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Présentation du LPT
Le LPT (UMR 5152, Laboratoire de Physique Théorique) est un laboratoire de recherche localisé sur le campus de l'Université de Toulouse. Il a été fondé en 1991 et a été créé administrativement en 2003. Les chercheurs du LPT étaient rattachés au Laboratoire de Physique Quantique au sein du Groupe de Physique Théorique. L'expertise du LPT couvre les domaines de la matière condensée et la matière molle ainsi que la physique statistique et la physique non-linéaire.
Le LPT est membre de la Fédération de recherche FeRMI (Fédération de recherche Matière et Interactions - FR2051), anciennement IRSAMC (Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes).
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Despite enormous efforts devoted to the study of the many-body localization (MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a strong random magnetic field is lacking consensus. Here, we take a step back by exploring the weak interaction limit starting from the Anderson localized (AL) insulator. Through shift-invert diagonalization, we find that below a certain disorder threshold $h^*$, weak interactions necessarily lead to ergodic instability, whereas at strong disorder the AL insulator directly turns into MBL. This agrees with a simple interpretation of the avalanche theory for restoration of ergodicity. We further map the phase diagram for the generic XXZ model in the disorder $h$-- interaction $\Delta$ plane. Taking advantage of the total magnetization conservation, our results unveil the remarkable behavior of the spin-spin correlation functions: in the regime indicated as MBL by standard observables, their exponential decay undergoes a unique inversion of orientation $\xi_z>\xi_x$. We find that the longitudinal length $\xi_z$ is a key quantity for capturing ergodic instabilities, as it increases with system size near the thermal phase, in sharp contrast to its transverse counterpart $\xi_x$.
The corner transfer matrix renormalization group (CTMRG) algorithm has been extensively used to investigate both classical and quantum two-dimensional (2D) lattice models. The convergence of the algorithm can strongly vary from model to model depending on the underlying geometry and symmetries, and the presence of algebraic correlations. An important factor in the convergence of the algorithm is the lattice symmetry, which can be broken due to the necessity of mapping the problem onto the square lattice. We propose a variant of the CTMRG algorithm, designed for models with C3-symmetry, which we apply to the conceptually simple yet numerically challenging problem of the triangular lattice Ising antiferromagnet in a field, at zero and low temperatures. We study how the finite-temperature three-state Potts critical line in this model approaches the ground-state Kosterlitz-Thouless transition driven by a reduced field (h/T). In this particular instance, we show that the C3-symmetric CTMRG leads to much more precise results than both existing results from exact diagonalization of transfer matrices and Monte Carlo.
Motivated by recent debates around the many-body localization (MBL) problem, and in particular its stability against systemwide resonances, we investigate long-distance spin-spin correlations across the phase diagram of the random-field XXZ model, with a particular focus on the strong disorder regime. Building on state-of-the-art shift-invert diagonalization techniques, we study the high-energy behavior of transverse and longitudinal correlation functions, computed at the largest possible distance, for a broad range of disorder and interaction strengths. Our results show that while transverse correlations display a fairly stable exponential decay over the entire XXZ phase diagram, longitudinal correlations exhibit markedly different behavior, revealing distinct physical regimes. More precisely, we identify an intermediate disorder region where standard observables show well-converged MBL behavior [J. Colbois et al., Phys. Rev. Lett. 133, 116502 (2024)] while the distributions of longitudinal correlations reveal unexpected fat-tails towards large values. These rare events strongly influence the average decay of longitudinal correlations, which we find to be algebraic in a broad region inside the supposed MBL phase, whereas the typical decay remains mostly exponential. At stronger disorder and weaker interactions, this intermediate regime is replaced by a more conventional exponential decay with short correlation lengths for both typical and average correlators, as expected for standard localization. Our findings shed light on the systemwide instabilities and raise important questions about the impact of such rare but large long-range correlations on the stability of the MBL phase. Finally, we discuss the possible fate of the intermediate region in the context of recent perspectives in the field.
We analyze the Google matrix of directed networks of Wikipedia articles related to eight recent Wikipedia language editions representing different cultures (English, Arabic, German, Spanish, French, Italian, Russian, Chinese). Using the reduced Google matrix algorithm, we determine relations and interactions of 23 society concepts and 17 religions represented by their respective articles for each of the eight editions. The effective Markov transitions are found to be more intense inside the two blocks of society concepts and religions while transitions between the blocks are significantly reduced. We establish five poles of influence for society concepts (Law, Society, Communism, Liberalism, Capitalism) as well as five poles for religions (Christianity, Islam, Buddhism, Hinduism, Chinese folk religion) and determine how they affect other entries. We compute inter-edition correlations for different key quantities providing a quantitative analysis of the differences or the proximity of views of the eight cultures with respect to the selected society concepts and religions.
We discuss the kinetic theory of stellar systems and two-dimensional vortices and stress their analogies. We recall the derivation of the Landau and Lenard–Balescu equations from the Klimontovich formalism. These equations take into account two-body correlations and are valid at the order 1/N, where N is the number of particles in the system. They have the structure of a Fokker–Planck equation involving a diffusion term and a drift term. The systematic drift of a vortex is the counterpart of the dynamical friction experienced by a star. At equilibrium, the diffusion and the drift terms balance each other establishing the Boltzmann distribution of statistical mechanics. We discuss the problem of kinetic blocking in certain cases and how it can be solved at the order by the consideration of three-body correlations. We also consider the behaviour of the system close to the critical point following a recent suggestion by Hamilton and Heinemann (2023). We present a simple calculation, valid for spatially homogeneous systems with long-range interactions described by the Cauchy distribution, showing how the consideration of the Landau modes regularizes the divergence of the friction by polarization at the critical point. We mention, however, that fluctuations may be very important close to the critical point and that deterministic kinetic equations for the mean distribution function (such as the Landau and Lenard–Balescu equations) should be replaced by stochastic kinetic equations.