We study a system of
N interacting triplons (the elementary excitations of a valence-bond solid) described by an effective interacting boson model derived within the bond operator formalism in order to determine the stability and the properties of many-triplon states. In particular, we consider the square lattice spin-$1/2\phantom{\rule{4pt}{0ex}}{J}_{1}\ensuremath{-}{J}_{2}$ antiferromagnetic Heisenberg model, focus on the intermediate parameter region where a quantum paramagnetic phase sets in, and consider the columnar valence-bond solid as a reference state. Within the bond operator theory, the Heisenberg model is mapped into an effective boson model in terms of triplet operators
t. The effective boson model is studied at the harmonic approximation and the energy of the triplons and the expansion of the triplon operators
b in terms of the triplet operators
t are determined. Such an expansion allows us to perform a second mapping and, therefore, determine an effective interacting boson model in terms of the triplon operators
b. We then consider systems with a fixed number
N of triplons and study the stability of many-triplon states within a mean-field approximation. We show that many-triplon states are stable, the lowest-energy ones are constituted by a small number of triplons, and the excitation gaps are finite. For
J2=0.48J1 and
0.52J1, we also calculate spin-spin and dimer-dimer correlation functions, dimer order parameters, and the bipartite von Neumann entanglement entropy within our mean-field formalism in order to determine the properties of the many-triplon state as a function of the triplon number
N. We find that the spin and the dimer correlations decay exponentially and that the entanglement entropy obeys an area law, regardless of the triplon number
N. Moreover, only for
J2=0.48J1, the spin correlations indicate that the many-triplon states with large triplon number
N might display a more homogeneous singlet pattern than the columnar valence-bond solid. We also comment on possible relations between the many-triplon states with large triplon number
N and gapped spin-liquid states.
Sufficiently dimerized quantum antiferromagnets display elementary S =1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl 3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J 1 ≈− 2.3 meV, J 2 ≈1.2 meV, J 3 ≈2.9 meV and J 4 ≈− 0.3 meV. These couplings determine IPA-CuCl 3 as system of coupled asymmetric S =1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model.
We report on terahertz spectroscopic measurements of quantum spin dynamics on single crystals of a spin-1/2 frustrated spin-ladder antiferromagnet
BiCu2PO6 as a function of temperature, polarization, and applied external magnetic fields. Spin triplon excitations are observed at zero field and split in applied magnetic fields. For magnetic fields applied along the crystallographic
a axis, a quantum phase transition at
Bc1=21.4 T is featured by a low-energy excitation mode emerging above
Bc1, which indicates a gap reopening. For fields along the
b axis and the
c axis, different field dependencies are observed for the spin triplon excitations, whereas no low-lying modes could be resolved at field-induced phase transitions. We perform a theoretical analysis of the magnetic field dependence of the spin triplon modes by using continuous unitary transformations to determine an effective low-energy Hamiltonian. Through an exhaustive parameter search we find numerically optimized parameters to very well describe the experimentally observed modes, which corroborate the importance of significant magnetic anisotropy in the system.
In sufficiently dimerized quantum antiferromagnets the elementary excitations are given by gapped spin S = 1 triplon quasiparticles. Although these triplons are protected by a gap at low energies they may decay spontaneously at higher energies where the one-triplon dispersion merges with the two-triplon continuum. First, we illustrate and characterize such a spontaneous decay in low-dimensional quantum antiferromagnets on the basis of a simple one-dimensional bosonic model. The decay implies the breakdown of the quasiparticle picture. No quantitative description by a Lorentzian resonance is possible. In particular, three qualitatively different scenarios are identified depending on the one-triplon dispersion and the two-triplon interaction. To describe unstable quasiparticles in more complex models we introduced an adapted generator for continuous unitary transformations. Its general properties are derived and discussed. Next, we investigate asymmetric antiferromagnetic and asymmetric ferroantiferromagnetic spin S = ½ Heisenberg ladders, which allow for spontaneous triplon decay, to illustrate this approach. Results for the low-energy spectra and the dynamical structure factors for these systems are presented. We show that quasiparticle decay is more pronounced in the case of ferro-antiferromagnetic ladders than in solely antiferromagnetic ladders. Finally, we use continuous unitary transformations and high temperature series expansions to determine a quantitative model for the compound IPA-CuCl3 based on data of inelastic neutron scattering and measurements of the magnetic susceptibility. Our calculations reveal IPA-CuCl3 as system of coupled asymmetric spin S = ½ Heisenberg ladders with the four magnetic couplings J 1 ˜ -2.3 meV, J2 ˜ 1.2 meV, J3 ˜ 2.9 meV and J4 ˜ -0.3 meV. Based on this microscopic model for IPA-CuCl3 the adapted continuous unitary transformation is used to describe the quasiparticle decay in IPA-CuCl3. The results agree very well with the experimental data. In addition the magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate our microscopic model.
The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaux at 1/3 and 2/3 can be associated with the array of quasi-spinons such as soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful to understand magnetization curves in BiCu2PO6.
Low dimensional quantum magnets which display a collective singlet ground state and a gap in their magnetic excitation spectrum provide a framework for much exotic phase behavior in new materials, with high temperature superconductivity being the best appreciated example. Neutron scattering techniques can be applied to study a wide variety of problems in condensed matter physics. These techniques are particularly useful as applied to understanding the magnetic properties of quantum magnets that display exotic phases. SrCu2(BO3)2, is a rare example of a two-dimensional quantum magnet for which an exact theoretical solution describing its ground state is known to be a collective singlet. Previous high resolution neutron scattering measurements identified the most prominent features of the spin excitation spectrum in SrCu2(BO3)2, including the presence of one and two triplet excitations and weak dispersion characteristic of subleading terms in the spin Hamiltonian. The resemblance between the spin gap behavior in the Mott insulator SrCu2(BO3)2 and that associated with high temperature superconductors motivated the consideration of the significance of doping in order to understand the properties of this quantum magnetic system. For this reason, a series of neutron scattering studies on doped SrCu2(BO3)2 were initiated. These series of investigations began with the performance of neutron scattering measurements on a SrCu(2-x)Mgx(BO3)2 single crystal in order to introduce magnetic vacancies to the system. These results revealed the presence of new spin excitations within the singlet-triplet gap of this system. Application of a magnetic field induces Zeeman-split states associated with un-paired spins which exist as a consequence of doping with quenched non-magnetic impurities. Additional substantial broadening of both the one and two triplet excitations is observed in the doped system as compared to the pure system. Theoretical calculations are shown to qualitatively account for these features. These studies were extended to neutron scattering measurements on Sr(1-x)LaxCu2(BO3)2, with an aim of introducing charged carriers into this system. The broadening of the one and two triplet excitations is observed and compared to the thermally induced finite lifetime of the pure system. The temperature dependence of this broadening in Sr(1-x)LaxCu2(BO3)2 is different compared to that observed in both SrCu2(BO3)2 and SrCu(2-x)Mgx(BO3)2. It has also been suggested that there is a relation between the spin-lattice interaction in SrCu2(BO3)2 and the magnetic dynamics at low temperatures and high magnetic fields. For this reason there has been increased interest in the study of the crystalline structure and vibrational modes of SrCu2(BO3)2. In order to investigate the role of the lattice in the formation of the singlet ground state in SrCu2(BO3)2, a series of low and high energy neutron scattering measurements were carried out on this system to study both the crystalline structure as well as the normal modes of vibration of the lattice, the transverse acoustic and optical phonons. Transverse acoustic phonons with energies comparable to and higher than the onset of the two triplet continuum show substantially increased lifetimes on entering the singlet ground state below ~ 10 K. This may indicate the removal of the decay channel for the phonons due to the gapping of the spin excitation spectrum in SrCu2(BO3)2 at low temperatures. In high energy inelastic neutron scattering we observe broadening of optic phonons in the ~ 52 to 65 meV region on entering the low temperature singlet ground state. Additionally, the magnetic properties of CuMoO4, which is a triclinic quantum magnet system based on S=1/2 moments at the Cu2+ site, were studied using elastic and inelastic neutron scattering experiments. This material exhibits a first order structural phase transition at ~ 190 K as well as a magnetic phase transition at ~ 1.75 K. We were primarily interested in the low temperature magnetic properties of this material. Magnetization and heat capacity measurements as well as elastic and inelastic neutron scattering measurements were conducted on this system within the low temperature ordered phase. These studies confirm that this material has a magnetic phase transition at ~ 1.7 K. Neutron scattering results indicate that this magnetically ordered phase is characterized by a doubling of the a axis. Inelastic neutron scattering measurements revealed a gapped magnetic excitation spectrum in zero magnetic field, which could be filled in by the application of magnetic fields approaching 7 T.