08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access Quantum phase transitions in constrained Bose systems(2011) Bonnes, Lars; Weßel, Stefan (Prof. Dr.)This doctoral thesis studies low dimensional quantum systems that can be realized in recent cold atom experiments. From the viewpoint of quantum statistical mechanics, the main emphasis is on the detailed study of the different quantum and thermal phases and their transitions using numerical methods, such as quantum Monte Carlo and the Tensor Network Renormalization Group. The first part of this work deals with a lattice Boson model subject to strong three-body losses. In a quantum-Zeno like manner, a dynamical three-body constraint arises that restricts the evolution of the quantum system to the subspace with at most two particles per site i.e., three-body losses will be suppressed. Its low-energy description by a Feshbach model leads to the appearance of a pair condensate phase with intriguing quantum critical properties controlled by the Coleman-Weinberg mechanism. A comprehensive numerical study, presented in Chapter 3, identifies the pair phase and provides evidence for an unconventional Berezinksii-Kosterlitz-Thouless transition due to the unbinding of half-vortices. The study of the pair phase with worm-like algorithms turns out to be challenging and an extension of the directed loop algorithm is presented that overcomes the sampling limitations posed by the appearance of fat-tail distributions. In the following chapters, attention is drawn to lattice systems of polar molecules in optical lattices. Their intriguing dipolar interaction and sensitivity towards external fields make them ideal candidates to realize new states of matter. Particularly, it has been shown that one can drive these systems into a regime where the interaction is dominated by competing two- and three-body potentials. First, the triangular lattice supersolid is considered in Chapter 4. An extensive numerical study combined with a detailed symmetry analysis answers the question of the nature of the supersolid quantum nucleation transition. Following this discussion, Chapter 5 investigates whether the characteristic features of this model persist in the presence of interactions for a realistic system with polar molecules. The three-body interaction regime in a honeycomb Bose-Hubbard model turns out to give rise to a set of highly complex phases in terms of valence bond solids and leads to frustration. Chapter 6 studies the phase diagram and shows how the competition between two- and three-body interactions exhibiting a cascade of phases in the regime of intermediate couplings. In addition, it is demonstrated how the Tensor Network Renormalization Group can be applied to systems with multibody interactions and generic algorithmic limitations are described. Finally, preliminary results concerning the effect of quantum disorder on the triangular supersolid and recent calculations for the entropy of one-dimensional trapped SU(N) Hubbard models are discussed in Chapter 7.