We study a quantum quench in which a magnetic impurity is suddenly coupled to Hubbard chains, whose low-energy physics is described by Tomonaga-Luttinger liquid theory. Using the time-dependent density-matrix renormalization-group (tDMRG) technique, we analyze the propagation of charge, spin, and entanglement in the chains after the quench and relate the light-cone velocities to the dispersion of holons and spinons. We find that the local magnetization at the impurity site decays faster if we increase the interaction in the chains, even though the spin velocity decreases. We derive an analytical expression for the relaxation of the impurity magnetization which is in good agreement with the tDMRG results at intermediate timescales, providing valuable insight into the time evolution of the Kondo screening cloud in interacting systems.
We study a quantum quench in which a magnetic impurity is suddenly coupled to Hubbard chains, whose low-energy physics is described by Tomonaga-Luttinger liquid theory. Using the time-dependent density-matrix renormalization-group (tDMRG) technique, we analyze the propagation of charge, spin, and entanglement in the chains after the quench and relate the light-cone velocities to the dispersion of holons and spinons. We find that the local magnetization at the impurity site decays faster if we increase the interaction in the chains, even though the spin velocity decreases. We derive an analytical expression for the relaxation of the impurity magnetization which is in good agreement with the tDMRG results at intermediate timescales, providing valuable insight into the time evolution of the Kondo screening cloud in interacting systems.
We study the real-time dynamics of the Kondo effect after a quantum quench in which a magnetic impurity is coupled to two metallic Hubbard chains. Using an effective field theory approach, we find that for noninteracting electrons the charge current across the impurity is given by a scaling function that involves the Kondo time. In the interacting case, we show that the Kondo time decreases with the strength of the repulsive interaction and the time dependence of the current reveals signatures of the Kondo effect in a Luttinger liquid. In addition, we verify that the relaxation of the impurity magnetization does not exhibit universal scaling behavior in the perturbative regime below the Kondo time. Our results highlight the role of nonequilibrium dynamics as a valuable tool in the study of quantum impurities in interacting systems.
The equilibrium physics of quantum impurities frequently involves a universal crossover from weak to strong reservoir-impurity coupling, characterized by single-parameter scaling and an energy scale TK (Kondo temperature) that breaks scale invariance. For the noninteracting resonant level model, the nonequilibrium time evolution of the Loschmidt echo after a local quantum quench was recently computed explicitly [R. Vasseur, K. Trinh, S. Haas, and H. Saleur, Phys. Rev. Lett. 110, 240601 (2013)]. It shows single-parameter scaling with variable TKt. Here, we scrutinize whether similar universal dynamics can be observed in various interacting quantum impurity systems. Using density matrix and functional renormalization group approaches, we analyze the time evolution resulting from abruptly coupling two noninteracting Fermi or interacting Luttinger liquid leads via a quantum dot or a direct link. We also consider the case of a single Luttinger liquid lead suddenly coupled to a quantum dot. We investigate whether the field-theory predictions for the universal scaling as well as for the large-time behavior successfully describe the time evolution of the Loschmidt echo and the entanglement entropy of microscopic models. Our study shows that for the considered local quench protocols the above quantum impurity models fall into a class of problems for which the nonequilibrium dynamics can largely be understood based on the knowledge of the corresponding equilibrium physics.
In this thesis we investigate the physics of two strongly correlated electron systems. The part I of this document is dedicated to the study of the real-time dynamics of the Kondo effect produced by a quench protocol. For it, we consider one or two metallic chains of interacting electrons (Hubbard chains) coupled to a magnetic impurity of spin 1/2. The quench protocol consists of assuming that, for times τ < 0, the chains are decoupled from the impurity, at τ = 0 the coupling is suddenly turned on and, for τ > 0 , the system evolves unitarily in time. We determine an analytical expression for the relaxation of the impurity magnetization in the time regime τ ≪ τK , where τK is the Kondo time. This result was confirmed by numerical calculations performed in our group. Based on these numerical results, we observe that the increase in the interaction U between the electrons in the chains leads to a faster decay of the impurity magnetization, showing that the electron-electron interaction favors the formation of the Kondo effect. Further we studied the time-dependent transport through the impurity, from which we determine, in the interacting case, an analytical expression for the time scale equivalent to the Kondo time. According to the expression we obtained, we conclude that the Kondo scale is reduced when U increases, in agreement with the numerical results mentioned above. In part II of this thesis we investigate the physics of superconducting cuprates, motivated by electronic Raman spectroscopy measurements of the charge density wave (CDW) phase observed in these materials. Through a phenomenological approach, we describe a charge order in the CuO2 plane. Analyzing the spectral properties of the system, we establish that the CDW phase should be more easily detectable in the ω > 0 (above the Fermi level) region of the local density of states. Our results for the B2g Raman response show a general dip-hump behavior, as actually seen in the experiments, which is independent of the system band structure. In contrast, the B1g Raman response is strongly band structure dependent. In the second part of the work, a more general model was proposed, based on the Yang-Rice-Zhang ansatz, which also takes into account the pseudogap (PG) phase. We conclude that the PG phase drives the doping dependence of the CDW energy scale, in agreement with the experiments. This result is suggestive of a PG phase governing the different energy scales of the exotic phases that appear in the underdoped region of the cuprate phase diagram.
We study the nonequilibrium formation of a spin screening cloud that accompanies the quenching of a local magnetic moment immersed in a Fermi sea at zero temperature. Based on high-precision density matrix renormalization-group results for the interacting single-impurity Anderson model, we discuss the real-time evolution after a quantum quench in the impurity-reservoir hybridization using time-evolving block decimation. We report emergent length and time scales in the spatiotemporal structure of nonlocal correlation functions in the spin and the charge density channel. At equilibrium, our data for the correlation functions and the extracted length scales show good agreement with existing results, as do local time-dependent observables at the impurity. In the time-dependent data, we identify a major signal which defines a ``light cone'' moving at the Fermi velocity and a ferromagnetic component in its wake. Inside the light cone we find that the structure of the nonequilibrium correlation functions emerges on two time scales. Initially, the qualitative structure of the correlation functions develops rapidly at the lattice Fermi velocity. Subsequently the spin correlations converge to the equilibrium results on a much larger time scale. This process sets a dynamic energy scale, which we identify to be proportional to the Kondo temperature. Outside the light cone we observe two different power-law decays of the correlation functions in space, with time- and interaction-strength-independent exponents.
We propose and explore the physics of a toy multiferroic model by coupling two distinct dipolar XXZ models in transverse fields. We determine first the rich ground-state phase diagram of the model using density matrix renormalization group techniques. Then, we explore the dynamics of the system after global and local quenches, using the time-evolving block decimation algorithm. After a global quench, the system displays decaying coupled oscillations of the electric and magnetic spins, in agreement with the Eigenstate Thermalization Hypothesis (ETH) for many-body interacting quantum systems. Notably, the spin-spin interactions lead to a sizeable quadratic shift in the oscillation frequency as the inter-chain coupling is increased. Local quenches lead to a light-cone-like propagation of excitations. In this case, the inter-chain coupling drives a transfer of energy between the chains that generates a novel fast spin-wave mode along the 'magnetic' chain at the speed of the 'electric' spin-wave. This suggests a limited control mechanism for faster information transfer in magnetic spin chains using electric fields that harnesses the electric dipoles as intermediaries.
We investigate the out-of-equilibrium dynamics after a local quench that connects two spin-1/2 XXZ chains prepared in the ground state of the Hamiltonian in different phases, one in the ferromagnetic phase and the other in the critical phase. We analyze the time evolution of the on-site magnetization and bipartite entanglement entropy via adaptive time-dependent density matrix renormalization group. In systems with short-range interactions, such as the one we consider, the velocity of information transfer is expected to be bounded, giving rise to a light-cone effect. Interestingly, our results show that, when the anisotropy parameter of the critical chain is sufficiently close to that of the isotropic ferromagnet, the light cone is determined by the velocity of spin-wave bound states that propagate faster than single-particle (``spinon'') excitations. Furthermore, we investigate how the system approaches equilibrium in the inhomogeneous ground state of the connected system, in which the ferromagnetic chain induces a nonzero magnetization in the critical chain in the vicinity of the interface.