Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets

Abstract

We study a one-dimensional disordered Bose fluid using bosonization, the replica method and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale k, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width of the QBL depends on an effective Luttinger parameter K k ∼ k θ that vanishes with an exponent θ = 1/2, thus yielding a dynamical critical exponent z = 3/2. The QBL encodes the existence of rare "superfluid" regions, controls the low-energy dynamics and yields a (dissipative) conductivity vanishing as ω 2 in the low-frequency limit. These results reveal the glassy properties (pinning, "shocks" or static avalanches) of the Bose-glass phase and can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.

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

“…In the absence of linearly confining interactions, i.e. for a disordered fluid with short-range interactions, the main features of the FRG flow are well understood [20,21]. There p-1 arXiv:2001.05682v1 [cond-mat.quant-gas] 16 Jan 2020 is an attractive line of fixed points at vanishing disorder corresponding to the superfluid phase.…”

“…The cutoff function R k (q, iω) is chosen so that fluctuation modes satisfying |q|, |ω|/v k k are suppressed while those with |q| k or |ω|/v k k are left unaffected (v k denotes the k-dependent sound-mode velocity, see below); its precise form is given in Ref. [21]. The partition function…”

“…The form of the effective action is strongly constrained by the statistical tilt symmetry (STS) [29] which originates from the invariance of the disorder part of the action (4) in the change ϕ a (x, τ ) → ϕ a (x, τ ) + w(x) with w(x) an arbitrary time-independent function [21]:…”

“…In the absence of linearly confining interactions (e = 0) the ansatz (10) corresponds to the one used in Refs. [20,21] to study the Bose-glass phase. In the disordered Schwinger model the effective action includes the additional mass term (e 2 /2π 2 )φ 2 a .…”

“…The only modification coming from the linearly confining interaction is the presence of the nonzero mass in the propagator ( 12) which enters the "threshold" functions l 1 , l2 , l1 (iω), mτ (see Appendix D4 in Ref. [21] for an explicit definition of the threshold functions). Note that the propagator in dimensionless form, Pk (q, iω) = Z x k 2 P k (q, iω) with q = q/k, is naturally expressed in terms of the dimensionless square charge ẽ2 k = e 2 /Z x k 2 .…”