Critical Behavior of the Random Potts Chain

TL;DR

This paper investigates the critical behavior of the random q-state Potts quantum chain using density matrix renormalization, revealing q-independence of critical properties and analyzing multiscaling and dynamical correlations.

Contribution

It provides the first detailed numerical analysis of critical exponents and multiscaling in the disordered quantum Potts chain, confirming q-independence predicted by renormalization group theory.

Findings

Critical exponents are independent of q.

Accurate determination of critical exponents via moments of magnetization.

Multiscaling and dynamical correlation functions are characterized.

Abstract

We study the critical behavior of the random q-state Potts quantum chain by density matrix renormalization techniques. Critical exponents are calculated by scaling analysis of finite lattice data of short chains ($L \leq 16$) averaging over all possible realizations of disorder configurations chosen according to a binary distribution. Our numerical results show that the critical properties of the model are independent of q in agreement with a renormalization group analysis of Senthil and Majumdar (Phys. Rev. Lett.{\bf 76}, 3001 (1996)). We show how an accurate analysis of moments of the distribution of magnetizations allows a precise determination of critical exponents, circumventing some problems related to binary disorder. Multiscaling properties of the model and dynamical correlation functions are also investigated.