In this report we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides accurate analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate of the fermionic system and prove that within the considered model the fastest rate of long-time decoherence is given by γ = π k B T / 4 . We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects can prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between different exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures T / T F ≲ 0.2 where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid 3 He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology.

We study entanglement properties of free-fermion systems without Hermiticity by use of correlation matrix and overlap matrix in the biorthogonal basis. We find at a critical point in the non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry (PT symmetry) the entanglement entropy exhibits a logarithmic scaling with corresponding central charge $c=-2$, signaling the emergence of nonunitary conformal field theory. In addition, we demonstrate that, in the PT-symmetric SSH model and the non-Hermitian Chern insulators, the entanglement spectrum characterizes the topological properties in terms of the existence of mid-gap states.

We study the quantum nonlinear Hall effect in two-dimensional (2D) materials with time-reversal symmetry. When only one mirror line exists, a transverse charge current occurs in the second-order response to an external electric field, as a result of the Berry curvature dipole in momentum space. Candidate 2D materials to observe this effect are two-dimensional transition metal dichalcogenides (TMDCs). First, we use an ab initio based tight-binding approach to demonstrate that monolayer $T_d$-structure TMDCs exhibit a finite Berry curvature dipole. In the $1H$ and $1T^{\prime }$ phase of TMDCs, we show the emergence of a finite Berry curvature dipole with the application of strain and an electrical displacement field, respectively.

Transitions between topologically distinct electronic states have been predicted in different classes of materials and observed in some. A major goal is the identification of measurable properties that directly expose the topological nature of such transitions. Here, we focus on the giant Rashba material bismuth tellurium iodine which exhibits a pressure-driven phase transition between topological and trivial insulators in three dimensions. We demonstrate that this transition, which proceeds through an intermediate Weyl semimetallic state, is accompanied by a giant enhancement of the Berry curvature dipole which can be probed in transport and optoelectronic experiments. From first-principles calculations, we show that the Berry dipole—a vector along the polar axis of this material—has opposite orientations in the trivial and topological insulating phases and peaks at the insulator-to-Weyl critical points, at which the nonlinear Hall conductivity can increase by over 2 orders of magnitude.

The explorations of non-Hermiticity have been devoted to investigate the disorder-induced many-body localization (MBL). However, the sensitivity of the spatial boundary conditions and the interplay of the non-Hermitian skin effect with many-body phenomena are not yet clear. For a MBL system in the presence of nonreciprocal tunnelings and random disorder potential, we identify two different complex-real spectral transitions, one is present for both open and periodic boundaries while the other is present only for open boundaries of coupled non-Hermitian chains. The later is driven due to the interchain coupling at weak disorder where the level statistics of the real eigenenergy phase follows a Gaussian orthogonal ensemble. We further characterize wave functions through the (biorthogonal) inverse participation ratio and fractal dimension, which reveal the suppression of skin effect in the non-Hermitian MBL phase. Finally, we demonstrate that the quench dynamics of the local particle density, spin imbalance, and entanglement entropy also signify the hallmark of the boundary effects and nonergodic character of many-body localization.