Coefficients of bosonized dimer operators in spin-1/2 XXZ chains and their applications

TL;DR

This paper numerically determines coefficients of bosonized dimer operators in spin-1/2 XXZ chains and applies these to analyze phase diagrams, optical conductivity, and electric polarization in related quantum spin and Mott insulator systems.

Contribution

It provides precise numerical values for bosonized dimer operator coefficients and demonstrates their applications in various quantum spin chain and Mott insulator models.

Findings

Coefficients d_xy and d_z are numerically evaluated for XXZ chains.

Ground-state phase diagrams are constructed using these coefficients.

Optical conductivity and electric polarization are quantitatively analyzed.

Abstract

Comparing numerically evaluated excitation gaps of dimerized spin-1/2 XXZ chains with the gap formula for the low-energy effective sine-Gordon theory, we determine coefficients d_xy and d_z of bosonized dimerization operators in spin-1/2 XXZ chains, which are defined as (-1)j(S^x_j S^x_j+1 +S^y_j S^y_j+1) = d_xy sin(\sqrt{4pi}phi(x))+ ... and (-1)^j S^z_j S^z_j+1 = d_z sin(sqrt{4pi}phi(x)) + .... We also calculate the coefficients of both spin and dimer operators for the spin-1/2 Heisenberg antiferromagnetic chain with a nearest-neighbor coupling J and a next-nearest-neighbor coupling J2 = 0.2411J. As applications of these coefficients, we present ground-state phase diagrams of dimerized spin chains in a magnetic field and antiferromagnetic spin ladders with a four-spin interaction. The optical conductivity and electric polarization of one-dimensional Mott insulators with Peierls instability are also evaluated quantitatively.