Junctions of anyonic Luttinger wires

Abstract

We present an extended study of anyonic Luttinger liquids wires jointing at a single point. The model on the full line is solved with bosonization and the junction of an arbitrary number of wires is treated imposing boundary conditions that preserve exact solvability in the bosonic language. This allows us to reach, in the low momentum regime, some of the critical fixed points found with the electronic boundary conditions. The stability of all the fixed points is discussed.

One-body reduced density matrix of trapped impenetrable anyons in one dimension

“…In fact all the most relevant formulae in that section, Eqs. (10)- (12), have a correspondence in [43]. Also Fig.…”

“…In two dimensions, the fractional statistics of the elementary excitation of the quantum Hall effect has certainly represented a huge physical motivation in this direction [2]. In one dimension, numerous models of anyons have been proposed ( [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] among others), but most of them have been thought to be essentially playgrounds for theoreticians for quite a long time. This perspective seems bound to change in view of the new experimental achievements, in particular concerning cold atoms in optical lattices.…”

Junctions of multiple quantum wires with different Luttinger parameters

“…21,22 Due to their rich transport behavior, junctions of quantum wires and their networks have thus attracted much attention. [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] Most of the previous works on the transport properties of junctions of TLL wires focus on wires with the same Luttinger parameter. However, experimentally, there is no reason for all the TLLs emanating from a junction to be identical.…”

Power dissipation for systems with junctions of multiple quantum wires

“…On the other hand, if we have strongly interacting electrons in one dimension, then it is natural to use bosonization. The electrons in the wire are then expressed in terms of free bosonic excitations described by TLL theory, and the fixed point theory of the junction can be described in terms of a current splitting matrix M which is obtained by imposing a linear boundary condition on the incoming and outgoing bosonic fields at the junction [12,13,16,[18][19][20][21][22][23][24]. One can use free bosonic fields to describe either non-interacting or interacting electrons in the bulk of the one-dimensional wires depending on whether the Luttinger parameter g is equal to or not equal to 1.…”

“…Junctions of several quantum wires have also been studied in recent years since they can now be experimentally realized in carbon nanotubes [7][8][9][10][11]. The existing studies of junctions of quantum wires, which are usually modeled as TomonagaLuttinger liquids (TLL), have mainly looked at their lowtemperature fixed points and the corresponding conductance matrices [12][13][14][15][16][17][18][19][20][21][22][23][24]. Many of these studies have focused on situations in which there is no power dissipation in the system.…”