Correlações quânticas em sistemas críticos
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2015-07-24
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Universidade Federal de Goiás
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Correlations are ubiquitous in nature and have played an extremely important role in human
life for a long time. For example, in economy, correlations between price and demand
are extremely important for a businessman (or even a government) to make decisions regarding
their investment policy. In the field of biology, genetic correlations are central to follow
individual characteristics. The relationship between income distribution and crime rate is
just one example coming from the social sciences. Mathematically, correlation is a number
that describes the degree of relationship between two variables. In the classical domain, this
number can be computed in the context of information theory, developed by Shannon in
1948. Focusing on the subject of the present work, the discussion regarding the quantum
nature of the correlations permeates physics since Einstein, Podolski and Rosen published
their famous article criticizing quantum mechanics. Since then, the so-called quantum correlations
have been shown to be a very important tool in the study of many-bodies physics.
Another feature of many-body physics is that certain systems, under certain conditions,
exhibit what we call quantum phase transition. Such transitions are analogous to the
classical transitions, but being governed by purely quantum fluctuations and, as such, may
occur at zero temperature, unlike the former, which are guided by thermal fluctuations. One
of the main phenomenon that characterizes these transitions is the fact that the correlation
length (defined between two subsystems of the global system) highly increases at the transition
point. This means that such subsystems can be strongly correlated even if they are
separated by a large distance.
The main goal of the present work is the study of quantum correlations, specifically
the entanglement and the local quantum uncertainty (LQU), in systems presenting one or
more quantum phase transitions. Specifically, we consider three models of spin chains: 1)
The XY and the XY T, which describes chains of spins- 1=2 —the second considering three
spins interaction while the first one takes into account only pairwise interactions; 2) A model describing a chain formed by bosonic spins, i.e. particles with spin-1. As a general conclusion,
quantum correlation provides a very powerful tool for the study of critical phenomena,
providing, among other things, a means to identify a quantum phase transition.
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NASCIMENTO, A. B. Correlações quânticas em sistemas críticos. 2015. 90 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2015.