1. B3 Correlations in antiferromagnets
Sebastian Eggert (TU Kaiserslautern)
(i) Frustrated spin systems
(iii) Dimensional crossover
Coupled one dimensional quantum systems (chains) can be created with spin chains and ladders as well as quasi one-dimensional ultra-cold gases [P1]. We want to study the quantum phase transition from 1D behavior to a 3D interacting condensate.
Topics
Luttinger liquids theory and chain mean field:
higher order corrections
Quantum Monte Carlo simulations
Mott vs. superfluid in quasi 1D: Transport
Frustrated systems are of large current interest due to the possibility of new phases and exotic excitations due to the large residual entropy at low T. The most relevant realization are spin systems, ultra-cold gases, ion traps, and charge transfer salts, all of which play a central role in the TR 49.
Topics
Kagome lattice at incommensurate filling:
Role of string excitations
XXZ model on the anisotropic triangular lattice: Domain walls and possible spin liquid A5 A8 A9 A8
A10 B1 B2 B4 B6
Fig. 8: Coupled 1D boson gases and spin ladders in a magnetic field have the equivalent bosonic descritiion.
Fig. 6: Triangular lattice and kagome lattice with 1/3 magnetization.
Work programme
First year
numerical analysis of string excitations in the kagome lattice.
numerical analysis of higher order critical points in coupled trimer systems.
set up field theoretical calculations for higher order corrections in coupled chain systems.
numerical simulations of coupled chain systems.
Second year
analytic analysis of string excitations for positive xy-coupling in the kagome lattice.
analysis of boundary induced behavior in anisotropic triangular lattices.
interacting boson theory for higher order critical points in trimer systems.
Third/fourth year
analysis of impurities in frustrated systems.
critical behavior for larger spin clusters N > 3 and different inter-cluster couplings.
analysis of transport experiments in coupled chain systems of project A9 (Ott).
(ii) Coupled spin clusters
Coupled spin clusters have played an important role in the TR 49 as versatile systems, where critical points can be reached either by tuning the magnetic field or the coupling strengths via the chemical composition and/or pressure.
Topics
Magneto-caloric effect, susceptibility, specific heat
Critical scaling
Higher order critical points:
magnetization plateaus in larger spin clusters A8 B1 B2 B4 B5
B13N
Fig. 7: Above: coupled trimers. Right: corresponding magnetization plateaus, which lead to higher order critical points
Transregional Collaborative Research Centre SFB/TR 49
Frankfurt / Kaiserslautern / Mainz