Chaos in the Bose-glass phase of a one-dimensional disordered Bose fluid

We show that the Bose-glass phase of a one-dimensional disordered Bose fluid exhibits a chaotic behavior, i.e., an extreme sensitivity to external parameters. Using bosonization, the replica formalism and the nonperturbative functional renormalization group, we find that the ground state is unstable to any modification of the disorder configuration (disorder chaos) or variation of the Luttinger parameter (quantum chaos, analog to the temperature chaos in classical disordered systems). This result is obtained by considering two copies of the system, with slightly different disorder configurations or Luttinger parameters, and showing that intercopy statistical correlations are suppressed at length scales larger than an overlap length xi(ov) similar to vertical bar epsilon vertical bar(-1/alpha) (vertical bar epsilon vertical bar << 1 is a measure of the difference between the disorder distributions or Luttinger parameters of the two copies). The chaos exponent alpha can be obtained by computing xi(ov) or by studying the instability of the Bose-glass fixed point for the two-copy system when epsilon not equal 0. The renormalized, functional, intercopy disorder correlator departs from its fixed-point value-characterized by cuspy singularities-via a chaos boundary layer, in the same way as it approaches the Bose-glass fixed point when epsilon = 0 through a quantum boundary layer. Performing a linear analysis of perturbations about the Bose-glass fixed point, we find alpha = 1.

Automated summary

The one-dimensional disordered Bose fluid in the Bose-glass phase exhibits chaotic behavior with extreme sensitivity to external parameters. Statistical correlations between two slightly different copies of the system are suppressed at certain length scales, leading to chaotic phenomena.