Is there a Mott-glass phase in a one-dimensional disordered quantum fluid with linearly confining interactions?

Abstract

We study a one-dimensional disordered quantum fluid with linearly confining interactions (disordered Schwinger model) using bosonization and the nonperturbative functional renormalization group. We find that the long-range interactions make the Anderson insulator (or, for bosons, the Bose-glass) fixed point (corresponding to a compressible state with a gapless optical conductivity) unstable, even if the latter may control the flow at intermediate energy scales. The stable fixed point describes an incompressible ground state with a gapped optical conductivity similar to a Mott insulator. These results disagree with the Gaussian variational method that predicts a Mott glass, namely a state with vanishing compressibility but a gapless optical conductivity.

Mott-glass phase of a one-dimensional quantum fluid with long-range interactions

“…The case σ = −2 (disordered Schwinger model) requires a separate study since Z x q 2 f q does not vanish for q → 0. Although there are contradicting results in the literature regarding the possible existence of a Mott glass in the disordered Schwinger model [6,9,10], our results regarding the stability of the Wigner crystal against disorder when −2 < σ < −3/2 are in line with a recent FRG study predicting the absence of a Mott glass when σ = −2, the ground state being similar to a Mott insulator (vanishing compressibility and gapped conductivity) [10].…”

“…Following previous FRG studies of one-dimensional disordered boson systems [10,20,21], we consider the following truncation of the effective action,…”

“…The π-periodic function V k (u) can be interpreted as a renormalized second cumulant of the disorder. The form of the ansatz (10) is strongly constrained by the so-called statistical tilt symmetry (STS) [21,31]. In particular the term Z x q 2 f q is not renormalized and no other space-derivative terms can be generated.…”

“…On the one hand it has been proposed that the interplay between disorder and a commensurate periodic potential could stabilize a Mott glass [5,6] but this conclusion, when the interactions are short range, has been challenged [7,8]. On the other hand, the existence of a Mott glass in a disordered system with linearly confining interactions mediated by a (1 + 1)-dimensional gauge field (disordered Schwinger model) has been predicted by the Gaussian Variational Method [9] and the perturbative functional renormalization group (FRG) [6], but this conclusion is in conflict with a recent study based on the nonperturbative FRG [10]. The only system that seems to certainly satisfy the basic properties of the Mott glass is the one-dimensional electron gas with (unscreened) Coulomb interactions [11].…”

Flowing bosonization in the nonperturbative functional renormalization-group approach

“…Bosonization is one of the most popular methods to describe one-dimensional quantum fluids [1]. It has recently been used in combination with the nonperturbative functional renormalization (FRG) group to study the Mott-insulating phase induced by a periodic potential (in the framework of the sine-Gordon model) [2,3] and the Bose-glass phase of disordered bosons [4][5][6][7][8]. These studies are based on an action S[ϕ] expressed solely in terms of the "density" field ϕ, its conjugate partner, the phase ϑ of the superfluid order parameter (the field operator ψ for bosons), being integrated out from the outset.…”