arXiv subjects

Cristiane Morais Smith

Publications and source records attributed to Cristiane Morais Smith.

At least 37 records · Page 2Linked to original sources

arXiv2024

The Fractal-Lattice Hubbard Model

Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte Carlo. We focus on the Sierpinski triangle with Hausdorff dimension $1.58$ and consider several generations. In the tight-binding limit, we find compact localised states, which are also explained in terms of symmetry and linked to the formation of a ferrimagnetic phase at weak interaction. Simulations at half-filling revealed the persistence of this type of magnetic order for every value of interaction strength and a Mott transition for U/t $\sim$ 4.5. In addition, we found a remarkable dependence on the Hausdorff dimension regarding $i)$ the number of compact localised states in different generations, $ii)$ the scaling of the total many-body ground-state energy in the tight-binding limit, and $iii)$ the density of the states at the corners of the lattice for specific values of electronic filling. Moreover, in the presence of an intrinsic spin-orbit coupling, the zero-energy compact localized states become entangled and give rise to inner and outer corner modes.

cond-mat.str-el↗

arXiv2024

Emergent time crystal from a fractional Langevin equation with white and colored noise

We study the fractional Langevin equation with fractional $α$-order and linear friction terms of a system coupled to white and colored thermal baths using both analytical and numerical methods. We find analytical expressions for the position and the mean squared displacement (MSD) of the system using the Prabhakar-Mittag-Leffler function. The MSD exhibits long-term sub-diffusive regimes $t^α$ driven by colored noise and $t^{2α-1}$ driven by white noise. When the linear friction is neglected, periodic ordered phases emerge for small fractional orders $α\lesssim 0.1$. In particular, the zero-linear friction system driven only by colored noise manifests the properties of a time crystal, with a ground state satisfying the fluctuation-dissipation theorem and a periodicity proportional to $2π$. On the other hand, the zero-linear friction system driven only by white noise displays an out-of-equilibrium time glass phase with periodicity proportional to $π$. A mixed phase with contributions from both ground and out-of-equilibrium states is encountered when the system couples to both baths. In that case, the periodicity deviates from $2π$ due to damping effects. We test all the analytical results numerically by implementing a discrete recursive expression, where the random forces of the system are modeled as the derivative of the fractional Brownian motion. A microscopic description for the system is also provided by an extension of the Caldeira-Leggett model.

cond-mat.stat-mech↗

arXiv2023

Fractal Nodal Band Structures

Non-Hermitian systems exhibit interesting band structures, where novel topological phenomena arise from the existence of exceptional points at which eigenvalues and eigenvectors coalesce. One important open question is how this would manifest at non-integer dimension. Here, we report on the appearance of fractal eigenvalue degeneracies and Fermi surfaces in Hermitian and non-Hermitian topological band structures. This might have profound implications on the physics of black holes and Fermi surface instability driven phenomena, such as superconductivity and charge density waves.

cond-mat.mes-hall↗

arXiv2023

Emergent non-Hermitian models

The Hatano-Nelson and the non-Hermitian Su-Schrieffer-Heeger model are paradigmatic examples of non-Hermitian systems that host non-trivial boundary phenomena. In this work, we use recently developed graph-theoretical tools to design systems whose isospectral reduction -- akin to an effective Hamiltonian -- has the form of either of these two models. In the reduced version, the couplings and on-site potentials become energy-dependent. We show that this leads to interesting phenomena such as an energy-dependent non-Hermitian skin effect, where eigenstates can simultaneously localize on either ends of the systems, with different localization lengths. Moreover, we predict the existence of various topological edge states, pinned at non-zero energies, with different exponential envelopes, depending on their energy. Overall, our work sheds new light on the nature of topological phases and the non-Hermitian skin effect in one-dimensional systems.

quant-ph↗

arXiv2023

Dissipative systems fractionally coupled to a bath

Quantum diffusion is a major topic in condensed-matter physics, and the Caldeira-Leggett model has been one of the most successful approaches to study this phenomenon. Here, we generalize this model by coupling the bath to the system through a Weyl fractional derivative. The Weyl fractional Langevin equation is then derived without imposing a non-Ohmic macroscopic spectral function for the bath. By investigating the short- and long-time behavior of the mean squared displacement (MSD), we show that this model is able to describe a large variety of anomalous diffusion. Indeed, we find ballistic, sub-ballistic, and super-ballistic behavior for short times, whereas for long times we find saturation, and sub- and super-diffusion.

cond-mat.stat-mech↗

arXiv2023

Quantized valley Hall response from local bulk density variations

The application of a mechanical strain to a 2D material can create pseudo-magnetic fields and lead to a quantized valley Hall effect. However, measuring valley-resolved effects remains a challenging task due to their inherent fragility and dependence on the sample's proper design. Additionally, non-local transport probes based on multiterminal devices have often proven to be inadequate in yielding conclusive evidence of the valley Hall signal. Here, we introduce an alternative way of detecting the quantized valley Hall effect, which entirely relies on local density measurements, performed deep in the bulk of the sample. The resulting quantized signal is a genuine Fermi sea response, independent of the edge physics, and reflects the underlying valley Hall effect through the Widom-Středa formula. Specifically, our approach is based on measuring the variation of the particle density, locally in the bulk, upon varying the strength of the applied strain. This approach to the quantized valley Hall effect is particularly well suited for experiments based on synthetic lattices, where the particle density (or integrated density of states) can be spatially resolved.

cond-mat.mes-hall↗

arXiv2023

Spectral Properties of Two Coupled Fibonacci Chains

The Fibonacci chain, i.e., a tight-binding model where couplings and/or on-site potentials can take only two different values distributed according to the Fibonacci word, is a classical example of a one-dimensional quasicrystal. With its many intriguing properties, such as a fractal eigenvalue spectrum, the Fibonacci chain offers a rich platform to investigate many of the effects that occur in three-dimensional quasicrystals. In this work, we study the eigenvalues and eigenstates of two identical Fibonacci chains coupled to each other in different ways. We find that this setup allows for a rich variety of effects. Depending on the coupling scheme used, the resulting system (i) possesses an eigenvalue spectrum featuring a richer hierarchical structure compared to the spectrum of a single Fibonacci chain, (ii) shows a coexistence of Bloch and critical eigenstates, or (iii) possesses a large number of degenerate eigenstates, each of which is perfectly localized on only four sites of the system. If additionally, the system is infinitely extended, the macroscopic number of perfectly localized eigenstates induces a perfectly flat quasi band. Especially the second case is interesting from an application perspective, since eigenstates that are of Bloch or of critical character feature largely different transport properties. At the same time, the proposed setup allows for an experimental realization, e.g., with evanescently coupled waveguides, electric circuits, or by patterning an anti-lattice with adatoms on a metallic substrate.

cond-mat.str-el↗

arXiv2023

Multifractal Properties of Tribonacci Chains

We introduce two 1D tight-binding models based on the Tribonacci substitution, the hopping and on-site Tribonacci chains, which generalize the Fibonacci chain. For both hopping and on-site models, a perturbative real-space renormalization procedure is developed. We show that the two models are equivalent at the fixed point of the renormalization group flow, and that the renormalization procedure naturally gives the Local Resonator Modes. Additionally, the Rauzy fractal, inherent to the Tribonacci substitution, is shown to serve as the analog of conumbering for the Tribonacci chain. The renormalization procedure is used to repeatedly subdivide the Rauzy fractal into copies of itself, which can be used to describe the eigenstates in terms of Local Resonator Modes. Finally, the multifractal dimensions of the energy spectrum and eigenstates of the hopping Tribonacci chain are computed, from which it can be concluded that the Tribonacci chains are critical.

cond-mat.dis-nn↗

arXiv2022

The fractional Landau-Lifshitz-Gilbert equation

The dynamics of a magnetic moment or spin are of high interest to applications in technology. Dissipation in these systems is therefore of importance for improvement of efficiency of devices, such as the ones proposed in spintronics. A large spin in a magnetic field is widely assumed to be described by the Landau-Lifshitz-Gilbert (LLG) equation, which includes a phenomenological Gilbert damping. Here, we couple a large spin to a bath and derive a generic (non-)Ohmic damping term for the low-frequency range using a Caldeira-Leggett model. This leads to a fractional LLG equation, where the first-order derivative Gilbert damping is replaced by a fractional derivative of order $s \ge 0$. We show that the parameter $s$ can be determined from a ferromagnetic resonance experiment, where the resonance frequency and linewidth no longer scale linearly with the effective field strength.

cond-mat.mes-hall↗

arXiv2022

Field Theoretical Study of Disorder in Non-Hermitian Topological Models

Non-Hermitian systems have provided a rich platform to study unconventional topological phases.These phases are usually robust against external perturbations that respect certain symmetries of thesystem. In this work, we provide a new method to analytically study the effect of disorder, usingtools from quantum field theory applied to discrete models around phase-transition points. Weinvestigate two different one-dimensional models, the paradigmatic non-Hermitian SSH model andas-wave superconductor with imbalanced pairing. These analytic results are compared to numericalsimulations in the discrete models. An universal behavior is found for the two investigated models,namely that the systems are driven from a topological to a trivial phase for disorder strengths equalto about four times the energy scale of the model.

cond-mat.dis-nn↗

arXiv2022

Median-point approximation and its application for the study of fermionic systems

We consider a system of fermions with local interactions on a lattice (Hubbard model) and apply a novel extension of the Laplace's method (saddle-point approximation) for evaluating the corresponding partition function. There, we introduce dual free bosonic fields, with a propagator corresponding to an effective (renormalized) interaction with Maki-Thompson and Aslamazov-Larkin type corrections and beyond, and demonstrate that the superconducting pairing originates as an instability of the effective interaction. We derive the corresponding Bethe-Salpeter equation (instability criterion) and show that the interaction enters the equation only in its effective form to all orders, including the exchange part of the self-energy. An important implication of this result is that the effective interaction always remains finite, even at phase-transition points, directly contradicting the often used assumption of linear relationship between the interaction and susceptibility, established within the random-phase approximation. By analyzing the Bethe-Salpeter equation in the context of unconventional superconductivity, we find that the presence of a flat band close the Fermi level, found in materials such as twisted bilayer graphene, has a twofold favorable impact persisting beyond the weak-coupling approximation: a reduced kinetic energy cost of the gap formation and an increased anisotropy of the effective interaction, favoring a momentum dependent order parameter.

cond-mat.str-el↗

arXiv2021

Effects of Disorder in the Fibonacci Quasicrystal

We study the properties of the one-dimensional Fibonacci chain, subjected to the placement of on-site impurities. The resulting disruption of quasiperiodicity can be classified in terms of the renormalization path of the site at which the impurity is placed, which greatly reduces the possible amount of disordered behavior that impurities can induce. Moreover, it is found that, to some extent, the addition of multiple, weak impurities can be treated by superposing the individual contributions together and ignoring nonlinear effects. This means that a transition regime between quasiperiodic order and disorder exists, in which some parts of the system still exhibit quasiperiodicity, while other parts start to be characterized by different localisation behaviours of the wavefunctions. This is manifested through a symmetry in the wavefunction amplitude map, expressed in terms of conumbers, and through the inverse participation ratio. For the latter, we find that its average of states can also be grouped in terms of the renormalization path of the site at which the impurity has been placed.

cond-mat.dis-nn↗

arXiv2021

Robustness of chiral edge modes in fractal-like-lattices below two dimensions: A case study

One of the most prominent characteristics of two-dimensional Quantum Hall systems are chiral edge modes. Their existence is a consequence of the bulk-boundary correspondence and their stability guarantees the quantization of the transverse conductance. In this work, we study two microscopic models, the Hofstadter lattice model and an extended version of Haldane's Chern insulator. Both models host Quantum Hall phases in two dimensions. We transfer them to lattice implementations of fractals with a dimension between one and two and study the existence and robustness of their edge states. Our main observation is that, contrary to their two-dimensional counterpart, there is no universal behavior of the edge modes in fractals. Instead, their presence and stability critically depends on details of the models and the lattice realization of the fractal.

cond-mat.mes-hall↗

arXiv2021

Quantizing Lévy flights

The Caldeira-Leggett model of quantum Brownian motion is generalized using a generic velocity-dependent coupling. That leads to the description of a set of models able to capture Markovian and non-Markovian versions of Brownian and Lévy statistics, depending on the functional form of the coupling and on the spectral function of the reservoir. One specific coupling force is found that establishes a connection with Lévy statistics of cold atoms in \textit{Sisyphus} laser cooling. In the low-velocity limit, this also gives rise to additional inertia of the Brownian particle, reproducing the Abraham-Lorentz equation from first principles for a superohmic bath. Through path-integral quantization in Euclidean time, the environment is integrated out, leaving a set of non-local effective actions. These results further serve as starting points for several numerical calculations, particularly decoherence properties of non-ohmic baths.

cond-mat.stat-mech↗

arXiv2021

Time Glass: A Fractional Calculus Approach

Out of equilibrium states in glasses and crystals have been a major topic of research in condensed-matter physics for many years, and the idea of time crystals has triggered a flurry of new research. Here, we provide the first description for the recently conjectured Time Glasses using fractional calculus methods. An exactly solvable effective theory is introduced, with a continuous parameter describing the transition from liquid through normal glass, Time Glass, into the Gardner phase. The phenomenological description with a fractional Langevin equation is connected to a microscopic model of a particle in a sub-Ohmic bath in the framework of a generalized Caldeira-Leggett model.

cond-mat.stat-mech↗

arXiv2020

Internal Geometric Friction in a Kitaev Chain Heat Engine

We investigate a heat engine with a finite-length Kitaev chain in an ideal Otto cycle. It is found that the critical point of the topological phase transition coincides with the maxima of the efficiency and work output of the total Otto engine. Finite-size effects are taken into account using the method of Hill's nanothermodynamics, as well as using the method of temperature-dependent energy levels. We identify the bulk and boundary thermal cycles of the Kitaev chain engine and find that they are non-ideal Otto cycles. The physics of deviation from ideal Otto cycle is identified as a finite size effect, which we dub as "internal geometric friction", leading to heat transfer from the bulk to the boundary during adiabatic transformation of the whole system. Besides, we determine the regimes allowing for independently running an ideal Otto refrigerator at the boundary and an ideal Otto engines in the bulk and in the whole system. Furthermore, we show that the first-order phase transition in the boundary and the second-order phase transition in the bulk can be identified through their respective contributions to the engine work output.

cond-mat.stat-mech↗

arXiv2020

p Orbital flat band and Dirac cone in the electronic honeycomb lattice

Theory anticipates that the in-plane px, py orbitals in a honeycomb lattice lead to new and potentially useful quantum electronic phases. So far, p orbital bands were only realized for cold atoms in optical lattices and for light and exciton-polaritons in photonic crystals. For electrons, in-plane p orbital physics is difficult to access since natural electronic honeycomb lattices, such as graphene and silicene, show strong s-p hybridization. Here, we report on electronic honeycomb lattices prepared on a Cu(111) surface in a scanning tunneling microscope that, by design, show (nearly) pure orbital bands, including the p orbital flat band and Dirac cone.

cond-mat.mes-hall↗

arXiv2020

Visualising the connection between edge states and the mobility edge in adiabatic and non-adiabatic topological charge transport

The ability to pump quantised amounts of charge is one of the hallmarks of topological materials. An archetypical example is Laughlin's gauge argument for transporting an integer number of electrons between the edges of a quantum Hall cylinder upon insertion of a magnetic flux quantum. This is mathematically equivalent to the equally famous suggestion of Thouless' that an integer number of electrons are pumped between two ends of a one-dimensional quantum wire upon sliding a charge-density wave over a single wave length. We use the correspondence between these descriptions to visualise the detailed dynamics of the electron flow during a single pumping cycle, which is difficult to do directly in the quantum Hall setup, because of the gauge freedom inherent to its description. We find a close correspondence between topological edge states and the mobility edges in charge-density wave, quantum Hall, and other topological systems. We illustrate this connection by describing an alternative, non-adiabatic mode of topological transport that displaces precisely the opposite amount of charge as compared to the adiabatic pump. We discuss possible experimental realisations in the context of ultracold atoms and photonic waveguide experiments.

cond-mat.str-el↗