arXiv subjects

Eduardo R. Mucciolo

Publications and source records attributed to Eduardo R. Mucciolo.

At least 37 records · Page 2Linked to original sources

arXiv2019

Localization properties of a two-channel 3D Anderson model

We study two coupled 3D lattices, one of them featuring uncorrelated on-site disorder and the other one being fully ordered, and analyze how the interlattice hopping affects the localization-delocalization transition of the former and how the latter responds to it. We find that moderate hopping pushes down the critical disorder strength for the disordered channel throughout the entire spectrum compared to the usual phase diagram for the 3D Anderson model. In that case, the ordered channel begins to feature an effective disorder also leading to the emergence of mobility edges but with higher associated critical disorder values. Both channels become pretty much alike as their hopping strength is further increased, as expected. We also consider the case of two disordered components and show that in the presence of certain correlations among the parameters of both lattices, one obtains a disorder-free channel decoupled from the rest of the system.

cond-mat.dis-nn↗

arXiv2019

Fast counting with tensor networks

We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.

cond-mat.stat-mech↗

arXiv2019

Obstacles to quantum annealing in a planar embedding of XORSAT

We introduce a planar embedding of the k-regular k-XORSAT problem, in which solutions are encoded in the ground state of a classical statistical mechanics model of reversible logic gates arranged on a square grid and acting on bits that represent the Boolean variables of the problem. The special feature of this embedding is that the resulting model lacks a finite-temperature phase transition, thus bypassing the first-order thermodynamic transition known to occur in the random graph representation of XORSAT. In spite of this attractive feature, the thermal relaxation into the ground state displays remarkably slow glassy behavior. The question addressed in this paper is whether this planar embedding can afford an efficient path to solution of k-regular k-XORSAT via quantum adiabatic annealing. We first show that our model bypasses an avoided level crossing and consequent exponentially small gap in the limit of small transverse fields. We then present quantum Monte Carlo results for our embedding of the k-regular k-XORSAT that strongly support a picture in which second-order and first-order transitions develop at a finite transverse field for k = 2 and k = 3, respectively. This translates into power-law and exponential dependences in the scaling of energy gaps with system size, corresponding to times-to-solution which are, respectively, polynomial and exponential in the number of variables. We conclude that neither classical nor quantum annealing can efficiently solve our reformulation of XORSAT, even though the original problem can be solved in polynomial time by Gaussian elimination.

cond-mat.stat-mech↗

arXiv2018

Ultra-slow dynamics in a translationally invariant spin model for multiplication and factorization

We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We prove that, for open boundary conditions, the model exhibits no finite-temperature phase transition. Yet we find that it displays glassy dynamics with astronomically slow relaxation times, numerically consistent with a double exponential dependence on the inverse temperature. The slowness of the dynamics arises due to errors that occur during thermal annealing that cost little energy but flip an extensive number of spins. We argue that the energy barrier that needs to be overcome in order to heal such defects scales linearly with the correlation length, which diverges exponentially with inverse temperature, thus yielding the double exponential behavior of the relaxation time.

cond-mat.stat-mech↗

arXiv2018

Tensor network method for reversible classical computation

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs/outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

cond-mat.stat-mech↗

arXiv2017

Spin relaxation in disordered graphene: Interplay between puddles and defect-induced magnetism

We study the spin relaxation in graphene due to magnetic moments induced by defects. We propose and employ in our studies a microscopic model that describes magnetic impurity scattering processes mediated by charge puddles. This model incorporates the spin texture related to the defect-induced state. We calibrate our model parameters using experimentally-inferred values. The results we obtain for the spin relaxation times are in very good agreement with experimental findings. Our study leads to a comprehensive explanation for the short spin relaxation times reported in the experimental literature. We also propose a new interpretation for the puzzling experimental observation of enhanced spin relaxation times in hydrogenated graphene samples in terms of a combined effect due to disorder configurations that lead to an increased coupling to the magnetic moments and the tunability of the defect-induced $π$-like magnetism in graphene.

cond-mat.mes-hall↗

arXiv2017

A microscopic formulation of dynamical spin injection in ferromagnetic-nonmagnetic heterostructures

We develop a microscopic formulation of dynamical spin injection in heterostructure comprising nonmagnetic metals in contact with ferromagnets. The spin pumping current is expressed in terms of Green's function of the nonmagnetic metal attached to the ferromagnet where a precessing magnetization is induced. The formulation allows for the inclusion of spin-orbit coupling and disorder. The Green's functions involved in the expression for the current are expressed in real-space lattice coordinates and can thus be efficiently computed using recursive methods.

cond-mat.mes-hall↗

arXiv2017

Entanglement Complexity in Quantum Many-Body Dynamics, Thermalization and Localization

Entanglement is usually quantified by von Neumann entropy, but its properties are much more complex than what can be expressed with a single number. We show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns of the spectrum of the reduced density matrix for a state evolved after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit the universal distribution is asymptotically reached within very different time scales in these two cases. We further show that the complexity of entanglement, revealed by the possibility of disentangling the state through a Metropolis-like algorithm, is signaled by whether the entanglement spectrum level spacing is Poisson or Wigner-Dyson distributed.

cond-mat.str-el↗

arXiv2017

Surface code fidelity at finite temperatures

We study the dependence of the fidelity of the surface code in the presence of a single finite-temperature massless bosonic environment after a quantum error correction cycle. The three standard types of environment are considered: super-Ohmic, Ohmic, and sub-Ohmic. Our results show that, for regimes relevant to current experiments, quantum error correction works well even in the presence of environment-induced, long-range inter-qubit interactions. A threshold always exists at finite temperatures, although its temperature dependence is very sensitive to the type of environment. For the super-Ohmic case, the critical coupling constant separating high- from low-fidelity decreases with increasing temperature. For both Ohmic and super-Ohmic cases, the dependence of the critical coupling on temperature is weak. In all cases, the critical coupling is determined by microscopic parameters of the environment. For the sub-Ohmic case, it also depends strongly on the duration of the QEC cycle.

quant-ph↗

arXiv2017

Electronic transport in disordered MoS$_2$ nanoribbons

We study the electronic structure and transport properties of zigzag and armchair monolayer molybdenum disulfide nanoribbons using an 11-band tight-binding model that accurately reproduces the material's bulk band structure near the band gap. We study the electronic properties of pristine zigzag and armchair nanoribbons, paying particular attention to the edges states that appear within the MoS$_2$ bulk gap. By analyzing both their orbital composition and their local density of states, we find that in zigzag-terminated nanoribbons these states can be localized at a single edge for certain energies independent of the nanoribbon width. We also study the effects of disorder in these systems using the recursive Green's function technique. We show that for the zigzag nanoribbons, the conductance due to the edge states is strongly suppressed by short-range disorder such as vacancies. In contrast, the local density of states still shows edge localization. We also show that long-range disorder has a small effect on the transport properties of nanoribbons within the bulk gap energy window.

cond-mat.mes-hall↗

arXiv2016

Disorder effect on the anisotropic resistivity of phosphorene determined by a tight-binding model

In this work we develop a compact multi-orbital tight-binding model for phosphorene that accurately describes states near the main band gap. The model parameters are adjusted using as reference the band structure obtained by a density-functional theory calculation with the hybrid HSE06 functional. We use the optimized tight-binding model to study the effects of disorder on the anisotropic transport properties of phosphorene. In particular, we evaluate how the longitudinal resistivity depends on the lattice orientation for two typical disorder models: dilute scatterers with high potential fluctuation amplitudes, mimicking screened charges in the substrate, and dense scatterers with lower amplitudes, simulating weakly bounded adsorbates. We show that the intrinsic anisotropy associated to the band structure of this material, although sensitive to the type and intensity of the disorder, is robust.

cond-mat.mes-hall↗

arXiv2016

A Single-Level Tunnel Model to Account for Electrical Transport through Single Molecule- and Self-Assembled Monolayer-based Junctions

We present a theoretical analysis aimed at understanding electrical conduction in molecular tunnel junctions. We focus on discussing the validity of coherent versus incoherent theoretical formulations for single-level tunneling to explain experimental results obtained under a wide range of experimental conditions, including measurements in individual molecules connecting the leads of electromigrated single-electron transistors and junctions of self-assembled monolayers (SAM) of molecules sandwiched between two macroscopic contacts. We show that the restriction of transport through a single level in solid state junctions (no solvent) makes coherent and incoherent tunneling formalisms indistinguishable when only one level participates in transport. Similar to Marcus relaxation processes in wet electrochemistry, the thermal broadening of the Fermi distribution describing the electronic occupation energies in the electrodes accounts for the exponential dependence of the tunneling current on temperature. We demonstrate that a single-level tunnel model satisfactorily explains experimental results obtained in three different molecular junctions (both single-molecule and SAM-based) formed by ferrocene-based molecules. Among other things, we use the model to map the electrostatic potential profile in EGaIn-based SAM junctions in which the ferrocene unit is placed at different positions within the molecule, and we find that electrical screening gives rise to a strongly non-linear profile across the junction.

cond-mat.mes-hall↗

arXiv2015

Two-component Structure in the Entanglement Spectrum of Highly Excited States

We study the entanglement spectrum of highly excited eigenstates of two known models that exhibit a many-body localization transition, namely the one-dimensional random-field Heisenberg model and the quantum random energy model. Our results indicate that the entanglement spectrum shows a "two-component" structure: a universal part that is associated with random matrix theory, and a nonuniversal part that is model dependent. The non-universal part manifests the deviation of the highly excited eigenstate from a true random state even in the thermalized phase where the eigenstate thermalization hypothesis holds. The fraction of the spectrum containing the universal part decreases as one approaches the critical point and vanishes in the localized phase in the thermodynamic limit. We use the universal part fraction to construct an order parameter for measuring the degree of randomness of a generic highly excited state, which is also a promising candidate for studying the many-body localization transition. Two toy models based on Rokhsar-Kivelson type wave functions are constructed and their entanglement spectra are shown to exhibit the same structure.

cond-mat.stat-mech↗

arXiv2015

Critical delocalization of chiral zero energy modes in graphene

Graphene subjected to chiral-symmetric disorder is believed to host zero energy modes (ZEMs) resilient to localization, as suggested by the renormalization group analysis of the underlying nonlinear sigma model. We report accurate quantum transport calculations in honeycomb lattices with in excess of $10^{9}$ sites and fine meV resolutions. The Kubo dc conductivity of ZEMs induced by vacancy defects (chiral BDI class) is found to match $4e^{2}/πh$ within 1% accuracy, over a parametrically wide window of energy level broadenings and vacancy concentrations. Our results disclose an unprecedentedly robust metallic regime in graphene, providing strong evidence that the early field-theoretical picture for the BDI class is valid well beyond its controlled weak-coupling regime.

cond-mat.mes-hall↗

arXiv2014

Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits

We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. These results open a new way to characterize irreversibility in quantum systems.

quant-ph↗

arXiv2014

Fidelity Threshold of the Surface Code Beyond Single-Qubit Error Models

The surface code is one the most promising alternatives for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attrative features. We develop an exact formulation for the fidelity of the surface code that allows us to probe much further on this promise of strong protection. This formulation goes beyond the stochastic single-qubit error model approximation and can take into account both correlated errors and inhomogeneities in the coupling between physical qubits and the environment. For the case of a bit-flipping environment, we map the complete evolution after one quantum error correction cycle onto the problem of computing correlation functions of a two-dimensional Ising model with boundary fields. Exact results for the fidelity threshold of the surface code are then obtained for several relevant types of noise. Analytical predictions for a representative case are confirmed by Monte Carlo simulations.

quant-ph↗

arXiv2014

Numerical evaluation of the fidelity error threshold for the surface code

We study how the resilience of the surface code is affected by the coupling to a non-Markovian environment at zero temperature. The qubits in the surface code experience an effective dynamics due to the coupling to the environment that induces correlations among them. The range of the effective induced qubit-qubit interaction depends on parameters related to the environment and the duration of the quantum error correction cycle. We show numerically that different interaction ranges set different intrinsic bounds on the fidelity of the code. These bounds are unrelated to the error thresholds based on stochastic error models. We introduce a definition of stabilizers based on logical operators that allows us to efficiently implement a Metropolis algorithm to determine upper bounds to the fidelity error threshold.

quant-ph↗

arXiv2014

Emergent irreversibility and entanglement spectrum statistics

We study the problem of irreversibility when the dynamical evolution of a many-body system is described by a stochastic quantum circuit. Such evolution is more general than a Hamiltonian one, and since energy levels are not well defined, the well-established connection between the statistical fluctuations of the energy spectrum and irreversibility cannot be made. We show that the entanglement spectrum provides a more general connection. Irreversibility is marked by a failure of a disentangling algorithm and is preceded by the appearance of Wigner-Dyson statistical fluctuations in the entanglement spectrum. This analysis can be done at the wave-function level and offers an alternative route to study quantum chaos and quantum integrability.

quant-ph↗