Strongly disordered Hubbard model in one dimension: spin and orbital infinite randomness and Griffiths phases

TL;DR

This paper investigates the low-energy phases of a disordered one-dimensional Hubbard model using strong disorder RG, revealing two critical phases with infinite randomness and associated Griffiths phases, supported by numerical simulations.

Contribution

It identifies and characterizes two distinct infinite randomness critical phases in the disordered Hubbard model, connecting them to Griffiths phases with specific scaling behaviors.

Findings

Identification of spin and orbital infinite randomness fixed points

Existence of Griffiths phases with well-defined scaling laws

Good agreement between theoretical predictions and numerical RG results

Abstract

We study by the strong disorder renormalization group (RG) method the low-energy properties of the one-dimensional Hubbard model with random-hopping matrix-elements $t_{min}<t<t_{max}$, and with random on-site Coulomb repulsion terms $0 \le U_{min}<U<U_{max}$. There are two critical phases, corresponding to an infinite randomness spin random singlet for strong interactions ($U_{min} > t_{max}$) and to an orbital infinite randomness fixed point for vanishing interactions ($U_{max}/t_{max} \to 0$). To each critical infinite randomness fixed point is connected a Griffiths phase, the correlation length and dynamical exponent of which have well defined asymptotic dependences on the corresponding quantum control parameter. The theoretical predictions for the scaling in the vicinity of the critical points compare well to numerical RG simulations.