Random free-fermion quantum spin chain with multi-spin interactions

TL;DR

This paper investigates the effects of quenched disorder on a class of free-fermion quantum spin chains with multi-spin interactions, revealing different critical behaviors and phases depending on how disorder couples to the system.

Contribution

It introduces a detailed analysis of disorder effects in multi-spin interaction chains, identifying universal and nonuniversal critical points and phases, using advanced numerical and renormalization techniques.

Findings

Disorder coupled to all interactions leads to infinite-randomness critical points.

Disorder coupling to some interactions leaves the clean critical behavior stable.

Disorder stabilizes a line of finite-randomness critical points with nonuniversal exponents.

Abstract

We study the effects of quenched disorder in a class of quantum chains with (p+1)-multispin interactions exhibiting a free fermionic spectrum, paying special attention to the case p=2. Depending if disorder couples to (i) all the couplings or just to (ii) some of them, we have two distinct physical scenarios. In case (i), we find that the transitions of the model are governed by a universal infinite-randomness critical point surrounded by quantum Griffiths phases similarly as happens to the random transverse-field Ising chain. In case (ii), we find that quenched disorder becomes an irrelevant perturbation: the clean critical behavior is stable and Griffiths phases are absent. Beyond the perturbative regime, disorder stabilizes a line of finite-randomness critical points (with nonuniversal critical exponents), that ends in a multicritical point of infinite-randomness type. In that case, quantum Griffiths phases also appear surrounding the finite-disorder transition point. We have characterized the correlation functions and the low-temperature thermodynamics of these chains. Our results are derived from a strong-disorder renormalization-group technique and from finite-size scaling analysis of the spectral gap computed exactly (up to sizes ~10^{7}) via an efficient new numerical method recently introduced in the literature [Phys. Rev. B 104, 174206 (2021)].