New Criticality of 1D Fermions [Phys. Rev. Lett. 73, 561 (1994)]

Mikolaj D. Uryszek, Elliot Christou, Akbar Jaefari +2 more

Pierre Le Doussal, Thierry Giamarchi, E. Orignac

Comment on the paper "Absence of the Mott Glass Phase in 1D Disordered Fermionic Systems" by T. Nattermann, A. Petkovic, Z. Ristivojevic, and F. Schutze, Phys. Rev. Lett. 99, 186402 (2007).

L. Merker, Stefan Kirchner, Enrique Muñoz +1 more

The Comment of A. A. Aligia claims that the superperturbation theory (SPT) approach [E. Mu\~noz, C. J. Bolech, and S. Kirchner, Phys. Rev. Lett. 110, 016601 (2013)] formulated using dual fermions [A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 77, 033101 (2008)] and used by us to compare with numerical renormalization group (NRG) results for the conductance [L. Merker, S. Kirchner, E. Mu\~noz, and T. A. Costi, Phys. Rev. B 87, 165132 (2013)], fails to correctly extend the results of the symmetric Anderson impurity model (SIAM) for general values of the local level ${E}_{d}$ in the Kondo regime. We answer this criticism. We also compare new NRG results for ${c}_{B}$, with ${c}_{B}$ calculated directly from the low-field conductance, with new higher-order SPT calculations for this quantity, finding excellent agreement for all ${E}_{d}$ and for $U/\ensuremath{\pi}\ensuremath{\Delta}$ extending into the strong coupling regime.

Yang Li, Liming Guan, Han Pu

Minoru Kimura, Hiroyuki Fukuyama

Martin Gärttner, Sergey Syzranov, Ana María Rey +2 more

We study a one-dimensional (1D) system with a power-law quasiparticle dispersion ${\ensuremath{\propto}|k|}^{\ensuremath{\alpha}}sgnk$ in the presence of a short-range-correlated random potential, and demonstrate that for $\ensuremath{\alpha}<1/2$ it exhibits a disorder-driven quantum phase transition with critical properties similar to those of the localization transition near the edge of the band of a semiconductor in high dimensions, as studied recently [Phys. Rev. Lett. 114, 166601 (2015); Phys. Rev. B 91, 035133 (2015)]. Despite the absence of localization in the considered 1D system, the disorder-driven transition manifests itself, for example, in a critical form of the disorder-averaged density of states. We confirm the existence of the transition by numerical simulations and find the critical exponents and the critical disorder strength as a function of $\ensuremath{\alpha}$. The proposed system thus presents a convenient platform for numerical studies of the recently predicted unconventional high-dimensional localization effects and has the potential for experimental realizations in chains of ultracold atoms in optical traps.