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Résumé |
The deconfined quantum critical point (DQCP) provides a paradigmatic example of unconventional phase
transitions beyond the Landau–Ginzburg–Wilson framework, yet its nature has remained controversial for
decades. Extensive theoretical and numerical studies have led to two competing scenarios:
pseudocriticality and multicriticality.
In the first lecture, I will review the basic physics of the DQCP and discuss in some detail the motivations
and evidence for these two scenarios. In the pseudocritical scenario, the apparently critical behavior is
attributed to a prolonged walking regime, potentially governed by nearby complex conformal fixed points. I
will contrast this with the multicritical scenario, in which the observed scaling is controlled by a nearby real
but unstable fixed point with additional relevant directions. I will also review recent large-scale quantum
Monte Carlo results and discuss how they constrain these possibilities.
In the second lecture, I will turn to two complementary approaches that provide new perspectives on this
problem: the fuzzy-sphere method and the conformal bootstrap. After briefly introducing the basic ideas
behind these methods, I will present recent evidence in favor of the multicritical scenario. In particular, I
will discuss a distinguished unitary solution of the conformal bootstrap that is consistent with numerical
results from both quantum Monte Carlo and the fuzzy sphere. Remarkably, this solution contains a strongly
relevant SO(5)-singlet scalar operator, providing further support for the multicritical interpretation of the
DQCP. I will conclude by discussing how these different approaches can be combined to develop a more
comprehensive picture of the DQCP and its nearby renormalization-group structure.
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