arXiv subjects

A. M. Marques

Publications and source records attributed to A. M. Marques.

At least 19 recordsLinked to original sources

arXiv2026

Scalable topological quantum computing based on Sine-Cosine chain models

This work proposes a scalable framework for topological quantum computing using Matryoshka-type Sine-Cosine chains. These chains support high-dimensional qudit encoding within single systems, reducing the physical resource overhead compared to conventional qubit arrays. We describe how these chains can be used in Y-junction braiding protocols for gate operations and in extended memory architectures capable of storing multiple qubits simultaneously. Fidelity analysis shows partial topological protection against disorder, suggesting this approach is a possible pathway toward low-overhead quantum hardware.

quant-ph↗

arXiv2026

Quantum transfer in high-root topological insulators

This paper focuses on the quantum state transfer in a one-dimensional (1D) high-root topological insulator (HRTI) with an arbitrary number of domains. We present the possibility of having multiple transfer processes in the same model due to the existence of various edge states in distinct energy gaps, which may benefit recent (de)multiplexing technologies. We also derived the relations between transfer times of different root models and different gaps in the same model. We show how the exponential decay in transfer time caused by the fragmentation of a parent chain into domains can be generalized to its higher-root versions while maintaining a high transfer fidelity, and how the increasing number of domain wall states leads to a higher transfer fidelity against a general disorder regime due to the topological protection inherited from the parent model.

cond-mat.mes-hall↗

arXiv2026

Exceptional horns in $n$-root graphene and Lieb photonic ring lattices

We present a systematic construction of non-Hermitian tight-binding lattices whose Bloch spectra are $n$th roots of those of Hermitian parent two-dimensional (2D) lattices, namely graphene and the Lieb lattice. The $n$-roots of these models are constructed from connecting loop modules of unidirectional couplings whose geometrical arrangements match that of the corresponding parent system. Their energy spectrum is shown to consist of $n$ rotated and equivalent branches in the complex energy plane, each matching the real spectrum of the parent model when raised to the $n$th power, together with extra zero-energy flat bands (FBs) accounted for by the generalized index theorem. We show how the low-energy Dirac cones of the parent models translate, for an appropriate choice of phase configuration for the couplings of the $n$-root lattices, as what we call an "exceptional horn" appearing at each branch, with the central Dirac point (DP) converted into zero-energy exceptional points (EPs) of order $n$ or higher at high-symmetry momenta. These exceptional horns reflect the behavior of low-lying excitations that scale with momentum as $E\sim\vert \mathbf{q}\vert^{\frac{1}{n}}$, with $n\geq 3$, as opposed to the linear massless modes that characterize a Dirac cone. Moreover, we derive analytic expressions for the associated Landau levels (LLs), whose energies scale with magnetic flux as $E\sim\phi^{\frac{1}{2n}}$. For the case of the $n$-root Lieb lattice, the zeroth LL is shown to be exceptional. These results are analytically derived for both $n$-root models and numerically demonstrated for certain values of $n$. Finally, we propose a realistic photonic implementation based on coupled ring resonators with a split configuration of optical gain and loss.

cond-mat.mes-hall↗

arXiv2025

High-root topological edge-state bands

This paper presents a complex band analysis of one-dimensional (1D) square and high-root topological insulators (HRTIs). We show that edge-state bands of HRTIs are sliced sections of impurity bands of a uniform tight-binding chain. A simplified topological characterization of HRTIs with generalized boundary conditions is carried out based on the existence of edge-state bands in the infinite HRTI and the restrictions imposed by the boundary conditions. Edge states in finite or semi-infinite 1D HRTIs are shown to be a subset of evanescent states of the infinite system and mapped onto impurity states of the uniform chain with effective energy-dependent edge potentials. The latter result allows the determination of the edge state levels without needing the diagonalization of real space or bulk Hamiltonians.

cond-mat.mes-hall↗

arXiv2022

Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices

Square-root topology describes models whose topological properties can be revealed upon squaring the Hamiltonian, which produces their respective parent topological insulators. This concept has recently been generalized to $2^n$-root topology, characterizing models where $n$ squaring operations must be applied to the Hamiltonian in order to arrive at the topological source of the model. In this paper, we analyze the Hofstadter regime of quasi-one-dimensional (quasi-1D) and two-dimensional (2D) $2^n$-root models, the latter of which has the square lattice (SL) (known for the Hofstadter Butterfly) as the source model. We show that upon increasing the root-degree of the model, there appear multiple magnetic flux insensitive flat bands, and analytically determine corresponding eigenstates. These can be recast as compact localized states (CLSs) occupying a finite region of the lattice. For a finite flux, these CLSs correspond to different harmonics contained within the same Aharonov-Bohm (AB) cage. Furthermore, as the root-degree increases, a kaleidoscope of butterflies is seen to appear in the Hofstadter diagram, with each butterfly constituting a topologically equivalent replica of the original one of the SL. As such, the index $n$, which uniquely identifies the root-degree of the model, can be seen as an additional fractal dimension of the $2^n$-root model present in its Hofstadter diagram. We discuss how these dynamics could be realized in experiments with ultracold atoms, and measured by Bragg spectroscopy or through observing dynamics of initially localized atoms in a quantum gas microscope.

cond-mat.quant-gas↗

arXiv2022

Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices

Hermitian bipartite models are characterized by the presence of chiral symmetry and by Lieb's theorem, which derives the number of zero-energy flat bands of the model from the imbalance of sites between its two sublattices. Here, we introduce a class of non-Hermitian models with an arbitrary number of sublattices connected in a unidirectional and cyclical way and show that the number of zero-energy flat bands of these models can be found from a generalized version of Lieb's theorem, in what regards its application to noninteracting tight-binding models, involving the imbalance between each sublattice and the sublattice of lowest dimension. Furthermore, these models are also shown to obey a generalized chiral symmetry, of the type found in the context of certain clock or parafermionic systems. The main results are illustrated with a simple toy model, and possible realizations in different platforms of the models introduced here are discussed.

cond-mat.other↗

arXiv2022

Long-range hopping and indexing assumption in one-dimensional topological insulators

In this paper, we show that the introduction of long-range hoppings in 1D topological insulator models implies that different possibilities of site indexing must be considered when determining the bulk topological invariants in order to avoid the existence of hidden symmetries. The particular case of the extended SSH chain is addressed as an example where such behavior occurs. In this model, the introduction of long-range hopping terms breaks the bipartite property and a band inversion occurs in the band structure as the relative values of the hopping terms change, signaling a crossover between hopping parameter regions of "influence" of different chiral symmetries. Furthermore, edge states become a linear combination of edge-like states with different localization lengths and reflect the gradual transition between these different chiral symmetries.

cond-mat.mes-hall↗

arXiv2021

$2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals

Recently, we have introduced in [A. M. Marques et al., Phys. Rev. B 103, 235425 (2021)] the concept of $2^n$-root topology and applied it to one-dimensional systems. These models require $n$ squaring operations to their Hamiltonians, intercalated with different constant energy downshifts at each level, in order to arrive at a decoupled block corresponding to a known topological insulator (TI) that acts as the source of the topological features of the starting $2^n$-root TI ($\sqrt[2^n]{\text{TI}}$). In the process, $n$ non-topological residual models with degenerate spectra and in-gap impurity states appear, which dilute the topologically protected component of the starting edge states. Here, we generalize this method to several two-dimensional models, by finding the 4-root version of lattices hosting weak and higher-order boundary modes (both topological and non-topological) of a Chern insulator and of a topological semimetal. We further show that a starting model with a non-Hermitian region in parameter space and a complex energy spectrum can nevertheless display a purely real spectrum for all its successive squared versions, allowing for an exact mapping between certain non-Hermitian models and their Hermitian lower root-degree counterparts. A comment is made on the possible realization of these models in artificial lattices.

cond-mat.mes-hall↗

arXiv2021

One-dimensional $2^n$-root topological insulators and superconductors

Square-root topology is a recently emerged subfield describing a class of insulators and superconductors whose topological nature is only revealed upon squaring their Hamiltonians, i.e., the finite energy edge states of the starting square-root model inherit their topological features from the zero-energy edge states of a known topological insulator/superconductor present in the squared model. Focusing on one-dimensional models, we show how this concept can be generalized to $2^n$-root topological insulators and superconductors, with $n$ any positive integer, whose rules of construction are systematized here. Borrowing from graph theory, we introduce the concept of arborescence of $2^n$-root topological insulators/superconductors which connects the Hamiltonian of the starting model for any $n$, through a series of squaring operations followed by constant energy shifts, to the Hamiltonian of the known topological insulator/superconductor, identified as the source of its topological features. Our work paves the way for an extension of $2^n$-root topology to higher-dimensional systems.

cond-mat.mes-hall↗

arXiv2021

Matryoshka approach to Sine-Cosine topological models

We address a particular set of extended Su-Schrieffer-Heeger models with $2n$ sites in the unit cell [SSH($2n$)], that we designate by Sine-Cosine models [SC$(n)$], with hopping terms defined as a sequence of $n$ sine-cosine pairs of the form $\{\sin(θ_j),\cos(θ_j)\}$, $j=1, \cdots,n$. These models, when squared, generate a block-diagonal matrix representation with one of the blocks corresponding to a chain with uniform local potentials. We further focus our study on the subset of SC$(2^{n-1})$ chains that, when squared an arbitrary number of times (up to $n$), always generate a block which is again a Sine-Cosine model, if an energy shift is applied and if the energy unit is renormalized. We show that these $n$-times squarable models [SSC$(n)$] and their band structure are uniquely determined by the sequence of energy unit renormalizations and by the energy shifts associated to each step of the squaring process. Chiral symmetry is present in all Sine-Cosine chains and edge states levels at the respective central gaps are protected by it. Zero-energy edge states in a SSC$(j)$ chain (with $j<n$) of the Matryoshka sequence obtained squaring the SSC$(n)$ chain with open boundary conditions (OBC), become finite energy edge states in non-central band gaps of the SSC$(n)$ chain. The extension to higher dimensions is discussed.

cond-mat.mes-hall↗

arXiv2020

Interaction-induced topological properties of two bosons in flat-band systems

In flat-band systems, destructive interference leads to the localization of non-interacting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighbouring single-particle localized eigenstates may enable the propagation of bound pairs of particles. In this work, we show how these interaction-induced hoppings can be tuned to obtain a variety of two-body topological states. In particular, we consider two interacting bosons loaded into the orbital angular momentum $l=1$ states of a diamond-chain lattice, wherein an effective $π$ flux may yield a completely flat single-particle energy landscape. In the weakly-interacting limit, we derive effective single-particle models for the two-boson quasiparticles which provide an intuitive picture of how the topological states arise. By means of exact diagonalization calculations, we benchmark these states and we show that they are also present for strong interactions and away from the strict flat-band limit. Furthermore, we identify a set of doubly localized two-boson flat-band states that give rise to a special instance of Aharonov-Bohm cages for arbitrary interactions.

cond-mat.quant-gas↗

arXiv2020

One-dimensional topological insulators with noncentered inversion symmetry axis

In this paper, we discuss the characteristic features of one-dimensional topological insulators with inversion symmetry but noncentered inversion axis in the unit cell, for any choice of the unit cell. In these systems, the global inversion operation generates a k-dependent inversion operator within the unit cell and this implies a nonquantized Zak's phase both for the trivial and nontrivial topological phases. By relating the Zak's phase with the eigenvalues of modified parity operators at the inversion invariant momenta, a corrected quantized form of the Zak's phase is derived. We show that finite energy topological edge states of this family of chains are symmetry protected not by usual chiral symmetry but by a hidden sublattice chiral-like symmetry. A simple justification is presented for shifts in the polarization quantization relation for any choice of endings of these chains.

cond-mat.mes-hall↗

arXiv2019

Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices

We propose a realization of a two-dimensional higher-order topological insulator with ultracold atoms loaded into orbital angular momentum (OAM) states of an optical lattice. The symmetries of the OAM states induce relative phases in the tunneling amplitudes that allow to describe the system in terms of two decoupled lattice models. Each of these models displays one-dimensional edge states and zero-dimensional corner states that are correlated with the topological properties of the bulk. We show that the topologically non-trivial regime can be explored in a wide range of experimentally feasible values of the parameters of the physical system. Furthermore, we propose an alternative way to characterize the second-order topological corner states based on the computation of the Zak's phases of the bands of first-order edge states.

cond-mat.quant-gas↗

arXiv2018

Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum

We show that bosonic atoms loaded into orbital angular momentum $l=1$ states of a lattice in a diamond-chain geometry provides a flexible and simple platform for exploring a range of topological effects. This system exhibits robust edge states, and the relative phases arising naturally in the tunnelling amplitudes lead to the appearance of Aharanov-Bohm caging in the lattice. We discuss how these properties can be realised and observed in ongoing experiments.

physics.atom-ph↗

arXiv2018

Topological edge states with ultracold atoms carrying orbital angular momentum in a diamond chain

We study the single-particle properties of a system formed by ultracold atoms loaded into the manifold of $l=1$ Orbital Angular Momentum (OAM) states of an optical lattice with a diamond chain geometry. Through a series of successive basis rotations, we show that the OAM degree of freedom induces phases in some tunneling amplitudes of the tight-binding model that are equivalent to a net $π$ flux through the plaquettes and give rise to a topologically non-trivial band structure and protected edge states. In addition, we demonstrate that quantum interferences between the different tunneling processes involved in the dynamics may lead to Aharanov-Bohm caging in the system. All these analytical results are confirmed by exact diagonalization numerical calculations.

physics.atom-ph↗

arXiv2018

Topological bound states in interacting Su-Schrieffer-Heeger rings

We study two-particle states in a Su-Shrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.

cond-mat.str-el↗

arXiv2017

Generalization of Zak's phase for lattice models with non-centered inversion symmetry axis

We show how the presence of inversion symmetry in a one-dimensional (1D) lattice model is not a sufficient condition for a quantized Zak's phase. This is only the case when the inversion axis is at the center of the unit cell. When the inversion axis is not at the center, the modified inversion operator within the unit cell gains a k-dependence in some of its matrix elements which adds a correction term to the usual Zak's phase expression1, making it in general deviate from its quantized value. A general expression that recovers a quantized Zak's phase in a lattice model with a unit cell of arbitrary size and arbitrarily positioned inversion axis is provided in this paper, which relates the quantized value with the eigenvalues of a modified parity operator at the inversion invariant momenta.

cond-mat.mes-hall↗

arXiv2017

Multihole edge states in Su-Schrieffer-Heeger chains with interactions

We address the effect of nearest-neighbor (NN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) chain, with alternating hopping amplitudes t1 and t2. Both numerically and analytically, we show that the presence of interactions induces phase transitions between topologically different regimes. In the particular case of one-hole excitations in a half-filled SSH chain, the V=t2 vs. t1=t2 phase diagram has topological phases at diagonal regions of the phase plane. The interaction acts in this case as a passivation potential. For general filling of the SSH chain, different eigensubspaces of the SSH Hamiltonian may be classified as topologically trivial and non-trivial. The two-hole case is studied in detail in the large interaction limit, and we show that a mapping can be constructed of the two-hole SSH eigensubspaces into one-particle states of a non-interacting one-dimensional (1D) tight-binding model, with interfaces between regions with different hopping constants and local potentials. The presence of topological edge states in the equivalent chain can be readily identifed, as well as their correspondence to the original two-hole states. Furthermore, we found that the presence of the NN interaction generates a state where two holes occupy two consecutive edge states. Such many-body states should also occur for arbitrary filling leading to the possibility of a macroscopic hole gathering at the surface (at consecutive edge states).

cond-mat.str-el↗