Spectral and transport properties of quantum wires with bond disorder

Abstract

Systems with bond disorder are defined through lattice Hamiltonians that are of pure nearest neighbour hopping type, i.e., do not contain on-site contributions. They stand representative for the general family of disordered systems with chiral symmetries. Application of the Dorokhov–Mello–Pereyra–Kumar transfer matrix technique P.W. Brouwer et al. [Phys. Rev. Lett 81 (1998) 862; Phys. Rev. Lett. 84 (2000) 1913] has shown that both spectral and transport properties of quasi one-dimensional systems belonging to this category are highly unusual. Most notably, regimes with absence of exponential Anderson localization are observed, the single particle density of states exhibits singular structure in the vicinity of the band centre, and the manifestation of these phenomena depends in an apparently topological manner on the even- or oddness of the channel number. In this paper we re-consider the problem from the complementary perspective of the nonlinear σ -model. Relying on the standard analogy between one-dimensional statistical field theories and zero-dimensional quantum mechanics, we will relate the problem to the behaviour of a quantum point particle subject to an Aharonov–Bohm flux. We will build on this analogy to re-derive earlier DMPK results, identify a new class of even/odd staggering phenomena (now dependent on the total number of sites in the system) and trace back the anomalous behaviour of the bond disordered system to a simple physical mechanism, viz. the flux periodicity of the quantum Aharonov–Bohm system. We will also touch upon connections to the low energy physics of other lattice systems, notably disordered chiral systems in 0 and 2 dimensions and antiferromagnetic spin chains.