Emaranhamento e estados de produto de matrizes em transições de fase quanticas / Entanglement and matrix product states in quantum phase transitions

AUTOR(ES)
DATA DE PUBLICAÇÃO

2008

RESUMO

This thesis attempts to contribute to the understanding of possible connections between Quantum Information and Condensed Matter theories, a new field of research in broad development. Specifically, we investigated the role of entanglement, or quantumcorrelations, in continuous quantum phase transitions. While the importance of the first in the theory of Quantum Information is well known dispense presentation, the latter are of great interest as they exhibit a universal behavior, which descent fromthe divergence of the correlation length. This mutual origin of both in correlations is what creates an expectation of a possible link between them. Our work, based on the study of XY dimensional model in a transverse field, brings evidence of multipartite entanglement being favored, in detriment of bipartite in the transition, and thus in the importance of the first in the establishment of long-range correlations. During our journey, we define a class of measures of multipartite entanglement, generalising the Global Entanglement introduced by Meyer and Wallach in 2002. We show that some of these classes provide additional information to the Global Entanglement, as well as being written in a simple way in terms of correlation functions . This simplicity allows the establishment of a formal relationship between those classes and phases transitions marked by non-analycities in the energy. At the end, we studied the role of spontaneous symmetry breaking in the bipartite and multipartite entanglement, demonstrating once again a major role of the last over the first. In a second part, we examine the use of Matrix Product States to approximate ground states of critical systems. This class of states can be seen as the ansatz used in the Density Matrix Renormalization Group (DMRG), when this one is understood as a variational method. Analyzing the power of approximation of these states, now in Ising model, we found that the "dimension" of the ansatz (or number of renormalized degrees of freedom) is a relevant variable in the renormalization group, in a analogous way to the finite size of the system. This enables an analysis of scaling regarding the "size" of Matrix Product States, with a possible acquisition of critical properties at low computation cost

ASSUNTO(S)

quantum phase transitions transições de fase quanticas criticality (nuclear engineering) matrix product states estados de produto de matrizes criticalidade (engenharia nuclear) quantum erntanglement emaranhamento quantico

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