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Application of extended conformal theories to statistical physics problems

Abstract : The study of critical phenomena in two-dimensional statistical physics is mainly performed with the help of conformal field theory and integrable models. The relationship between these two formalisms is an active field of research, particularly in the framework of the so-called non-rational theories. This thesis is focused on certain critical systems described by an extended conformal theory : a theory that presents additional symmetries. The first problem studied is the fully packed loop model (FPL). Loop models are non-local statistical models based on the description of assembly of polymers. In particular, they represent the interfaces formed by spin models. The FPL model is integrable and its spectrum reflects an underlying symmetry Uq(sl(3)). The link between this model and the W3 symmetry, a conformal symmetry extended by a three-dimensional field, is studied in detail, numerically (by exact diagonalization) and analytically. The relationship with loop models leads to the study of the non-scalar operator content of the W3 theory. The second problem concerns the calculation of entanglement in unidimensional quantum systems. In this context, the preferred object of study is the entropy of entanglement between a subsystem and its complement. For the fundamental state of a spin chain, the behaviour of this entropy as a function of the size of the subsystem is a clear marker of the criticality of the chain. In this manuscript, a new way of calculating these entropies in critical models is presented. It is based on conformal theories extended by a symmetry called orbifold. This method is particularly applicable to entropies of excited states or disjointed subsystems.
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Thomas Dupic. Application of extended conformal theories to statistical physics problems. Mathematical Physics [math-ph]. Sorbonne Université, 2018. English. ⟨NNT : 2018SORUS260⟩. ⟨tel-02868488⟩

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