Macroscopic Entanglement and Phase Transitions

This paper summarises the results of our research on macroscopic entanglement in spin systems and free Bosonic gases. We explain how entanglement can be observed using entanglement witnesses which are themselves constructed within the framework of thermodynamics and thus macroscopic observables. These thermodynamical entanglement witnesses result in bounds on macroscopic parameters of the system, such as the temperature, the energy or the susceptibility, below which entanglement must be present. The derived bounds indicate a relationship between the occurrence of entanglement and the establishment of order, possibly resulting in phase transition phenomena. We give a short overview over the concepts developed in condensed matter physics to capture the characteristics of phase transitions in particular in terms of order and correlation functions. Finally we want to ask and speculate whether entanglement could be a generalised order concept by itself, relevant in (quantum induced) phase transitions such as BEC, and that taking this view may help us to understand the underlying process of high-T superconductivity.Comment: 9 pages, 7 figures (color), Submitted to special OSID issue, Proceedings of the 38th Symposium on Mathematical Physics - Quantum Entanglement & Geometry, Torun (Poland), June 200

Exact Solution of a Yang-Baxter Spin-1/2 Chain Model and Quantum Entanglement

Entanglement is believed to be crucial in macroscopic physical systems for understanding the collective quantum phenomena such as quantum phase transitions. We start from and solve exactly a novel Yang-Baxter spin-1/2 chain model with inhomogeneous and anisotropic short-range interactions. For the ground state, we show the behavior of neighboring entanglement in the parameter space and find that the inhomogeneous coupling strengths affect entanglement in a distinctive way from the homogeneous case, but this would not affect the coincidence between entanglement and quantum criticality.Comment: 7 pages, 3 figure

A Computational Model for Quantum Measurement

Is the dynamical evolution of physical systems objectively a manifestation of information processing by the universe? We find that an affirmative answer has important consequences for the measurement problem. In particular, we calculate the amount of quantum information processing involved in the evolution of physical systems, assuming a finite degree of fine-graining of Hilbert space. This assumption is shown to imply that there is a finite capacity to sustain the immense entanglement that measurement entails. When this capacity is overwhelmed, the system's unitary evolution becomes computationally unstable and the system suffers an information transition (`collapse'). Classical behaviour arises from the rapid cycles of unitary evolution and information transitions. Thus, the fine-graining of Hilbert space determines the location of the `Heisenberg cut', the mesoscopic threshold separating the microscopic, quantum system from the macroscopic, classical environment. The model can be viewed as a probablistic complement to decoherence, that completes the measurement process by turning decohered improper mixtures of states into proper mixtures. It is shown to provide a natural resolution to the measurement problem and the basis problem.Comment: 24 pages; REVTeX4; published versio

Pattern Universes

In this essay we explore analogies between macroscopic patterns, which result from a sequence of phase transitions/instabilities starting from a homogeneous state, and similar phenomena in cosmology, where a sequence of phase transitions in the early universe is believed to have separated the fundamental forces from each other, and also shaped the structure and distribution of matter in the universe. We discuss three distinct aspects of this analogy: (i) Defects and topological charges in macroscopic patterns are analogous to spins and charges of quarks and leptons; (ii) Generic (3+1) stripe patterns carry an (energy) density that accounts for phenomena that are currently attributed to dark matter; (iii) Space-time patterns of interacting nonlinear waves display behaviors reminiscent of quantum phenomena including inflation, entanglement and dark energy.Comment: 15 Pages, Essay with 3 technical appendice