We investigate the dynamic phase transition properties of the two-dimensional anisotropic kinetic Ising model driven by a square-wave magnetic field. Spatial anisotropy is introduced through direction-dependent coupling strengths, and the system is analyzed using large-scale Monte Carlo simulations combined with finite-size scaling techniques. Several observables are computed to characterize the critical behavior and identify the transition points. Our results show that the presence of spatial anisotropy does not alter the universal nature of the transition, which remains consistent with that of the equilibrium Ising model. The findings highlight the robustness of the equilibrium Ising universality class even under spatial anisotropy and a time-dependent driving magnetic field.

A composite impurity in a metal explores different configurations, where its net magnetic moment may be screened by the electrons in the host. An interesting example is the two-stage Kondo (TSK) system where screening sets in with successively smaller energy scales. In contrast, the impurities may prefer a local singlet disconnected from the metal. This competition is decided by fine-tuning the couplings in the system, as has been studied before. A double quantum dot T-shape geometry, where a hanging dot is connected to current leads only via another dot, represents a flexible system in which these different regimes can be explored experimentally. It has been difficult, however, to clearly differentiate the two regimes. Here we provide a prescription to better identify the regime where the TSK occurs in such double dot geometry. The TSK regime requires a balance of the ratio t01/P0 between the interdot coupling (t01) and the coupling of the QD connected to the Fermi sea (P0). Above a certain value of this ratio, the system crosses over to a molecular regime, where the quantum dots form a local singlet and no Kondo screening occurs. Here we establish that there is a region in the t01 - P0 parameter space where a pure TSK regime occurs, i.e., where the properties of the second Kondo stage can be accurately described by a single impurity Anderson model with effective or renormalized parameters. By examining the magnetic susceptibility of the hanging QD, we show that a single parameter, Peff, can accurately simulate this susceptibility. This effective model also provides the hanging QD spectral function with great accuracy in a limited range of the t01 - P0 parameter space, thus defining the region where a true TSK regime occurs. We also show that in this parameter range, the spin correlations between both quantum dots show a universal behavior. Our results may guide experimental groups to choose parameter values that will place the system either in the TSK regime or in the crossover to the molecular regime.

The principles of ergodicity and thermalization constitute the foundation of statistical mechanics, positing that a many-body system progressively loses its local information as it evolves. Nevertheless, these principles can be disrupted when thermalization dynamics lead to the conservation of local information, as observed in the phenomenon known as many-body localization. Quantum spin chains provide a fundamental platform for exploring the dynamics of closed interacting quantum many-body systems. This study explores the dynamics of a spin chain with $S\geq 1/2$ within the Majumdar-Ghosh model, incorporating a non-uniform magnetic field and single-ion anisotropy. Through the use of exact numerical diagonalization, we unveil that a nearly constant-gradient magnetic field suppress thermalization, a phenomenon termed Stark many-body localization (SMBL), previously observed in $S=1/2$ chains. Furthermore, our findings reveal that the sole presence of single-ion anisotropy is sufficient to prevent thermalization in the system. Interestingly, when the magnitudes of the magnetic field and anisotropy are comparable, they compete, favoring delocalization. Despite the potential hindrance of SMBL by single-ion anisotropy in this scenario, it introduces an alternative mechanism for localization. Our interpretation, considering local energetic constraints and resonances between degenerate eigenstates, not only provides insights into SMBL but also opens avenues for future experimental investigations into the enriched phenomenology of disordered free localized $S\geq 1/2$ systems.

The principles of ergodicity and thermalization constitute the foundation of statistical mechanics, positing that a many-body system progressively loses its local information as it evolves. Nevertheless, these principles can be disrupted when thermalization dynamics lead to the conservation of local information, as observed in the phenomenon known as many-body localization. Quantum spin chains provide a fundamental platform for exploring the dynamics of closed interacting quantum many-body systems. This study explores the dynamics of a spin chain with $S\geq 1/2$ within the $J_1-J_2$, incorporating a non-uniform magnetic field and single-ion anisotropy. Through the use of exact numerical diagonalization, we unveil that a nearly constant-gradient magnetic field suppress thermalization, a phenomenon termed Stark many-body localization (SMBL), previously observed in $S=1/2$ chains. Furthermore, our findings reveal that the sole presence of single-ion anisotropy is sufficient to prevent thermalization in the system. Interestingly, when the magnitudes of the magnetic field and anisotropy are comparable, they compete, favoring delocalization. Despite the potential hindrance of SMBL by single-ion anisotropy in this scenario, it introduces an alternative mechanism for localization. Our interpretation, considering local energetic constraints and resonances between degenerate eigenstates, not only provides insights into SMBL but also opens avenues for future experimental investigations into the enriched phenomenology of disordered free localized $S\geq 1/2$ systems.

We have studied the Kondo effect of a spin-1/2 impurity coupled to a two-dimensional altermagnet host material. To attain the low-temperature many-body Kondo physics of the system, we have performed a numerical renormalization group calculations that allows us to access the spectral properties of the system at zero temperature. The impurity spectral function and the Kondo temperature were calculated for different set of parameters, including Rashba spin-orbit coupling (RSOC) and an external magnetic field. Interestingly, in the RSOC and altermagnetic fields, the hybridization function is spin independent, despite the characteristic broken time-reversal symmetry of the altermagnet. This is because the alternating sign of the spin splitting of the bands in the momentum space renders equal contributions for both spin components of the hybridization function. Our results demonstrate that, although the hybridization function is time-reversal symmetric, the Kondo temperature is substantially suppressed by the altermagnet coupling. Moreover, we have investigated the effect of an external magnetic field applied in the altermagnet along different directions. Interestingly, we observe an important restraining of the Kondo peak which depends strongly on the direction of the field. This anisotropic effect is, however, masked if strong Zeeman splitting takes place at the impurity, as it shatters the Kondo-singlet state.

We study the physics of the strong-coupling Hubbard model in a kagome lattice ribbon under mechanical tension and half filling. It is known that in the absence of strain, the lattice symmetry of the system and strong electronic interactions induce magnetic frustration. As uniaxial strain is applied, the ribbon exhibits various configurations with energy oscillations that depend on the direction of the strain axis. The ground states are obtained by density-matrix renormalization-group calculations. We find that the system is characterized by strong antiferromagnetic bonds distributed throughout the lattice in directions and patterns that depend on the strain directions and may coexist with easily polarizable sites that are only weakly correlated to their neighbors. We identify frustration and correlation measures that follow the strain and interaction dependence of the system well. These results illustrate that strain-dependent magnetic susceptibility could be explored experimentally to help probe the role of symmetry and interactions in these systems.

We have investigated magnetic interactions between transition metal ions in bismuthene topological insulators with protected edge states. We find that these topological states have a crucial role in the magnetic interactions in 2D topological insulators. Using first-principles and model Hamiltonian, we make a comparative study of transition metal doped bulk and nanoribbon bismuthene. While a direct overlap between the transition metal prevails in gapped bulk bismuthene, at the borders of nanoribbons, a long-range magnetism is present. The exchange interactions are well described by a Ruderman–Kittel–Kasuya–Yosida-like Hamiltonian mediated by massive and topological states. Our results show a dominance of antiferromagnetism promoted by the topological states, preserving the spin-locked Dirac crossing states due to a global time-reversal symmetry preservation. This extended magnetic interactions mediated mainly by massless electrons can increase the spin diffusion length being promising for fast dissipationless spintronic devices.

In this work we investigate Majorana correlations in quantum impurities coupled to a topological superconducting wire. By employing a density matrix renormalization group approach, we have calculated the Majorana correlation functions in the ground state of the system for different positions of the impurities along the wire. We observe that the correlations decreases exponentially with the distance between the impurities and the ends of the wire. Moreover, different electron-electron interactions on the wire and on the impurities were also analyzed, and the results showed a stronger effect as the electron occupation in the wire is increased. Moreover, changing the occupation of the impurities by tuning their energy levels, we observe that for specific values of $\epsilon$ the absolute value of correlation is highly peaked when the chemical potential lies within the window of the topological regime. These peaks are associated to coulomb blockade phenomena in the impurities, revealing very clearly its effect on the Majorana bound states in the topological phase of the system.

We theoretically analyze the Fano interference in a single impurity multi-Weyl semimetal hybrid system and show the emergence of the topological charge Fano effect in the bulk local density of states. In multi-Weyl semimetals, the number of Fermi arcs at the system boundaries is determined by the topological charge J, a direct consequence of the "bulk-boundary" correspondence principle. Analogously, we find that J also modulates the bulk Fano profile of the system with an embedded quantum impurity. Thus by increasing J, the Fano line shape evolves from resonant, typical for J = 1 (single Weyl), towards antiresonant, extrapolating to the so-called hyper Weyl semimetals with J >> 1. Specially for the maximum case protected by the rotational symmetry C-2j=6, namely, the J = 3 (triple Weyl), which acquires asymmetric Fano profile, the Fano parameter absolute value is predicted to be tan(C-2J=6), where C-2J (360 degrees/2J) defines the rotational angle. Hence, the Fano discretization in the J term introduces the topological charge Fano effect in multi-Weyl semimetals. We also suggest a transport device where we expect that the proposed Fano effect could be detected.

Using the Numerical Renormalization Group method, we study the properties of a quantum impurity coupled to a zigzag silicene nanoribbon (ZSNR) that is subjected to the action of a magnetic field applied in a generic direction. We propose a simulation of what a scanning tunneling microscope will see when investigating the Kondo peak of a magnetic impurity coupled to the metallic edge of this topologically non-trivial nanoribbon. This system is subjected to an external magnetic field that polarizes the host much more strongly than the impurity. Thus, we are indirectly analyzing the ZSNR polarization through the STM analysis of the fate of the Kondo state subjected to the influence of the polarized conduction electron band. Our numerical simulations demonstrate that the spin-orbit-coupling-generated band polarization anisotropy is strong enough to have a qualitative effect on the Kondo peak for magnetic fields applied along different directions, suggesting that this contrast could be experimentally detected.

In recent years, the reassessment of quantum physical phenomena under the framework of resource theories has triggered the design of novel quantum technologies that take advantage from quantum resources, such as entanglement and quantum coherence. Bearing this in mind, in this work we study the dynamics of quantum resources for two solid-state fermionic quantum devices: (i) a system composed by a pair of Majorana fermions and (ii) another comprising a pair of regular fermions. In both systems, the fermionic species are coupled to a single-level quantum dot. From the interaction of these tripartite systems with a dissipative reservoir, we were able to characterize the dynamics of the devices for some initial states. By employing a time-nonlocal master-equation approach, we obtain the evolution for fermionic occupations, quantum correlations, and quantum coherences in both the Markovian and non-Markovian dissipating regimes. We investigate the interconversion of local coherence and bipartite correlations for the marginal states in each device. While the dynamics of the entanglement and quantum coherence depend quite strongly on the temperature of the reservoir for regular fermions, we found these evolutions are qualitatively similar for the case of Majorana bound states regardless of temperature. Our results illustrate the use of quantum information-theoretic measures to characterize the role of quantum resources in fermion systems.

Stark many-body localization (SMBL) is a phenomenon observed in interacting systems with a nearly uniform spatial gradient applied field. Contrasting to the traditional many-body localization phenomenon, SMBL does not require disorder. Here we investigate SMBL in a spin-$1/2$ described by a Heisenberg model including a next-nearest-neighbor exchange coupling. By employing an exact diagonalization approach and time evolution calculation we analyze both level spacing ratio (LSR) statistics of the Hamiltonian model as well as the dynamics of the system from a given initial state. Our results reveals that for zero field in our finite system, LSR statistics suggest localization while the dynamics shows thermalization, which has been attributed to a finite-size effect. Slightly nonuniform field gradient, LSR statistic predictions agree very well with the dynamics of the physical quantities indicating delocalization and localization for small and large field gradient, respectively. More interestingly, we find that localization is robust in the presence of next-nearest-neighbor coupling in the Hamiltonian. Moreover, this coupling can be tuned to enhance SMBL in the system, meaning that localized regimes can be obtained for smaller field gradient as compared to the traditional nearest-neighbor isotropic Heisenberg model.

We have investigated the Kondo physics of a single magnetic impurity embedded in multi-Dirac (Weyl) node fermionic systems. By using a generic effective model for the host material and employing a numerical renormalization group approach we access the low temperature behavior of the system, identifying the existence of Kondo screening in single-, double-, and triple-Dirac (Weyl) node models. We find that in any multi-Dirac node systems the low-energy regime lies within one of the known classes of pseudogap Kondo problem, extensively studied in the literature. Kondo screening is also observed for time reversal symmetry broken Weyl systems. This is, however, possible only in the particle-hole symmetry broken regime obtained for finite chemical potential mu. Although weakly, breaking time-reversal symmetry suppresses the Kondo resonance, especially in the single-node Weyl semimetals. More interesting Kondo screening regimes are obtained for inversion symmetry broken multi-Weyl fermions. In these systems the Kondo regimes of double- and triple-Weyl node models are much richer than in the single-Weyl node model. While in the single-Weyl node model the Kondo temperature increases monotonically with WI regardless the value of the inversion symmetry breaking parameter Q(o) , in double- and triple-Weyl node models there are two distinct regimes: (i) For Q(o) < vertical bar mu vertical bar the Kondo temperature depends strongly on pc, while (ii) for Q(o) > vertical bar mu vertical bar the Kondo temperature depends very weakly on mu, resembling the flat-band single impurity Anderson model.

Using the numerical renormalization group method, we study a magnetic impurity coupled to a quantum wire with Rashba and Dresselhaus spin-orbit coupling (SOC) in an external magnetic field. We consider the low-filling regime with the Fermi energy close to the bottom of the band and report the results for local static and dynamic properties in the Kondo regime. In the absence of the field, local impurity properties remain isotropic in spin space despite the SOC-induced magnetic anisotropy of the conduction band. In the presence of the field, clear fingerprints of anisotropy are revealed through the strong field-direction dependence of the impurity spin polarization and spectra, in particular of the Kondo peak height. The detailed behavior depends on the relative magnitudes of the impurity and band g factors. For the case of an impurity g factor somewhat lower than the band g factor, the maximal Kondo peak suppression is found for a field oriented along the effective SOC field axis, while for a field perpendicular to this direction we observe a compensation effect (revival of the Kondo peak): The SOC counteracts the Kondo peak splitting effects of the local Zeeman field. We demonstrate that the SOC-induced anisotropy, measurable by tunneling spectroscopy techniques, can help to determine the ratio of Rashba and Dresselhaus SOC strengths in the wire.

Studies of competing orders in 1D magnetic chains have attracted considerable attention in recent years, as the presence of long-range Heisenberg interactions is found to allow interesting quantum phase transitions. We investigate here the role of spin-orbit effects by considering spin-1/2 chains in the presence of both collinear and non-collinear long-range interactions. By employing exact diagonalization and density matrix renormalization group calculations we investigate the rich phase diagram of this system. We find transitions from collinear to transverse magnetic correlated order as the strength of the non-collinear coupling increases, accompanied by a jump in the vector spin chirality order parameter of the system. This shows that tuning long-range interactions allows control of the onset of sizable vector spin chirality in a system, which may be used to transmit information down the chain. We investigate the characteristic structure of the distinct phases and explore their possible physical implementation in different materials systems.

In this work, we consider a single-level quantum dot (QD) and a Majorana bound state (MBS) placed at the end of a topological superconducting nanowire (TSW). Both are coupled to the continuum and do not have a direct connection between them. We addressed the behavior of MBS leaking phenomena and its consequences into the QD physics in non-interacting and Coulomb blockade regime. By employing Green's function formalism via the equation of motion procedure, we calculate the physical quantities of interest. Our results show that the leakage of the MBS into the continuum state is achieved and can alter the physics of Coulomb blockade in the system through continuum-mediated coupling between MBS and QD. As a main consequence, we found a robust and non-trivial mechanism to accomplish a bound state in the continuum in the system.

The prospect of using semiconductor quantum dots as an experimental tool to distinguish Majorana zero modes (MZMs) from other zero-energy excitations such as Kondo resonances has brought up the fundamental question of whether topological superconductivity and the Kondo effect can coexist in these systems. Here, we study the Kondo effect in a quantum dot coupled to a metallic contact and to a pair of MZMs. We consider a situation in which the MBS are spin polarized in opposite directions. By using numerical renormalization-group calculations and scaling analysis of the renormalization group equations, we show that the Kondo effect takes place at low temperatures, regardless the coupling to the MZMs. Interestingly, we find that the Kondo singlet essentially decouples from the MZMs such that the residual impurity entropy can show local non-Fermi liquid properties characteristic of the single Majorana excitations. This offers the possibility of tuning between Fermi-liquid and non-Fermi-liquid regimes simply by changing the quantum dot-MZM couplings.

Using NRG, we show that a system containing a quantum impurity (QI), strongly coupled to a semiconductor (gap $2 \Delta$) and weakly coupled to a metal, displays a 'reentrant' Kondo stage at low temperatures. The NRG analysis of the corresponding Single Impurity Anderson Model (SIAM) shows that the reentrant stage is characterized by a second sequence of SIAM fixed points: free orbital (FO) > local moment (LM) > strong coupling (SC). In the first stage, the SC fixed point (Kondo temperature $T_{K1}$) is unstable, while the second stage exhibits a much lower Kondo temperature $T_{K2}$, associated to a stable SC fixed point. The results indicate that the reentrant Kondo screening is associated to an effective SIAM, with an effective repulsion $U_{eff}$. This low temperature effective SIAM, which we dub as 'reentrant' SIAM, behaves as a 'replica' of the high temperature (bare) SIAM. The intuitive picture that emerges is that the first Kondo state develops through impurity screening by semiconducting electrons, while the second Kondo state involves screening by metallic electrons, once the semiconducting electrons are out of reach to thermal excitations ($T < \Delta$) and only the metallic spectral weight inside the gap is available for impurity screening. In addition, we analyze a hybrid system formed by a QI `sandwiched' between an armchair graphene nanoribbon (AGNR) and a scanning tunneling microscope (STM) tip, with respective couplings set to reproduce the generic model described above. The energy gap in the AGNR can be externally tuned by an electric-field-induced Rashba spin-orbit interaction. We analyzed this system for realistic parameter values, using NRG, and concluded that the reentrant SIAM, with its associated second stage Kondo, is worthy of experimental investigation.