This article gives a short review of the recent progress on TT-deformation of quantum field theories in two dimensions, starting from the pioneering work by Alexander Zamolodchikov in 2004.⁴⁾ The TT-operator defined as the determinant of the energy-momentum tensor has some specific properties such as the factorization of the expectation values ⁴⁾ and the TT-flow equation.^{6, 7)} In particular, at the classical level, the TT-deformation of the set of free massless scalar fields is the Nambu–Goto action describing the classical dynamics of a string in flat space.⁶⁾ Furthermore, the energy spectrum of the TT-deformed conformal field theory (CFT) on an infinitely long cylinder is governed by a two-dimensional inviscid Burgers equation obtained as the expectation value of the flow equation.^{6, 7)} Among various topics on theTT-deformation, this article introduces some fundamental and significant progress by focusing on gravity duals of TT-deformed CFT.^{9, 11, 15)}

Recent technical advance in statistical mechanical informatics and its application to sparse modeling are explained. The focus is on a systematic derivation of a meanfield-type inference algorithm based on the belief-propagation from Bayesian inference and the cavity method from statistical mechanics. The derived algorithm is called approximate message passing, and its macroscopic behavior is analyzed by the so-called state evolution and has a direct connection to the equations of state derived using the replica method in the replica symmetric level. This framework is applied to compressed sensing in sparse modeling, which is a signal-processing technique exploiting the inherent sparseness of the true signal expressed in an appropriate basis. The limits of perfect reconstruction of the signal are derived using these techniques in the Bayesian and regularized linear regression frameworks, clarifying their natures as dynamical phenomena and phase transitions.

When a magnetic impurity exists in a metal, surrounding conducting electrons form a spin cloud that screens the impurity spin. This Kondo cloud has been observed using a Kondo correlated quantum dot coupled to a quasi-one-dimensional channel that houses a Fabry-Pérot interferometer of various lengths L. When the cloud size ξ_K exceeds L, the Kondo temperature is modulated by the interference, whereas when ξ_K is smaller than L, the interference has weaker influence on the Kondo temperature. The modulation of the Kondo temperature obeys a scaling function of a single parameter L /ξ_K , implying the universal shape of the Kondo cloud.

Ferroelectricity and antiferroelectricity are of great importance not only in condensed matter physics but also in technological applications due to their electrical controllability and cross-coupling effects such as electromechanical and electrocaloric responses. We here develop a simple model system composed of spheroid-like particles with a permanent dipole, which may capture an essence of phase transitions between ferroelectric and antiferroelectric phases. With this model, we reveal that energetic frustration between the dipole-dipole interaction and interparticle steric interaction is a key to control ferroelectric–antiferroelectric phase transition accompanied by electromechanical coupling. We also show that the inverse electrocaloric effect can be induced as a consequence of the entropy difference between the ferroelectric and antiferroelectric phases. Thus, we reveal a simple physical principle behind the coupling between polarization ordering and structural phase transition responsible for large electromechanical effects. It may apply to organic and macromolecular systems.