arXiv subjects

Ilias Amanatidis

Publications and source records attributed to Ilias Amanatidis.

At least 19 recordsLinked to original sources

arXiv2026

Mass generation in graphs

We demonstrate a mechanism for the production of massive excitations in graphs. We treat the number of neighbors at each vertex in the graph (degree) as a scalar field. Then we introduce a mechanism inspired by the Higgs mechanism in quantum field theory(QFT), that couples the degree field to a vector-like field, introduced via the graph edges, represented mathematically by the incident matrices of the graph. The coupling between the two fields produces a massless ground state and massive excitations, separated by a mass gap. The excitations can be treated as emergent massive particles, propagating inside the graph. We study how the size of the graph and its density, represented by the ratio of edges over vertices, affects the mass gap and the localization properties of the massive excitations. We show that the most massive excitations, corresponding to the heaviest emergent particles, localize on regions of the graph with high density, consisting of vertices with a large degree. On the other hand, the least massive excitations, corresponding to the lightest emergent particles localize on a few vertices but with a smaller degree. Excitations with intermediate masses are less localized, spreading on more vertices instead. Our study shows that emergence of matter-like structures with various mass properties, is possible in discrete physical models, relying only on a few fundamental properties like the connectivity of the models.

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arXiv2025

The principle of least action for random graphs

We study the statistical properties of the physical action $S$ for random graphs, by treating the number of neighbors at each vertex of the graph (degree), as a scalar field. For each configuration (run) of the graph we calculate the Lagrangian of the degree field by using a lattice quantum field theory(LQFT) approach. Then the corresponding action is calculated by integrating the Lagrangian over all the vertices of the graph. We implement an evolution mechanism for the graph by removing one edge per a fundamental quantum of time, resulting in different evolution paths based on the run that is chosen at each evolution step. We calculate the action along each of these evolution paths, which allows us to calculate the probability distribution of $S$. We find that the distribution approaches the normal(Gaussian) form as the graph becomes denser, by adding more edges between its vertices. The maximum of the probability distribution of the action corresponds to graph configurations whose spacing between the values of $S$ becomes zero $ΔS=0$, corresponding to the least-action (Hamilton) principle, which gives the path that the physical system follows classically. In addition, we calculate the fluctuations(variance) of the degree field showing that the graph configurations corresponding to the maximum probability of $S$, which follow the Hamilton's principle, have a balanced structure between regular and irregular graphs.

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arXiv2024

Quantum chaos, localization and phase transitions in random graphs

The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum chaotic and localized phases and transitions between them. Essentially the random geometry acts as disorder, whose strength is characterized by the ratio of edges over vertices R in the graphs. For dense graphs, with large ratio R, the spacing between successive energy levels follows the Wigner-Dyson distribution, leading to a quantum chaotic behavior and a metallic phase, characterized by level repulsion. For ratios near R=0.5, where a large dominating component in the graph appears, the level spacing follows the Poisson distribution with level crossings and a localized phase for the respective wavefunctions lying on the graph. For intermediate ratios R we observe a phase transition between the quantum chaotic and localized phases characterized by a semi-Poisson distribution. The values R of the critical regime where the phase transition occurs depend on the energy of the system. Our analysis shows that physical systems with random geometry, for example ones with a fluctuating/dynamical spatial dimension, contain novel universal phase transition properties, similar to those occuring in more traditional phase transitions based on symmetry breaking mechanisms, whose universal properties are strongly determined by the dimensionality of the system.

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arXiv2024

Emergent spacetime from purely random structures

We examine the fundamental question whether a random discrete structure with the minimal number of restrictions can converge to continuous metric space. We study the geometrical properties such as the dimensionality and the curvature emerging out of the connectivity properties of uniform random graphs. In addition we introduce a simple evolution mechanism for the graph by removing one edge per a fundamental quantum of time from an initially complete graph. We show an exponential growth of the radius of the graph, that ends up in a random structure with emergent average spatial dimension $D=3$ and zero curvature $K=0$, resembling a flat 3D manifold, that could describe the observed space in our universe and some of its geometrical properties. In addition, we introduce a generalized action for graphs based on physical quantities on different subgraph structures that helps to recover the well known properties of spacetime as described in general relativity, like time dilation due to gravity. Also, we show how various quantum mechanical concepts such as generalized uncertainty principles based on the statistical fluctuations can emerge from random discrete models. Moreover, our approach leads to a unification of space and matter-energy, for which we propose a mass-energy-space equivalence that leads to a way to transform between empty space and matter-energy via the cosmological constant.

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arXiv2023

From quantum to classical via crystallization

We show that classical states can emerge as pure ground state solutions of a quantum many-body system. We use a simple Hubbard model in 1D with strong short-range interactions and a second nearest neighbor hopping with N particles arranged among M sites. We show that the ground state of this Hubbard chain for M=2N-1 consists of a single many-body state where the strongly interacting particles arrange in a classical state with crystalline order. The ground state is separated by an energy gap from the first excited state, and survives in the thermodynamic limit for large N. The energy gap increases linearly with the strength of the interaction between the particles making the classical ground state robust to external perturbations like disorder. Our result is an example of how a quantum system can converge to a classical state, like a crystal, without requiring decoherence, wavefunction collapse or other external mechanisms.

cond-mat.str-el↗

arXiv2023

Energetical self-organization of a few strongly interacting particles

We study the quantum self-organization of a few interacting particles with strong short-range interactions. The physical system is modeled via a 2D Hubbard square lattice model, with a nearest-neighbor interaction term of strength U and a second nearest-neighbor hopping t. For t=0 the energy of the system is determined by the number of bonds between particles that lie on adjacent sites in the Hubbard lattice. We find that this bond order persists for the ground and some of the excited states of the system, for strong interaction strength, at different fillings of the system. For our analysis we use the Euler characteristic of the network/graph grid structures formed by the particles in real space (Fock states), which helps to quantify the energetical(bond) ordering. We find multiple ground and excited states, with integer Euler numbers, whose values persist from the $t=0$ case, for strong interaction $U>>t$. The corresponding quantum phases for the ground state contain either density-wave-order(DWO) for low fillings, where the particles stay apart form each other, or clustering-order(CO) for high fillings, where the particles form various structures as they condense into clusters. In addition, we find various excited states containing superpositions of Fock states, whose probability amplitudes are self-tuned in a way that preserves the integer value of the Euler characteristic from the $t=0$ limit.

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arXiv2023

Violation of Bell's inequalities in uniform random graphs

We demonstrate that quantum correlations can emerge from the statistical correlations of random discrete models, without an a priori assumption that the random models are quantum mechanical in nature, that is without considering superpositions of the random structures. We investigate the correlations between the number of neighbors(degree) for pairs of vertices in Erdos-Renyi uniform random graphs. We use the joint probabilities for the appearance of degree numbers between the vertices in the pairs, in order to calculate the respective Bell's inequalities. We find that the inequalities are violated for sparse random graphs with ratio of edges over vertices $R<2$, signifying the emergence of quantum correlations for these random structures. The quantum correlations persist independently of the graph size or the geodesic distance between the correlated vertices. For $R>2$, as the graph becomes denser by adding more edges between its vertices, the Bell's inequalities are satisfied and the quantum correlations disappear. Relations to our previous works concerning the emergence of spacetime and its geometrical properties from uniform random graphs, are also briefly discussed.

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arXiv2022

Robust non-integer conductance in disordered 2D Dirac semimetals

We study the conductance $G$ of 2D Dirac semimetal nanowires at the presence of disorder. For an even nanowire length $L$ determined by the number of unit cells, we find non-integer values for $G$ that are independent of $L$ and persist with weak disorder, indicated by the vanishing fluctuations of $G$. The effect is created by a combination of the scattering effects at the contacts(interface) between the leads and the nanowire, an energy gap present in the nanowire for even $L$ and the topological properties of the 2D Dirac semimetals. Unlike conventional materials the reduced $G$ due to the scattering at the interface, is stabilized at non-integer values inside the nanowire, leading to a topological phase for weak disorder. For strong disorder the system leaves the topological phase and the fluctuations of $G$ are increased as the system undergoes a transition/crossover toward the Anderson localized(insulating) phase, via a non-standard disordered phase. We study the scaling and the statistics of $G$ at these phases. In addition we have found that the effect of robust non-integer $G$ disappears for odd $L$, which results in integer $G$, determined by the number of open channels in the nanowire, due to resonant scattering.

cond-mat.mes-hall↗

arXiv2022

Physics in non-fixed spatial dimensions via random networks

We study the quantum statistical electronic properties of random networks which inherently lack a fixed spatial dimension. We use tools like the density of states (DOS) and the inverse participation ratio(IPR) to uncover various phenomena, such as unconventional properties of the energy spectrum and persistent localized states(PLS) at various energies, corresponding to quantum phases with with zero-dimensional(0D) and one-dimensional(1D) order. For small ratio of edges over vertices in the network $RT$ we find properties resembling graphene/honeycomb lattices, like a similar DOS containing a linear dispersion relation at the band center at energy E=0. In addition we find PLS at various energies including E=-1,0,1 and others, for example related to the golden ratio. At E=0 the PLS lie at disconnected vertices, due to partial bipartite symmetries of the random networks (0D order). At E=-1,1 the PLS lie mostly at pairs of vertices(bonds), while the rest of the PLS at other energies, like the ones related to the golden ratio, lie at lines of vertices of fixed length(1D order), at the spatial boundary of the network, resembling the edge states in confined graphene systems with zig-zag edges. As the ratio $RT$ is increased the DOS of the network approaches the Wigner semi-circle, corresponding to random symmetric matrices(Hamiltonians) and the PLS are reduced and gradually disappear as the connectivity in the network increases. Finally we calculate the spatial dimension $D$ of the network and its fluctuations, obtaining both integer and non-integer values and examine its relation to the electronic properties derived. Our results imply that universal physics can manifest in physical systems irrespectively of their spatial dimension. Relations to emergent spacetime in quantum and emergent gravity approaches are also discussed.

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arXiv2021

Fractional-quantum-Hall-effect (FQHE) in 1D Hubbard models

We study the quantum self-organization of interacting particles in one-dimensional(1D) many-body systems, modeled via Hubbard chains with short-range interactions between the particles. We show the emergence of 1D states with density-wave and clustering order, related to topology, at odd denominator fillings that appear also in the fractional-quantum-Hall-effect (FQHE), which is a 2D electronic system with Coulomb interactions between the electrons and a perpendicular magnetic field. For our analysis we use an effective topological measure applied on the real space wavefunction of the system, the Euler characteristic describing the clustering of the interacting particles. The source of the observed effect is the spatial constraints imposed by the interaction between the particles. In overall, we demonstrate a simple mechanism to reproduce many of the effects appearing in the FQHE, without requiring a Coulomb interaction between the particles or the application of an external magnetic field.

cond-mat.str-el↗

arXiv2020

Self-organization in many-body systems with short-range interactions: clustering, correlations and topology

We investigate the self-organization of point-particles with short-range interactions modeled via simple 1D and 2D Hubbard-like models. We show how various properties emerge such as, boson-like ordering leading to topological structures in real space, via the clustering of the particles at discrete energy levels, which can be analyzed using a network/graph mathematical language. We calculate analytically the number of clusters, the correlations between them and topological numbers like the Euler characteristic, deriving different organizational schemes and entanglement entropy scaling laws. All calculations are performed for an arbitrary number of particles N and energy of the system E. Our results demonstrate how orders with diverse topological/geometric and entanglement features, emerge in strongly interacting many-body systems, that follow minimal microscopic interaction rules.

cond-mat.str-el↗

arXiv2020

Entanglement and edge effects in superpositions of many-body Fock states with spatial constraints

We investigate how entangled states can be created by considering collections of point-particles arranged at different spatial configurations, i.e., Fock states with spatial constraints. This type of states can be realized in Hubbard chains of spinless hard-core bosons, at different fillings, which have gapped energy spectrum with a highly degenerate ground state. We calculate the bipartite entanglement entropy for superpositions of such Fock states and show that their entanglement can be controlled via the spatial freedom of the particles, determined by the system filling. In addition we study the effect of confinement/boundary conditions on the Fock states and show that edge modes appear at the ends of the system, when open boundary conditions are considered. Our result is an example of entangled many-body states in 1D systems of strongly interacting particles, without requiring the spin, long-range microscopic interactions or external fields. Instead, the entanglement can be tuned by the empty space in the system, which determines the spatial freedom of the interacting particles.

cond-mat.str-el↗

arXiv2019

Topological self-organization of strongly interacting particles

We investigate the self-organization of strongly interacting particles confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice models with short-range interactions. We show that many-body states with topological features emerge at different energy bands separated by large gaps. The topology manifests in the way the particles organize in real space to form states with different energy. Each of these states contains topological defects/condensations whose Euler characteristic can be used as a topological number to categorize states belonging to the same energy band. We provide analytical formulas for this topological number and the full energy spectrum of the system for both sparsely and densely filled systems. Furthermore, we analyze the connection with the Gauss-Bonnet theorem of differential geometry, by using the curvature generated in real space by the particle structures. Our result is a demonstration of how states with topological characteristics, emerge in strongly interacting many-body systems following simple underlying rules, without considering the spin, long-range microscopic interactions, or external fields.

cond-mat.str-el↗

arXiv2019

Exact results for the entanglement in 1D Hubbard models with spatial constraints

We investigate the entanglement in Hubbard models of hardcore bosons in $1D$, with an additional hardcore interaction on nearest neighbouring sites. We derive analytical formulas for the bipartite entanglement entropy for any number of particles and system size, whose ratio determines the system filling. At the thermodynamic limit the entropy diverges logarithmically for all fillings, except for half-filling, with the universal prefactor $1/2$ due to partial permutational invariance. We show how maximal entanglement can be achieved by controlling the interaction range between the particles and the filling which determines the empty space in the system. Our results show how entangled quantum phases can be created and controlled, by imposing spatial constraints on states formed in many-body systems of strongly interacting particles.

cond-mat.str-el↗

arXiv2017

Coherent wave transmission in quasi-one-dimensional systems with Lévy disorder

We study the random fluctuations of the transmission in disordered quasi-one-dimensional systems such as disordered waveguides and/or quantum wires whose random configurations of disorder are characterized by density distributions with a long tail known as Lévy distributions. The presence of Lévy disorder leads to large fluctuations of the transmission and anomalous localization, in relation to the standard exponential localization (Anderson localization). We calculate the complete distribution of the transmission fluctuations for different number of transmission channels in the presence and absence of time-reversal symmetry. Significant differences in the transmission statistics between disordered systems with Anderson and anomalous localizations are revealed. The theoretical predictions are independently confirmed by tight binding numerical simulations.

cond-mat.dis-nn↗

arXiv2015

Geometrical spin manipulation in Dirac flakes

We investigate numerically the spin properties of electrons in flakes made of materials described by the Dirac equation, at the presence of intrinsic spin-orbit-coupling(SOC). We show that electrons flowing along the borders of flakes via edge states, become helically spin-polarized for strong SOC, for materials with and without a gap at the Fermi energy, corresponding to the massive and massless Dirac equation respectively. The helically spin-polarized electrons cause geometrical spin splitting on opposite sides of the flakes, leading to spin-resolved transport controlled by the flake's geometry in a multi-terminal device setup. A simple analytical model containing the basic ingredients of the problem is introduced to get an insight of the helical mechanism, along with our numerical results which are based on an effective tight-binding model.

cond-mat.mes-hall↗

arXiv2014

Edge states versus diffusion in disordered graphene flakes

We study the localization properties of the wavefunctions in graphene flakes with short range disorder, via the numerical calculation of the Inverse Participation Ratio($IPR$) and it scaling which provides the fractal dimension $D_{2}$. We show that the edge states which exist at the Dirac point of ballistic graphene (no disorder) with zig-zag edges survive in the presence of weak disorder with wavefunctions localized at the boundaries of the flakes. We argue, that there is a strong interplay between the underlying destructive interference mechanism of the honeycomb lattice of graphene leading to edge states and the diffusive interference mechanism introduced by the short-range disorder. This interplay results in a highly abnormal behavior, wavefunctions are becoming progressively less localized as the disorder is increased, indicated by the decrease of the average $\langle IPR\rangle$ and the increase of $D_{2}$. We verify, that this abnormal behavior is absent for graphene flakes with armchair edges which do not provide edge states.

cond-mat.mes-hall↗

arXiv2013

Conductance through disordered graphene nanoribbons: Standard and anomalous electron localization

Conductance fluctuations produced by the presence of disorder in zigzag and armchair graphene nanoribbons are studied. We show that quantum transport in zigzag nanoribbons takes place via edge states which are exponentially localized, as in the standard Anderson localization problem, whereas for armchair nanoribbons the symmetry of the graphene sublattices produces anomalous localization, or delocalization. We show that these two different electron localizations lead to significant differences of the conductance statistics between zigzag and armchair nanoribbons. In particular, armchair nanoribbons show nonconventional large conductance fluctuations relative to those of Anderson-localized electrons. We calculate analytically the complete distribution of conductances for both types of ribbons. Without free fitting parameters, we verify our theoretical results by performing numerical simulations of disordered zigzag and armchair nanoribbons of experimentally achievable lengths and widths.

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