arXiv subjects

Pedro Ribeiro

Publications and source records attributed to Pedro Ribeiro.

At least 109 records · Page 6Linked to original sources

arXiv2020

Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos

We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and next-to-nearest neighbor spacings. We show that this quantity can successfully detect the chaotic or regular nature of complex-valued spectra. This is done in two steps. First, we show that, if eigenvalues are uncorrelated, the distribution of complex spacing ratios is flat within the unit circle, whereas random matrices show a strong angular dependence in addition to the usual level repulsion. The universal fluctuations of Gaussian Unitary and Ginibre Unitary universality classes in the large-matrix-size limit are shown to be well described by Wigner-like surmises for small-size matrices with eigenvalues on the circle and on the two-torus, respectively. To study the latter case, we introduce the Toric Unitary Ensemble, characterized by a flat joint eigenvalue distribution on the two-torus. Second, we study different physical situations where nonhermitian matrices arise: dissipative quantum systems described by a Lindbladian, non-unitary quantum dynamics described by nonhermitian Hamiltonians, and classical stochastic processes. We show that known integrable models have a flat distribution of complex spacing ratios whereas generic cases, expected to be chaotic, conform to Random Matrix Theory predictions. Specifically, we were able to clearly distinguish chaotic from integrable dynamics in boundary-driven dissipative spin-chain Liouvillians and in the classical asymmetric simple exclusion process and to differentiate localized from delocalized phases in a nonhermitian disordered many-body system.

cond-mat.stat-mech↗

arXiv2020

Spectral and Steady-State Properties of Random Liouvillians

We study generic open quantum systems with Markovian dissipation, focusing on a class of stochastic Liouvillian operators of Lindblad form with independent random dissipation channels (jump operators) and a random Hamiltonian. We establish that the global spectral features, the spectral gap, and the steady-state properties follow three different regimes as a function of the dissipation strength, whose boundaries depend on the particular quantity. Within each regime, we determine the scaling exponents with the dissipation strength and system size. We find that, for two or more dissipation channels, the spectral gap increases with the system size. The spectral distribution of the steady state is Poissonian at low dissipation strength and conforms to that of a random matrix once the dissipation is sufficiently strong. Our results can help to understand the long-time dynamics and steady-state properties of generic dissipative systems.

quant-ph↗

arXiv2019

A Survey on Subgraph Counting: Concepts, Algorithms and Applications to Network Motifs and Graphlets

Computing subgraph frequencies is a fundamental task that lies at the core of several network analysis methodologies, such as network motifs and graphlet-based metrics, which have been widely used to categorize and compare networks from multiple domains. Counting subgraphs is however computationally very expensive and there has been a large body of work on efficient algorithms and strategies to make subgraph counting feasible for larger subgraphs and networks. This survey aims precisely to provide a comprehensive overview of the existing methods for subgraph counting. Our main contribution is a general and structured review of existing algorithms, classifying them on a set of key characteristics, highlighting their main similarities and differences. We identify and describe the main conceptual approaches, giving insight on their advantages and limitations, and provide pointers to existing implementations. We initially focus on exact sequential algorithms, but we also do a thorough survey on approximate methodologies (with a trade-off between accuracy and execution time) and parallel strategies (that need to deal with an unbalanced search space).

cs.DS↗

arXiv2019

Disorder driven multifractality transition in Weyl nodal loops

The effect of short-range disorder in nodal line semimetals is studied by numerically exact means. For arbitrary small disorder, a novel semimetallic phase is unveiled for which the momentum-space amplitude of the ground-state wave function is concentrated around the nodal line and follows a multifractal distribution. At a critical disorder strength, a semimetal to compressible metal transition occurs, coinciding with a multi- to single-fractality transition. The universality class of this critical point is characterized by the correlation length and dynamical exponents. At considerably higher disorder, an Anderson metal-insulator transition takes place. Our results show that the nature of the semimetallic phase in non-clean samples is fundamentally different from a clean nodal semimetal.

cond-mat.dis-nn↗

arXiv2019

Priorities in tock-CSP

The $tock$-CSP encoding embeds a rich and flexible approach to modelling discrete timed behaviours in CSP where the event $tock$ is interpreted to mark the passage of time. The model checker FDR provides tailored support for $tock$-CSP, including a prioritisation operator that has typically been used to ensure maximal progress, where time only advances after internal activity has stabilised. Prioritisation may also be used on its own right as a modelling construct. Its operational semantics, however, is only congruent over the most discriminating semantic model of CSP: the finite-linear model. To enable sound and compositional reasoning in a $tock$-CSP setting, we calculate a denotational definition for prioritisation. For that we establish a Galois connection between a specialisation of the finite-linear model, with $tock$ and $\checkmark$, that signals termination, as special events, and $\checkmark$-$tock$-CSP, a model for $tock$-CSP that captures termination, deadlines, and is adequate for reasoning about timed refinement. Our results are mechanised using Isabelle/HOL.

cs.LO↗

arXiv2019

Classical and quantum liquids induced by quantum fluctuations

Geometrically frustrated interactions may render classical ground-states macroscopically degenerate. The connection between classical and quantum liquids and how the degeneracy is affected by quantum fluctuations is, however, less well understood. We study a simple model of coupled quantum and classical degrees of freedom, the so-called Falicov-Kimball model, on a triangular lattice and away from half-filling. For weak interactions the phase diagram features a charge disordered state down to zero temperature. We provide compelling evidence that this phase is a liquid and show that it is divided by a crossover line that terminates in a quantum critical point. Our results offer a new vantage point to address how quantum liquids can emerge from their classical counterparts.

cond-mat.str-el↗

arXiv2019

Many-body quantum dynamics of initially trapped systems due to a Stark potential --- thermalization vs. Bloch oscillations

We analyze the dynamics of an initially trapped cloud of interacting quantum particles on a lattice under a linear (Stark) potential. We reveal a dichotomy: initially trapped interacting systems possess features typical of both many-body-localized and self-thermalizing systems. We consider both fermions ($t$-$V$ model) and bosons (Bose-Hubbard model). For the zero and infinite interaction limits, both systems are integrable: we provide analytic solutions in terms of the moments of the initial cloud shape, and clarify how the recurrent dynamics (many-body Bloch oscillations) depends on the initial state. Away from the integrable points, we identify and explain the time scale at which Bloch oscillations decohere.

cond-mat.quant-gas↗

arXiv2019

Spin transfer torque induced paramagnetic resonance

We show how the spin-transfer torque generated by an ac voltage may be used to excite a paramagnetic resonance of an atomic spin deposited on a metallic surface. This mechanism is independent of the environment of the atom and may explain the ubiquity of the paramagnetic resonance reported by Baumann $\textit{et al.}$ [$\href{http://dx.doi.org/10.1126/science.aac8703}{Science \textbf{350}, 417 (2015)}$]. The current and spin dynamics are modeled by a time-dependent Redfield master equation generalized to account for the periodic driven voltage. Our approach shows that the resonance effect is a consequence of the nonlinearity of the coupling between the magnetic moment and the spin-polarized current which generates a large second-harmonic amplitude that can be measured in the current signal.

cond-mat.mes-hall↗

arXiv2018

Transmission across a bilayer graphene region

The transmission across a graphene bilayer region is calculated for two different types of connections to monolayer leads. A transfer matrix algorithm based on a tight binding model is developed to obtain the ballistic transmission beyond linear response. The two configurations are found to behave similarly when no gate voltage is applied. For a finite gate voltage, both develop a conductance gap characteristic of a biased bilayer, but only one shows a pronounced conductance step at the gap edge. A gate voltage domain wall applied to the bilayer region renders the conductance of the two configurations similar. For a microstructure consisting of equally spaced domain walls, we find a high sensitivity to the domain size. This is attributed to the presence of topologically protected in-gap states localized at domain walls, which hybridize as the domain size becomes of the order of their confining scale. Our results show that transmission through a bilayer region can be manipulated by a gate voltage in ways not previously anticipated.

cond-mat.mes-hall↗

arXiv2018

Dirac points merging and wandering in a model Chern insulator

We present a model for a Chern insulator on the square lattice with complex first and second neighbor hoppings and a sublattice potential which displays an unexpectedly rich physics. Similarly to the celebrated Haldane model, the proposed Chern insulator has two topologically non-trivial phases with Chern numbers $\pm1$. As a distinctive feature of the present model, phase transitions are associated to Dirac points that can move, merge and split in momentum space, at odds with Haldane's Chern insulator where Dirac points are bound to the corners of the hexagonal Brillouin zone. Additionally, the obtained phase diagram reveals a peculiar phase transition line between two distinct topological phases, in contrast to the Haldane model where such transition is reduced to a point with zero sublattice potential. The model is amenable to be simulated in optical lattices, facilitating the study of phase transitions between two distinct topological phases and the experimental analysis of Dirac points merging and wandering.

cond-mat.mes-hall↗

arXiv2018

GoT-WAVE: Temporal network alignment using graphlet-orbit transitions

Global pairwise network alignment (GPNA) aims to find a one-to-one node mapping between two networks that identifies conserved network regions. GPNA algorithms optimize node conservation (NC) and edge conservation (EC). NC quantifies topological similarity between nodes. Graphlet-based degree vectors (GDVs) are a state-of-the-art topological NC measure. Dynamic GDVs (DGDVs) were used as a dynamic NC measure within the first-ever algorithms for GPNA of temporal networks: DynaMAGNA++ and DynaWAVE. The latter is superior for larger networks. We recently developed a different graphlet-based measure of temporal node similarity, graphlet-orbit transitions (GoTs). Here, we use GoTs instead of DGDVs as a new dynamic NC measure within DynaWAVE, resulting in a new approach, GoT-WAVE. On synthetic networks, GoT-WAVE improves DynaWAVE's accuracy by 25% and speed by 64%. On real networks, when optimizing only dynamic NC, each method is superior ~50% of the time. While DynaWAVE benefits more from also optimizing dynamic EC, only GoT-WAVE can support directed edges. Hence, GoT-WAVE is a promising new temporal GPNA algorithm, which efficiently optimizes dynamic NC. Future work on better incorporating dynamic EC may yield further improvements.

cs.LG↗

arXiv2018

Temperature-driven gapless topological insulator

We investigate the phase diagram of the Haldane-Falicov-Kimball model -- a model combining topology, interactions and spontaneous disorder at finite temperatures. Using an unbiased numerical method, we map out the phase diagram on the interaction--temperature plane. Along with known phases, we unveil an \textit{insulating charge ordered state with gapless excitations }and a temperature-driven \textit{gapless topological insulating} phase. Intrinsic -- temperature generated -- disorder, is the key ingredient explaining the unexpected behavior. Our findings support the possibility of having temperature-driven topological phase transitions into gapped and gapless topological insulating phases in systems with a large mass unbalance in fermionic species.

cond-mat.str-el↗

arXiv2018

The Haldane model under quenched disorder

We study the half-filled Haldane model with Anderson and binary disorder and determine its phase diagram, as a function of the Haldane flux and staggered sub-lattice potential, for increasing disorder strength. We establish that disorder stabilizes topologically nontrivial phases in regions of the phase diagram where the clean limit is topologically trivial. At small disorder strength, our results agree with analytical predictions obtained using a first order self-consistent Born approximation, and extend to the intermediate and large disorder values where this perturbative approach fails. We further characterize the phases according to their gapless or gapped nature by determining the spectral weight at the Fermi level. We find that gapless topological nontrivial phases are supported for both Anderson and binary disorder. In the binary case, we find a reentrant topological phase where, starting from a trivial region, a topological transition occurs for increasing staggered potential $η$, followed by a second topological transition to the trivial phase for higher values of $η$.

cond-mat.str-el↗

arXiv2018

Integrable quantum dynamics of open collective spin models

We consider a collective quantum spin-$s$ in contact with Markovian spin-polarized baths. Using a conserved super-operator charge, a differential representation of the Liouvillian is constructed to find its exact spectrum and eigen-modes. We study the spectral properties of the model in the large-$s$ limit using a semi-classical quantization condition and show that the spectral density may diverge along certain curves in the complex plane. We exploit our exact solution to characterize steady-state properties, in particular at the discontinuous phase transition that arises for unpolarized environments, and to determine the decay rates of coherences and populations. Our approach provides a systematic way of finding integrable Liouvillian operators with non-trivial steady-states as well as a way to study their spectral properties and eigen-modes.

quant-ph↗

arXiv2018

Symmetry Breaking and Lattice Kirigami

In this work we consider an interacting quantum field theory on a curved two-dimensional manifold that we construct by geometrically deforming a flat hexagonal lattice by the insertion of a defect. Depending on how the deformation is done, the resulting geometry acquires a locally non-vanishing curvature that can be either positive or negative. Fields propagating on this background are forced to satisfy boundary conditions modulated by the geometry and that can be assimilated by a non-dynamical gauge field. We present an explicit example where curvature and boundary conditions compete in altering the way symmetry breaking takes place, resulting in a surprising behaviour of the order parameter in the vicinity of the defect. The effect described here is expected to be generic and of relevance in a variety of situations.

hep-th↗

arXiv2017

Relaxation and decoherence of qubits encoded in collective states of engineered magnetic structures

The quantum nature of a microscopic system can only be revealed when it is sufficiently decoupled from surroundings. Interactions with the environment induce relaxation and decoherence that turn the quantum state into a classical mixture. Here, we study the timescales of these processes for a qubit encoded in the collective state of a set of magnetic atoms deposited on a metallic surface. For that, we provide a generalization of the commonly used definitions of $T_{1}$ and $T_{2}$ characterizing relaxation and decoherence rates. We calculate these quantities for several atomic structures, including a collective spin, a setup implementing a decoherence-free subspace, and two examples of spin chains. Our work contributes to the comprehensive understanding of the relaxation and decoherence processes and shows the advantages of the implementation of a decoherence free subspace in these setups.

cond-mat.mes-hall↗

arXiv2017

Temporal Network Comparison using Graphlet-orbit Transitions

Networks are widely used to model real-world systems and uncover their topological features. Network properties such as the degree distribution and shortest path length have been computed in numerous real-world networks, and most of them have been shown to be both scale-free and small-world networks. Graphlets and network motifs are subgraph patterns that capture richer structural information than aforementioned global network properties, and these local features are often used for network comparison. However, past work on graphlets and network motifs is almost exclusively applicable only for static networks. Many systems are better represented as temporal networks which depict not only how a system was at a given stage but also how they evolved. Time-dependent information is crucial in temporal networks and, by disregarding that data, static methods can not achieve the best possible results. This paper introduces an extension of graphlets for temporal networks. Our proposed method enumerates all 4-node graphlet-orbits in each network-snapshot, building the corresponding orbit-transition matrix in the process. Our hypothesis is that networks representing similar systems have characteristic orbit transitions which better identify them than simple static patterns, and this is assessed on a set of real temporal networks split into categories. In order to perform temporal network comparison we put forward an orbit-transition-agreement metric (OTA). OTA correctly groups a set of temporal networks that both static network motifs and graphlets fail to do so adequately. Furthermore, our method produces interpretable results which we use to uncover characteristic orbit transitions, and that can be regarded as a network-fingerprint.

cs.SI↗

arXiv2017

Post-quench dynamics and suppression of thermalization in an open half-filled Hubbard layer

We study the time evolution of a half-filled Hubbard layer coupled to a magnon bath after a quench of the Hubbard interaction. Qualitatively different regimes, regarding the asymptotic long-time dynamics, are identified and characterized within the mean-field approximation. In the absence of the bath, the dynamics of the closed system is similar to that of a quenched BCS condensate. Though the presence of the bath introduces an additional relaxation mechanism, our numerical results and analytical arguments show that equilibration with the bath is not necessarily attained within the approximations used. Instead, nonequilibrium states, similar to the ones observed in the closed system, can emerge at long times as a consequence of the competition between the intrinsic relaxation mechanism (Landau damping, for example), and the bath-induced dissipation.

cond-mat.str-el↗