The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary transformations or by variational approaches. Even in the absence of further interactions the hard-core constraint makes the dynamics of the hard-core bosons nontrivial. Here, we develop a systematic diagrammatic approach to the spectral properties of hard-core bosons at finite temperature. Starting from an expansion in the density of thermally excited bosons in a system with an energy gap, our approach leads to a summation of ladder diagrams. Conceptually, the approach is not restricted to one dimension, but the one-dimensional case offers the opportunity to gauge the method by comparison to exact results obtained via a mapping to Jordan-Wigner fermions. In particular, we present results for the thermal broadening of single-particle spectral functions at finite temperature. The line shape is found to be asymmetric at elevated temperatures and the bandwidth of the dispersion narrows with increasing temperature. Additionally, the total number of thermally excited bosons is calculated and compared to various approximations and analytic results. Thereby, a flexible approach is introduced that can also be applied to more sophisticated and higher dimensional models.
We investigate how dynamic correlations of hard-core bosonic excitation at finite temperature are affected by additional interactions besides the hard-core repulsion which prevents them from occupying the same site. We focus especially on dimerized spin systems, where these additional interactions between the elementary excitations, triplons, lead to the formation of bound states, relevant for the correct description of scattering processes. In order to include these effects quantitatively, we extend the previously developed Br\"uckner approach to include also nearest-neighbor (NN) and next-nearest neighbor (NNN) interactions correctly in a low-temperature expansion. This leads to the extension of the scalar Bethe-Salpeter equation to a matrix-valued equation. As an example, we consider the Heisenberg spin ladder to illustrate the significance of the additional interactions on the spectral functions at finite temperature, which are proportional to inelastic neutron scattering rates.
In this thesis we investigate dynamical correlations of spin systems at finite temperature. Especially we focus on the anomalous decoherence effects found previously in experiments of several quantum magnets. We develop and apply a diagrammatic perturbative approach, which incorporates the hard-core bosonic nature of spin excitations. This allows for a computation of the leading low-temperature contributions to the spectral function. The Jordan-Wigner transformation is used to benchmark the approach against exact results of the XX-chain in a strong transverse field. To tackle also more complex problems and vertex corrections we combine the approach with effective models derived by continuous unitary transformations. We perform an in-depth analysis of the approach to assess its properties in the context of conserving approximations in the sense of Baym and Kadanoff. The key result of this thesis is the investigation of two quantum magnets: BaCu2V2O8 and Cu(NO3)2·2.5D2O. We show that the anomalous decoherence observed can be traced back to non-trivial scattering processes of the hard-core bosonic excitations. This indicates, that quantum coherence plays a significant rolein describing dynamical correlations, even at finite temperature. Finally we show, how additional interactions can be taken into account in the full diagrammatic approach, going beyond a mean-field decoupling.
Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material
SrCu2(BO3)2 show an almost complete destruction of the one-triplet excitation band at a temperature only 1/3 of its gap energy, accompanied by strong scattering intensities for apparent multi-triplet excitations. We investigate these questions in the frustrated spin ladder and present numerical results from exact diagonalization for the dynamical structure factor as a function of temperature. We find anomalously rapid transfer of spectral weight out of the one-triplet band and into both broad and sharp spectral features at a wide range of energies, including below the zero-temperature gap of this excitation. These features are multi-triplet bound states, which develop particularly strongly near the quantum phase transition, fall to particularly low energies there, and persist all the way to infinite temperature. Our results offer valuable insight into the physics of finite-temperature spectral functions in
SrCu2(BO3)2 and many other highly frustrated spin systems.
We study various properties of bosons in two dimensions interacting only via on-site hardcore repulsion. In particular, we use the lattice spin-wave approximation to calculate the ground-state energy, the density, the condensate density, and the superfluid density in terms of the chemical potential. We also calculate the excitation spectrum, \ensuremath{\omega}(k). In addition, we perform high precision numerical simulations using the stochastic series expansion algorithm. We find that the spin-wave results describe extremely well the numerical results over the whole density range 0\ensuremath{\leqslant}\ensuremath{\rho}\ensuremath{\leqslant}1. We also compare the lattice spin-wave results with continuum results obtained by summing the ladder diagrams at low density. We find that for \ensuremath{\rho}\ensuremath{\leqslant}0.1 there is good agreement, and that the difference between the two methods vanishes as ${\ensuremath{\rho}}^{2}$ for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\rho}}}$0. This offers the possibility of obtaining precise continuum results by taking the continuum limit of the spin-wave results for all densities. Finally, we study the finite-temperature phase transition numerically for the entire density range, and compare with low density predictions.
A finite-temperature (
T>0) study of a model of a mixture of spin-zero hardcore bosons and spinless fermions, with filling fractions
ρB and
ρF, respectively, on a two-dimensional square lattice with composite hopping
t is presented. The composite hopping swaps the locations of a fermion and a boson that occupy nearest-neighbor sites of the lattice. The superfluid order parameter
ψ, the femion hopping amplitude
ϕ, the chemical potential
μ, the free energy minimum
F~ and entropy
S are calculated in the limit
ρB+ρF=1 within a mean-field approximation, and lead to a phase diagram in the
ρF−T plane. This phase diagram consists of a metallic superfluid phase under a dome-shaped
T(ρF), and insulating normal liquid and insulating normal gas phases outside the dome. These phases are separated by coupled discontinuous transitions as indicated by jumps in
ψ and
ϕ. The maximum critical transition temperature
Tc is observed very close to
ρF=1/2. While
F~(T) is continuous with a derivative discontinuity at
T=Tc(ρF) for
01/2 (zeroth-order transition), where the entropy becomes negative for a range of temperatures below
Tc. The ratio of
Tc to Fermi band width agrees remarkably with the ratio of
Tc/
TF (where
TF is the Fermi temperature) of unconventional superfluids and superconductors like Fermi-Bose mixtures, the high-
Tc cuprates, iron-based and hydride superconductors, that exhibit experimental values of
Tc spread over nine orders of magnitude from
∼200nK to
∼260K.