arXiv subjects

C. Morais Smith

Publications and source records attributed to C. Morais Smith.

At least 19 recordsLinked to original sources

arXiv2026

SIM-GRAPH: A universal guide to symmetric interactions

Symmetry plays a central role throughout physics, from Fourier analysis on discrete lattices to the classification of elementary particles in the standard model. In finite quantum systems, symmetries are often discrete, such as reflection and rotational symmetries. Here, we present the SIM-GRAPH method (Symmetric Ising Models - Graph Reduction And Projected Hamiltonians), which uses such symmetries to efficiently calculate ground-state observables of interacting quantum systems. By projecting all interactions onto a symmetric subset of the system, the method effectively reduces the number of sites, thus providing an exponential speedup over standard exact diagonalization. Furthermore, we introduce two extensions that broaden the applicability of the method and allow for a controlled trade-off between computational cost and accuracy.

cond-mat.str-el↗

arXiv2025

Thermodynamics of analogue black holes in a non-Hermitian tight-binding model

We present a non-Hermitian model with gain/loss and non-reciprocal next-nearest-neighbor hopping that emulates black-hole physics. The model describes a one-dimensional lattice with a smooth connection between regions with distinct hopping parameters. By mapping the system to an effective Schwarzschild metric in the Painlev\'e-Gullstrand coordinates, we find that the interface is analogue to a black-hole event horizon. We obtain emission rates for particles and antiparticles, the Hawking temperature, the Bekenstein-Hawking entropy, and the mass of the analogue black hole as a function of the interface sharpness and the system parameters. An experimental realization of the theoretical model is proposed, thus opening the way to the detection of elusive black-hole features.

cond-mat.mes-hall↗

arXiv2025

Emergence of Imaginary Time Crystals in the non-Hermitian Su-Schrieffer-Heeger model

Parity-time symmetry constrains the spectrum of non-Hermitian systems to be either real or come in complex conjugate pairs. The transition between a symmetry-preserving phase with real energies and a symmetry-broken phase with complex energies is marked by exceptional points, one of the hallmarks of non-Hermitian systems. Because of these properties, these systems are widely studied, both theoretically and experimentally. In this work, we investigate the thermodynamic properties of the gain and loss Su-Schrieffer-Heeger model for both bosons and fermions, and establish the existence of an imaginary time crystal phase, an imaginary time analogue of a time crystal. This phase occurs when there is a resonance condition between the Matsubara frequencies and the spectrum of the system, making the Green's function of the system oscillate in imaginary time with the Matsubara frequency. We show that this phase appears in the symmetry-broken region. In particular, the topological edge states of this system exhibit oscillations that are present for bosons. Finally, we discuss the applicability of our results for experiments. We examine signatures of these phases in terms of correlation functions in real time and oscillations in thermodynamic potential in inverse temperature $\beta$, and explore possible experimental platforms to realize this system.

quant-ph↗

arXiv2024

Fractality-induced Topology

Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral reduction to effectively simplify complex fractal structures, revealing the presence of topologically protected boundary and corner states. Our approach demonstrates that fractals can support topological phases, even in the absence of traditional driving mechanisms such as magnetic fields or spin-orbit coupling. The isospectral reduction not only elucidates the underlying topological features but also makes this framework broadly applicable to a variety of fractal systems. Furthermore, our findings suggest that these topological phases may naturally occur in materials with fractal structures found in nature. This work opens new avenues for designing fractal-based topological materials, advancing both theoretical understanding and experimental exploration of topology in complex, self-similar geometries.

cond-mat.mes-hall↗

arXiv2024

Topological phases of the interacting Su-Schrieffer-Heeger model: An analytical study

The interacting SSH model provides an ideal ground to study the interplay between topologically insulating phases and electron-electron interactions. We study the polarization density as a topological invariant and provide an analytic treatment of its behavior in the low-energy sector of the one-dimensional interacting SSH model. By formulating the topological invariant in terms of Green's functions, we use the low-energy field theory of the Thirring model to derive the behavior of the polarization density. We show that the polarization density in the continuum theory describes the usual topological insulating phases. Still, it contains an extra factor from the fields' scaling dimensions in the low-energy quantum field theory. We interpret this as a measure of the modified charge of the new excitations in the system. We find two distinct contributions: a renormalization of the electronic charge $e$ of a Fermi liquid because of quasiparticle smearing and an additional contribution coming from the topological charge of the soliton arising in the bosonized version of the Thirring model, the sine-Gordon model.

cond-mat.str-el↗

arXiv2024

Thermodynamics and entanglement entropy of the non-Hermitian SSH model

Topological phase transitions are found in a variety of systems and were shown to be deeply related with a thermodynamic description through scaling relations. Here, we investigate the entanglement entropy, which is a quantity that captures the central charge of a critical model and the thermodynamics of the non-reciprocal Su-Schrieffer-Heeger (SSH) model. Although this model has been widely studied, the thermodynamic properties reveal interesting physics not explored so far. In order to analyze the boundary effects of the model, we use Hill's thermodynamics to split the grand potential in two contributions: the extensive one, related to the bulk, and the subdivision one, related to the boundaries. Then, we derive the thermodynamic entropy for both, the edges and the bulk and the heat capacity for the bulk at the topological phase transitions. The latter is related to the central charge when the underlying theory is a conformal field theory, whereas the first reveals the resilience of the topological edge states to finite temperatures. The phase transition between phases that are adiabatically connected with the Hermitian SSH model display the well-known behaviour of systems within the Dirac universality class, but the transition between phases with complex energies shows an unexpected critical behavior, which signals the emergence of an imaginary time crystal.

quant-ph↗

arXiv2024

Quantum metric of non-Hermitian Su-Schrieffer-Heeger systems

Topological insulators have been studied intensively over the last decades. Earlier research focused on Hermitian Hamiltonians, but recently, peculiar and interesting properties were found by introducing non-Hermiticity. In this work, we apply a quantum geometric approach to various Hermitian and non-Hermitian versions of the Su-Schrieffer-Heeger (SSH) model. We find that this method allows one to correctly identify different topological phases and topological phase transitions for all SSH models, but only when using the metric tensor containing both left and right eigenvectors. Whereas the quantum geometry of Hermitian systems is Riemannian, introducing non-Hermiticity leads to pseudo-Riemannian and complex geometries, thus significantly generalizing from the quantum geometries studied thus far. One remarkable example of this is the mathematical agreement between topological phase transition curves and lightlike paths in general relativity, suggesting a possibility of simulating space-times in non-Hermitian systems. We find that the metric in non-Hermitian phases degenerates in such a way that it effectively reduces the dimensionality of the quantum geometry by one. This implies that within linear response theory, one can perturb the system by a particular change of parameters while maintaining a zero excitation rate.

cond-mat.stat-mech↗

arXiv2024

Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides

Symmetry is one of the cornerstones of modern physics and has profound implications in different areas. In symmetry-protected topological systems, symmetries are responsible for protecting surface states, which are at the heart of the fascinating properties exhibited by these materials. When the symmetry protecting the edge mode is broken, the topological phase becomes trivial. By engineering losses that break the symmetry protecting a topological Hermitian phase, we show that a new genuinely non-Hermitian symmetry emerges, which protects and selects one of the boundary modes: the topological monomode. Moreover, the topology of the non-Hermitian system can be characterized by an effective Hermitian Hamiltonian in a higher dimension. To corroborate the theory, we experimentally investigated the non-Hermitian 1D and 2D SSH models using photonic lattices and observed dynamically generated monomodes in both cases. We classify the systems in terms of the (non-Hermitian) symmetries that are present and calculate the corresponding topological invariants.

cond-mat.mes-hall↗

arXiv2024

Higher-order topology protected by latent crystalline symmetries

We demonstrate that rotation symmetry is not a necessary requirement for the existence of fractional corner charges in Cn-symmetric higher-order topological crystalline insulators. Instead, it is sufficient to have a latent rotation symmetry, which may be revealed upon performing an isospectral reduction on the system. We introduce the concept of a filling anomaly for latent crystalline symmetric systems, and propose modified topological invariants. The notion of higher-order topology in two dimensions protected by Cn symmetry is thus generalized to a protection by latent symmetry. Our claims are corroborated by concrete examples of models that show non-trivial corner charge in the absence of Cn-symmetry. This work extends the classification of topological crystalline insulators to include latent symmetries.

cond-mat.mes-hall↗

arXiv2024

Anomalous Polarization in One-dimensional Aperiodic Insulators

By implementing a charge pumping scheme for one-dimensional aperiodic chains, we confirm the existence of topological phases in these systems whenever their finite-size realizations admit inversion symmetry. These phases are usually characterized by an anomalous edge response as a result of the bulk-boundary correspondence. We show that these signatures are all present in various chains, each representing a different class of structural aperiodicity: the Fibonacci quasicrystal, the Tribonacci quasicrystal, and the Thue-Morse chain. More specifically, we calculate three quantities: the Berry phase of the crystalline approximation of the finite-size systems, the polarization response to an inifintesimal static and constant electric field in systems with open boundary conditions, and the degeneracy of the entanglement spectrum. We find that all of them provide signatures of a topologically nontrivial phase.

cond-mat.dis-nn↗

arXiv2023

Compact localized boundary states in a quasi-1D electronic diamond-necklace chain

Zero-energy modes localized at the ends of one-dimensional (1D) wires hold great potential as qubits for fault-tolerant quantum computing. However, all the candidates known to date exhibit a wave function that decays exponentially into the bulk and hybridizes with other nearby zero-modes, thus hampering their use for braiding operations. Here, we show that a quasi-1D diamond-necklace chain exhibits a completely unforeseen type of robust boundary state, namely compact localized zero-energy modes that do not decay into the bulk. We theoretically engineer a lattice geometry to access this mode, and experimentally realize it in an electronic quantum simulator setup. Our work provides a general route for the realization of robust and compact localized zero-energy modes that could potentially be braided without the drawbacks of hybridization.

cond-mat.mes-hall↗

arXiv2023

Topological edge and corner states in Bi fractals on InSb

Topological materials hosting metallic edges characterized by integer quantized conductivity in an insulating bulk have revolutionized our understanding of transport in matter. The topological protection of these edge states is based on symmetries and dimensionality. However, only integer-dimensional models have been classified, and the interplay of topology and fractals, which may have a non-integer dimension, remained largely unexplored. Quantum fractals have recently been engineered in metamaterials, but up to present no topological states were unveiled in fractals realized in real materials. Here, we show theoretically and experimentally that topological edge and corner modes arise in fractals formed upon depositing thin layers of bismuth on an indium antimonide substrate. Scanning tunneling microscopy reveals the appearance of (nearly) zero-energy modes at the corners of Sierpi\'nski triangles, as well as the formation of outer and inner edge modes at higher energies. Unexpectedly, a robust and sharp depleted mode appears at the outer and inner edges of the samples at negative bias voltages. The experimental findings are corroborated by theoretical calculations in the framework of a continuum muffin-tin and a lattice tight-binding model. The stability of the topological features to the introduction of a Rashba spin-orbit coupling and disorder is discussed. This work opens the perspective to novel electronics in real materials at non-integer dimensions with robust and protected topological states.

cond-mat.mes-hall↗

arXiv2022

Non-Hermitian quantum gases: a platform for imaginary time crystals

One of the most important applications of quantum mechanics is the thermodynamic description of quantum gases. Despite the fundamental importance of this topic, a comprehensive description of the thermodynamic properties of non-Hermitian quantum gases is still lacking. Here, we investigate the properties of bosonic and fermionic non-Hermitian systems at finite temperatures. We show that non-Hermitian systems exihibit oscillations both in temperature and imaginary time. As such, they can be a possible platform to realize an imaginary time crystal (iTC) phase. The Hatano-Nelson model is identified as a simple lattice model to reveal this effect. In addition, we show that the conditions for the iTC to be manifest are the same as the conditions for the presence of disorder points, where the correlation functions show oscillating behavior. This analysis makes clear that our realization of iTC is effectively a way to filter one specific Matsubara mode. In this realization, the Matsubara frequency, that enters as a mathematical tool to compute correlation functions for finite temperatures, can be measured experimentally.

cond-mat.quant-gas↗

arXiv2022

Corner modes of the breathing kagome lattice: origin and robustness

We study the non-trivial phase of the two-dimensional breathing kagome lattice, displaying both edge and corner modes. The corner localized modes of a two-dimensional flake were initially identified as a signature of a higher-order topological phase but later shown to be trivial for perturbations that were thought to protect them. Using various theoretical and simulation techniques, we confirm that it does not display higher-order topology: the corner modes are of trivial nature. Nevertheless, they might be protected. First, we show a set of perturbations within a tight-binding model that can move the corner modes away from zero energy, also repeat some perturbations that were used to show that the modes are trivial. In addition, we analyze the protection of the corner modes in more detail and find that only perturbations respecting the sublattice or generalized chiral and crystalline symmetries, and the lattice connectivity, pin the corner modes to zero energy robustly. A destructive interference model corroborates the results. Finally, we analyze a muffin-tin model for the bulk breathing kagome lattice. Using topological and symmetry markers, such as Wilson loops and Topological Quantum Chemistry, we identify the two breathing phases as adiabatically disconnected different obstructed atomic limits.

cond-mat.mes-hall↗

arXiv2021

Spin-orbit gaps in the s and p orbital bands of an artificial honeycomb lattice

Muffin-tin methods have been instrumental in the design of honeycomb lattices that show, in contrast to graphene, separated s and in-plane p bands, a p orbital Dirac cone, and a p orbital flat band. Recently, such lattices have been experimentally realized using the 2D electron gas on Cu(111). A possible next avenue is the introduction of spin-orbit coupling to these systems. Intrinsic spin-orbit coupling is believed to open topological gaps, and create a topological flat band. Although Rashba coupling is straightforwardly incorporated in the muffin-tin approximation, intrinsic spin-orbit coupling has only been included either for a very specific periodic system, or only close to the Dirac point. Here, we introduce general intrinsic and Rashba spin-orbit terms in the Hamiltonian for both periodic and finite-size systems. We observe a strong band opening over the entire Brillouin zone between the p orbital flat band and Dirac cone hosting a pronounced edge state, robust against the effects of Rashba spin-orbit coupling.

cond-mat.mes-hall↗

arXiv2021

Design and characterization of electronic fractals

The dimensionality of an electronic quantum system is decisive for its properties. In 1D electrons form a Luttinger liquid and in 2D they exhibit the quantum Hall effect. However, very little is known about the behavior of electrons in non-integer, i.e. fractional dimensions. Here, we show how arrays of artificial atoms can be defined by controlled positioning of CO molecules on a Cu(111) surface, and how these sites couple to form electronic Sierpinski fractals. We characterize the electron wavefunctions at different energies with scanning tunneling microscopy and spectroscopy and show that they inherit the fractional dimension. Wavefunctions delocalized over the Sierpinski structure decompose into self-similar parts at higher energy, and this scale invariance can also be retrieved in reciprocal space. Our results show that electronic quantum fractals can be man-made by atomic manipulation in a scanning tunneling microscope. The same methodology will allow to address fundamental questions on the effects of spin-orbit interaction and a magnetic field on electrons in non-integer dimensions. Moreover, the rational concept of artificial atoms can readily be transferred to planar semiconductor electronics, allowing for the exploration of electrons in a well-defined fractal geometry, including interactions and external fields.

cond-mat.mes-hall↗

arXiv2020

Unconventional scaling at non-Hermitian critical points

Critical phase transitions contain a variety of deep and universal physics, and are intimately tied to thermodynamic quantities through scaling relations. Yet, these notions are challenged in the context of non-Hermiticity, where spatial or temporal divergences render the thermodynamic limit ill-defined. In this work, we show that a thermodynamic grand potential can still be defined in pseudo-Hermitian Hamiltonians, and can be used to characterize aspects of criticality unique to non-Hermitian systems. Using the non-Hermitian Su-Schrieffer-Heeger (SSH) model as a paradigmatic example, we demonstrate the fractional order of topological phase transitions in the complex energy plane. These fractional orders add up to the integer order expected of a Hermitian phase transition when the model is doubled and Hermitianized. More spectacularly, gap preserving highly degenerate critical points known as non-Bloch band collapses possess fractional order that are not constrained by conventional scaling relations, testimony to the emergent extra length scale from the skin mode accumulation. Our work showcases that a thermodynamic approach can prove fruitful in revealing unconventional properties of non-Hermitian critical points.

cond-mat.stat-mech↗

arXiv2020

Critical Behavior of Topological Kondo Insulators

A thermodynamic study of the Kondo insulator SmB$_6$ is pursued to elucidate the well-known anomalous low-temperature electronic-like specific heat contribution conjectured to arise from metallic surface states. A general thermodynamic description of topological Kondo insulators is developed using a mean-field slave-boson approximation and an approach inspired by Hill thermodynamics to study the phase transitions with the critical exponents of the model. The results show consistency with the Josephson hyper-scaling relation. We further apply this framework to SmB$_6$. By separating the bulk and boundary contributions to the heat capacity, we show that while the surface states contribute to an increase of the heat capacity upon lowering the temperature, the effect is immeasurably small. This suggests that an alternate explanation is required for the anomalous low-temperature contributions to the specific heat in this material.

cond-mat.str-el↗