DMRG study of scaling exponents in spin-1/2 Heisenberg chains with dimerization and frustration

TL;DR

This study uses DMRG to analyze how the energy gap and ground state energy scale with dimerization in spin-1/2 Heisenberg chains, revealing the effects of frustration and logarithmic corrections on critical exponents.

Contribution

It provides a detailed DMRG analysis of scaling exponents in frustrated spin chains, clarifying the impact of logarithmic corrections and frustration on critical behavior.

Findings

Logarithmic corrections vanish at J_2c=0.2411, aligning with field theory.

Exponents decrease from 3/4 to 2/3 for the spin gap as J_2 approaches J_2c.

Error bars in exponents decrease near the critical frustration point.

Abstract

In conformal field theory, key properties of spin-1/2 chains, such as the ground state energy per site and the excitation gap scale with dimerization delta as delta^alpha with known exponents alpha and logarithmic corrections. The logarithmic corrections vanish in a spin chain with nearest (J=1) and next nearest neighbor interactions (J_2), for J_2c=0.2411. DMRG analysis of a frustrated spin chain with no logarithmic corrections yields the field theoretic values of alpha, and the scaling relation is valid up to the physically realized range, delta ~ 0.1. However, chains with logarithmic corrections (J_2<0.2411 J) are more accurately fit by simple power laws with different exponents for physically realized dimerizations. We show the exponents decreasing from approximately 3/4 to 2/3 for the spin gap and from approximately 3/2 to 4/3 for the energy per site and error bars in the exponent also decrease as J_2 approaches to J_2c.