Exact Diag. Study of the 1D Disordered XXZ Model

TL;DR

This study uses exact diagonalization to analyze the 1D disordered XXZ model, confirming field-theoretical predictions about phase transitions and critical behavior with high accuracy.

Contribution

It provides the first exact diagonalization analysis of the disordered XXZ model, validating and refining previous field-theoretical phase diagrams and critical exponents.

Findings

Disorder destroys superfluidity for Δ between -1/2 and 1.

Superfluidity persists at finite disorder for Δ between -1 and -1/2.

Phase transitions are consistent with Kosterlitz-Thouless type transitions.

Abstract

We investigate the one-dimensional quantum $XXZ$ model in the presence of diagonal disorder. Recently the model has been analyzed with the help of field-theoretical renormalization group methods, and a phase diagram has been predicted. We study the model with exact diagonalization techniques up to chain lengths of 16 sites. Using finite-size scaling methods we estimate critical exponents and the phase diagram and find reasonably good agreement with the field-theoretical results, namely, that any amount of disorder destroys the superfluidity for $XXZ$ anisotropy $\Delta$ between $ -1/2 $ and $1$, while the superfluidity persists to finite disorder strength for $ -1 < \Delta < -1/2$ and then undergoes a Kosterlitz-Thouless type transition.