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The LPT is based at the University of Toulouse. It has been founded in 1991 and its administrative structure was established in 2003. Before 2003, researchers where rassembled in the Group of Theoretical Physics. This group was hosted by the Laboratoire de Physique Quantique (now LCPQ).

The LPT is member of FeRMI (Fédération de recherche Matière et Interactions).


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Many topological or critical aspects of the Kitaev chain are well known, with several classic results. In contrast, the study of the critical behavior of the strong Majorana zero modes (MZM) has been overlooked. Here we introduce two topological markers which, surprisingly, exhibit non-trivial signatures over the entire (1+1) Ising critical line. We first analytically compute the MZM fidelity ${\cal{F}}_{\rm MZM}$--a measure of the MZM mapping between parity sectors. It takes a universal value along the (1+1) Ising critical line, ${\cal{F}}_{\rm MZM}=\sqrt{8}/\pi$, independent of the energy. We also obtain an exact analytical result for the critical MZM occupation number ${{\cal N}}_{\rm MZM}$ which depends on the Catalan's constant ${\cal G}\approx 0.91596559$, for both the ground-state (${{\cal N}}_{\rm MZM}=1/2-4{\cal{G}}/\pi^2\approx 0.12877$) and the first excited state (${{\cal N}}_{\rm MZM}=1/2+(8-4{\cal{G}})/\pi^2\approx 0.93934$). We further compute finite-size corrections which identically vanish for the special ratio $\Delta/t=\sqrt{2}-1$ between pairing and hopping in the critical Kitaev chain.

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We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ antiferromagnetic (AFM) Heisenberg model. The ground state phase diagram is established with a rich variety of phases: AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe, and incommensurate spiral phases. The nature of the VBS region is revealed, containing a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlations in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exists several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice $J_1$-$J_2$-$J_3$ antiferromagnet at zero-temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum systems that may host nonuniform features by means of finite PEPS.

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Symmetry-breaking phase transitions are central to our understanding of states of matter. When a continuous symmetry is spontaneously broken, new excitations appear that are tied to fluctuations of the order parameter. In superconductors and fermionic superfluids, the phase and amplitude can fluctuate independently, giving rise to two distinct collective branches. However amplitude fluctuations are difficult to both generate and measure, as they do not couple directly to the density of fermions and have only been observed indirectly to date. Here, we excite amplitude oscillations in an atomic Fermi gas with resonant interactions by an interaction quench. Exploiting the sensitivity of Bragg spectroscopy to the amplitude of the order parameter, we measure the time-resolved response of the atom cloud, directly revealing amplitude oscillations at twice the frequency of the gap. The magnitude of the oscillatory response shows a strong temperature dependence, and the oscillations appear to decay faster than predicted by time-dependent BCS theory applied to our experimental setup.

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We revisit the study of amplitude oscillations in a pair condensate of fermions after an interaction quench, and generalize it to nonzero temperature. For small variations of the order parameter, we show that the energy transfer during the quench determines both the asymptotic pseudo-equilibrated value of the order parameter and the magnitude of the oscillations, after multiplication by, respectively, the static response of the order parameter and spectral weight of the pair-breaking threshold. Since the energy transferred to the condensed pairs decreases with temperature as the superfluid contact, the oscillations eventually disappear at the critical temperature. For deeper quenches, we generalize the regimes of persistent oscillations and monotonic decay to nonzero temperatures, and explain how they become more abrupt and are more easily entered at high temperatures when the ratio of the initial to final gap either diverges, when quenching towards the normal phase, or tends to zero, when quenching towards the superfluid phase. Our results are directly relevant for existing and future experiments on the non-equilibrium evolution of Fermi superfluids near the phase transition.

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We investigate theoretically the momentum-dependent frequency and damping of low-lying collective excitations of superconductors and charged superfluids in the BCS–BEC crossover regime. The study is based on the Gaussian pair-and-density fluctuation method for the propagator of Gaussian fluctuations of the pair and density fields. Eigenfrequencies and damping rates are determined in a mutually consistent nonperturbative way as complex poles of the fluctuation propagator. Particular attention is paid to new features with respect to preceding theoretical studies, which were devoted to collective excitations of superconductors in the far BCS regime. We find that at a sufficiently strong coupling, new branches of collective excitations appear, which manifest different behavior as functions of the momentum and the temperature.

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