Dynamical structure factor of the $J_1-J_2$ Heisenberg model in one dimension: the variational Monte Carlo approach

TL;DR

This paper uses a variational Monte Carlo approach with Gutzwiller-projected fermionic wave functions to accurately compute the dynamical spin structure factor of the one-dimensional J1-J2 Heisenberg model, capturing complex phases and incommensurate structures.

Contribution

It introduces a variational Monte Carlo method with Gutzwiller-projected fermionic wave functions to study dynamical properties of the 1D J1-J2 Heisenberg model, including incommensurate phases.

Findings

Excellent agreement with Lanczos calculations on small clusters.

Accurate characterization of dynamical properties in large clusters.

Identification of incommensurate structures for J2/J1 > 0.5.

Abstract

The dynamical spin structure factor is computed within a variational framework to study the one-dimensional $J_1-J_2$ Heisenberg model. Starting from Gutzwiller-projected fermionic wave functions, the low-energy spectrum is constructed from two-spinon excitations. The direct comparison with Lanczos calculations on small clusters demonstrates the excellent description of both gapless and gapped (dimerized) phases, also including incommensurate structures for $J_2/J_1>0.5$. Calculations on large clusters show how the intensity evolves when increasing the frustrating ratio and give an unprecedented accurate characterization of the dynamical properties of (non-integrable) frustrated spin models.