Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field (PhD thesis)

TL;DR

This thesis explores the static and dynamic properties of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field, combining numerical and analytical methods to analyze phase diagrams, excitation spectra, and experimental correlations.

Contribution

It provides a comprehensive analysis of spin-1/2 ladder systems using DMRG and mean field approaches, including detailed predictions for neutron scattering and NMR experiments.

Findings

Excellent agreement with neutron scattering data on BPCB

Predictions for high-energy spectral features

Analysis of magnetic field effects on spectra

Abstract

We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound $\mathrm{(C_5H_{12}N)_2CuBr_4}$ (BPCB). We use a combination of numerical and analytical methods, in particular the density matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic field dependence of the nuclear magnetic resonance (NMR) relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean field approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore we compute, using time dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to directly describe the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid (LL) or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high energy part of the spectrum that are potentially testable in future experiments.