations for the conductances of the system in the first order of fermionic interaction. In contrast to the well-known cases of two-lead and three-lead junctions, we show that the RG equations cannot be expressed solely in terms of conductances. The appearing ambiguity is resolved by choosing a certain sign defined at the level of S-matrix, but hidden in conductances. The origin of this Z 2 symmetry is traced back to the particle-hole symmetry of our Hamiltonian. We demonstrate two distinct RG flows from any point in the space of conductances. The scaling exponents at the fixed points are not affected by these observations.

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Real fermion modes, impurity entropy, and nontrivial fixed points in the phase diagram of junctions of interacting quantum wires and topological superconductors

Giuliano

Affleck

2019

Nuclear Physics B

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We discuss how to extend the impurity entropy to systems with boundary interactions depending on zero-mode real fermion operators (Majorana modes as well as Klein factors). As specific applications of our method, we consider a junction between N interacting quantum wires and a topological superconductor, as well as a Y-junction of three spinless interacting quantum wires. In addition we find a remarkable correspondence between the N = 2 topological superconductor junction and the Y-junction. On one hand, this allows us to determine the range of the system parameters in which a stable phase of the N = 2 junction is realized as a nontrivial, finite-coupling fixed point corresponding to the M-fixed point in the phase diagram of the Y-junction. On the other hand, it enables us to show the occurrence of a novel "planar" finite-coupling fixed point in the phase diagram of the Y-junction. Eventually, we discuss how to set the system's parameters to realize the correspondence.the TLL-approach, tunneling processes at a junction are described in terms of nonlinear vertex operators of the bosonic fields, with nonuniversal scaling dimensions continuously depending on the "bulk" interaction parameters [13,14]. This opens the way to a plethora of nonperturbative features in the phase diagram of those systems, including the remarkable emergence of intermediate, finite-coupling fixed points (FCFP's), either describing phase transitions between different phases (repulsive fixed points), or novel, nontrivial phases of the junction (attractive fixed points), thus generalizing to multi-wire junctions the Kane-Fisher FCFP emerging at a junction between two spinful QW's [15].In this context, the prediction that localized Majorana modes (MM's) can appear at a junction between a normal QW and a topological superconductor (TS) [16] has opened additional brandnew scenarios, as the direct coupling between a quantum wire and a localized MM can potentially give rise to relevant boundary interactions, typically not allowed at junctions between normal wires [17]. As a result, it has been possible to predict the emergence of novel FCFP's in the phase diagram of junctions between more-than-one interacting QW and TS's [18,19]. Moreover, due to ubiquity of the TLL-formalism, which successfully describes (junctions of) quantum spin chains [20,21,22,23], Josephson junction networks [24,25,26,27], as well as topological, Kondo-like systems [28,29,30,31], novel FCFP's have been predicted to emerge in the phase diagram of those systems, as well. Besides their theoretical interest, FCFP's have been argued to correspond to "decoherence-frustrated" phases, in which competing frustration effects can operate to reduce the unavoidable decoherence in the boundary quantum degrees of freedom coupled to the "bath" of bulk modes [32,33], thus making the junction, regarded as a localized quantum impurity, a good candidate to work as a frustration-protected quantum bit [24]. For this reason, it becomes of importance to search for FCFP's in the phase diagram of pert...

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Junctions of multiple quantum wires with different Luttinger parameters

Cited by 37 publications

References 68 publications

Chiral Y junction of Luttinger liquid wires at strong coupling: Fermionic representation

Chiral Y junction of Luttinger liquid wires at strong coupling: Fermionic representation

Ambiguity in renormalization of the conductance of an X-junction between quantum wires with a Luttinger-type interaction

Real fermion modes, impurity entropy, and nontrivial fixed points in the phase diagram of junctions of interacting quantum wires and topological superconductors

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