DMRG Study of Critical Behavior of the Spin-1/2 Alternating Heisenberg Chain

TL;DR

This study uses DMRG to analyze the critical behavior of the spin-1/2 alternating Heisenberg chain, revealing power-law approaches of energy and gap with specific exponents, and confirming RG predictions with logarithmic corrections.

Contribution

It provides detailed numerical analysis of critical exponents and logarithmic corrections in the alternating Heisenberg chain using DMRG, extending understanding of quantum criticality.

Findings

Ground-state energy approaches uniform chain limit with exponent p=1.45

Singlet-triplet gap scales with exponent p=0.73

Logarithmic corrections are significant in describing the data

Abstract

We investigate the critical behavior of the S=1/2 alternating Heisenberg chain using the density matrix renormalization group (DMRG). The ground-state energy per spin and singlet-triplet energy gap are determined for a range of alternations. Our results for the approach of the ground-state energy to the uniform chain limit are well described by a power law with exponent p=1.45. The singlet-triplet gap is also well described by a power law, with a critical exponent of p=0.73, half of the ground-state energy exponent. The renormalization group predictions of power laws with logarithmic corrections can also accurately describe our data provided that a surprisingly large scale parameter is present in the logarithm.