[Paper Review] Spin Reduction Transition in Spin-3/2 Random Heisenberg Chains

Gil Refael, Stefan Kehrein+1 more|arXiv (Cornell University)|Nov 15, 2001

Theoretical and Computational Physics4 citations

TL;DR

This paper investigates spin-3/2 random antiferromagnetic Heisenberg chains using asymptotically exact real-space renormalization group methods and discovers a novel quantum phase transition between two random-singlet phases, each governed by an infinite randomness fixed point. The transition separates a strong-randomness phase with effective S_eff = 3/2 spins from a weak-randomness phase with effective S_eff = 1/2 spins, with critical behavior featuring a non-trivial mixture of S = 1/2, S = 1, and S = 3/2 effective spins at low energies.

ABSTRACT

Random spin-3/2 antiferromagnetic Heisenberg chains are investigated using an asymptotically exact renormalization group. Randomness is found to induce a quantum phase transition between two random-singlet phases. In the strong randomness phase the effective spins at low energies are S_eff=3/2, while in the weak randomness phase the effective spins are S_eff=1/2. Separating them is a quantum critical point near which there is a non-trivial mixture of S=1/2, S=1, and S=3/2 effective spins at low temperatures.

Motivation & Objective

• To understand the low-energy behavior of random spin-3/2 antiferromagnetic Heisenberg chains, which are gapless in the pure case but may exhibit new quantum phases under disorder.
• To investigate whether randomness induces new types of quantum phase transitions in higher-spin chains beyond the well-known spin-1/2 random singlet phase.
• To determine if infinite randomness fixed points can govern not only single phases but also transitions between distinct random-singlet phases in higher-spin systems.
• To analyze the critical behavior at the transition, including the scaling of effective spin fractions and dynamical critical exponents.

Proposed method

• Application of asymptotically exact real-space renormalization group (RG) to iteratively decimate the strongest bonds in the chain, forming spin singlets and generating effective couplings between remaining spins.
• Use of the RG equation J_eff ≈ (1/2) * (J_left * J_right) / J_max to compute effective couplings after each decimation step, preserving the universal low-energy physics.
• Identification of fixed points in the RG flow to classify phases: strong randomness leads to an S_eff = 3/2 random singlet phase, weak randomness to an S_eff = 1/2 phase on a Haldane background.
• Analysis of the critical point using scaling forms for the effective spin fractions, susceptibility, and correlation functions, with universal scaling functions derived from the RG flow.
• Numerical extraction of critical exponents ν and ψ_c from the scaling of effective spin fractions and susceptibility, yielding ν ≈ 3.2 and ψ_c ≈ 0.26.
• Use of neutron scattering response functions to predict observable signatures in the magnetic structure factor S(q,ω) near the critical point.

Experimental results

Research questions

• RQ1 Does randomness in spin-3/2 Heisenberg chains lead to a quantum phase transition between two distinct random-singlet phases?
• RQ2 Can both the phases and the transition between them be governed by infinite randomness fixed points, as seen in spin-1/2 chains?
• RQ3 What is the nature of the critical point, and how do the effective spin quantum numbers (S = 1/2, 1, 3/2) mix at criticality?
• RQ4 How do the critical exponents ν and ψ_c govern the scaling of physical observables like susceptibility and spin fractions?
• RQ5 What experimental signatures, such as in neutron scattering, could reveal the critical spin mixture and anomalous dynamics?

Key findings

• The system exhibits a quantum phase transition between two random-singlet phases: one with effective S_eff = 3/2 spins in the strong-randomness regime, and another with effective S_eff = 1/2 spins in the weak-randomness regime.
• At the critical point, the effective spin fractions are universal: p_{1/2} = 0.32, p_1 = 0.34, p_{3/2} = 0.34, indicating a non-trivial mixture of S = 1/2, S = 1, and S = 3/2 effective spins.
• The dynamical critical exponent is found to be ψ_c = 1/3.85 ≈ 0.26, which is larger than in either phase, implying faster dynamics at the critical point.
• The correlation length exponent is ν ≈ 3.2 ± 0.3, derived from the scaling of effective spin fractions with energy scale.
• The linear susceptibility scales as χ(T) ≈ 1/(T ln^{1/ψ_c} T) near the critical point, with a logarithmic divergence in the scaling function.
• The critical point exhibits a universal scaling form for the susceptibility, with X(δ) vanishing as |δ - δ_c|^{(1 - 2ψ_c)ν} for large deviations from criticality.