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We develop a complete formulation of quantum gauge invariance in light-front dynamics for interacting theories with massless vector gauge fields in the framework of null-plane causal perturbation theory. We apply the general results to quantum electrodynamics, showing that the so-called "gauge terms" present in the photon commutation distribution when quantized under the null-plane gauge condition have no contribution in the calculation of the physical S-operator matrix elements at any order. We use this result to prove the normalizability of the theory, and to calculate the electron's self-energy at second order., Comment: To be published in Phys. Rev. D

We study quantum electrodynamics (QED) in the light-front dynamical form by using null-plane causal perturbation theory. We establish the equivalence with instant dynamics for the scattering processes, whose normalization allows to construct the instantaneous terms of the usual null-plane QED Lagrangian density. Then we study vacuum polarization and normalize it by studying its insertions into M{\o}ller's scattering process, obtaining the complete photon's propagator, which turns to be equivalent to the one of instant dynamics only when gauge invariance is taken into account., Comment: To be published in Phys. Rev. D

Practical calculations in light-front dynamics are, as a general rule, complicated, since there is no consensus about how to treat the poles which come from the instantaneous parts of Feynman's propagators of the fields. An alternative to solve this difficulty is null-plane causal perturbation theory, a recent developed framework which prevents the appearance of the mentioned poles by avoiding the usage of Feynman's propagators in "loop distributions", requiring no regularization of the amplitudes. In this study, we treat the radiative corrections in the neutral Yukawa's model in that framework. Particularly, we explicitly calculate the boson and fermion self-energies and show that the results obtained with this approach are equivalent to that of the instant dynamics., Comment: 12 pages; to be published in Phys. Rev. D

We use extensive numerical simulations based on matrix product state methods to study the quantum dynamics of spin chains with strong on-site disorder and power-law decaying ($1/r^\alpha$) interactions. We focus on two spin-$1/2$ Hamiltonians featuring power-law interactions: Heisenberg and XY and characterize their corresponding long-time dynamics using three distinct diagnostics: decay of a staggered magnetization pattern $I(t)$, growth of entanglement entropy $S(t)$, and growth of quantum Fisher information $F_Q(t).$ For sufficiently rapidly decaying interactions $\alpha>\alpha_c$ we find a many-body localized phase, in which $I(t)$ saturates to a non-zero value, entanglement entropy grows as $S(t)\propto t^{1/\alpha}$, and Fisher information grows logarithmically. Importantly, entanglement entropy and Fisher information do not scale the same way (unlike short range interacting models). The critical power $\alpha_c$ is smaller for the XY model than for the Heisenberg model.

The ability to modify light-matter coupling in time (e.g. using external pulses) opens up the exciting possibility of generating and probing new aspects of quantum correlations in many-body light-matter systems. Here we study the impact of such a pulsed coupling on the light-matter entanglement in the Dicke model as well as the respective subsystem quantum dynamics. Our dynamical many-body analysis exploits the natural partition between the radiation and matter degrees of freedom, allowing us to explore time-dependent intra-subsystem quantum correlations by means of squeezing parameters, and the inter-subsystem Schmidt gap for different pulse duration (i.e. ramping velocity) regimes -- from the near adiabatic to the sudden quench limits. Our results reveal that both types of quantities indicate the emergence of the superradiant phase when crossing the quantum critical point. In addition, at the end of the pulse light and matter remain entangled even though they become uncoupled, which could be exploited to generate entangled states in non-interacting systems., Comment: 15 pages, 4 figures, Accepted for publication in Journal of Physics B, special issue Correlations in light-matter interactions

We show that a pulsed stimulus can be used to generate many-body quantum coherences in light-matter systems of general size. Specifically, we calculate the exact real-time evolution of a driven, generic out-of-equilibrium system comprising an arbitrary number N qubits coupled to a global boson field. A novel form of dynamically-driven quantum coherence emerges for general N and without having to access the empirically challenging strong-coupling regime. Its properties depend on the speed of the changes in the stimulus. Non-classicalities arise within each subsystem that have eluded previous analyses. Our findings show robustness to losses and noise, and have potential functional implications at the systems level for a variety of nanosystems, including collections of N atoms, molecules, spins, or superconducting qubits in cavities -- and possibly even vibration-enhanced light harvesting processes in macromolecules., Comment: 9 pages, 4 figures

The Discrete Truncated Wigner Approximation (DTWA) is a semi-classical phase space method useful for the exploration of Many-body quantum dynamics. In this work we investigate Many-Body Localization (MBL) and thermalization using DTWA and compare its performance to exact numerical solutions. By taking as a benchmark case a 1D random field Heisenberg spin chain with short range interactions, and by comparing to numerically exact techniques, we show that DTWA is able to reproduce dynamical signatures that characterize both the thermal and the MBL phases. It exhibits the best quantitative agreement at short times deep in each of the phases and larger mismatches close to the phase transition. The DTWA captures the logarithmic growth of entanglement in the MBL phase, even though a pure classical mean-field analysis would lead to no dynamics at all. Our results suggest the DTWA can become a useful method to investigate MBL and thermalization in experimentally relevant settings intractable with exact numerical techniques, such as systems with long range interactions and/or systems in higher dimensions.

We investigate the non-equilibrium quantum dynamics of a canonical light-matter system, namely the Dicke model, when the light-matter interaction is ramped up and down through a cycle across the quantum phase transition. Our calculations reveal a rich set of dynamical behaviors determined by the cycle times, ranging from the slow, near adiabatic regime through to the fast, sudden quench regime. As the cycle time decreases, we uncover a crossover from an oscillatory exchange of quantum information between light and matter that approaches a reversible adiabatic process, to a dispersive regime that generates large values of light-matter entanglement. The phenomena uncovered in this work have implications in quantum control, quantum interferometry, as well as in quantum information theory., Comment: 9 pages and 4 figures

High precision macroscopic quantum control in interacting light-matter systems remains a significant goal toward novel information processing and ultra-precise metrology. We show that the out-of-equilibrium behavior of a paradigmatic light-matter system (Dicke model) reveals two successive stages of enhanced quantum correlations beyond the traditional schemes of near-adiabatic and sudden quenches. The first stage features magnification of matter-only and light-only entanglement and squeezing due to effective non-linear self-interactions. The second stage results from a highly entangled light-matter state, with enhanced superradiance and signatures of chaotic and highly quantum states. We show that these new effects scale up consistently with matter system size, and are reliable even in dissipative environments., Comment: 14 pages, 6 figures

A significant problem facing next-generation quantum technologies is how to generate and manipulate macroscopic entanglement in light and matter systems. Here we report a new regime of dynamical light-matter behavior in which a giant, system-wide entanglement is generated by varying the light-matter coupling at \emph{intermediate} velocities. This enhancement is far larger and broader-ranged than that occurring near the quantum phase transition of the same model under adiabatic conditions. By appropriate choices of the coupling within this intermediate regime, the enhanced entanglement can be made to spread system-wide or to reside in each subsystem separately., Comment: 7 pages, 7 figures

We present a computational scheme for orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values and preserves the OFDFT linear scaling as a function of the system size. Using the projector augmented-wave method (PAW) in combination with real-space methods we overcome some obstacles faced by other available implementation schemes. Specifically, the advantages of using the PAW method are two fold. First, PAW reproduces all-electron values offering freedom in adjusting the convergence parameters and the atomic setups allow tuning the numerical accuracy per element. Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham codes. Using PAW and real-space methods, our orbital-free results agree with the reference all-electron values with a mean absolute error of 10~meV and the number of iterations required by the self-consistent cycle is comparable to the KS method. The comparison of all-electron and pseudopotential bulk modulus and lattice constant reveal an enormous difference, demonstrating that in order to assess the performance of OFDFT functionals it is necessary to use implementations that obtain all-electron values. The proposed combination of methods is the most promising route currently available. We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained by the KS PBE method, exemplified with the case of diamond., Comment: accepted in Journal of Chemical Physics

We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions (QPTs) in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our findings, which lie beyond traditional critical exponent analysis and adiabatic perturbation approximations, are applicable even where excitations have not yet stabilized and hence provide a time-resolved understanding of QPTs encompassing a wide range of adiabatic regimes. We show explicitly that even though two systems may traditionally belong to the same universality class, they can have very different adiabatic evolutions. This implies more stringent conditions need to be imposed than at present, both for quantum simulations where one system is used to simulate the other, and for adiabatic quantum computing schemes., Comment: 5 pages, 3 figures, plus supplementary material (6 pages, 1 figure)

Multi-scale computer simulations combine the computationally efficient classical algorithms with more expensive but also more accurate ab-initio quantum mechanical algorithms. This work describes one implementation of multi-scale computations using the Atomistic Simulation Environment (ASE). This implementation can mix classical codes like LAMMPS and the Density Functional Theory-based GPAW. Any combination of codes linked via the ASE interface however can be mixed. We also introduce a framework to easily add classical force fields calculators for ASE using LAMMPS, which also allows harnessing the full performance of classical-only molecular dynamics. Our work makes it possible to combine different simulation codes, quantum mechanical or classical, with great ease and minimal coding effort.

Using ab-initio computational techniques on crystal determined clusters, we report on the similarities and differences of Al$_{50}$(C$_5$(CH$_3)_5)_{12}$, Ga$_{23}$(N(Si(CH$_3)_{3}$)$_{2}$)$_{11}$, and Au$_{102}$(SC$_7$O$_2$H$_5$)$_{44}$ ligand-protected clusters. Each of the ligand-protected clusters in this study show the similar stable character which can be described via a electronic shell model. We show here that the same type of analysis leads consistently to derive a superatomic electronic counting rule, independently of the metal and ligand compositions. One can define the cluster core as the set of atoms where delocalized single-angular-momentum-character orbitals have hight weight using a combination of Bader analysis and the evaluation of Khon-Sham orbitals. Subsequently one can derive the nature of the ligand-core interaction. These results yield further insight into the superatom analogy for the class of ligand-protected metal clusters.

Electrical conductance through various nanocontacts between gold electrodes is studied by using the density functional theory, scalar-relativistic pseudopotentials, generalized gradient approximation for the exchange-correlation energy and the recursion-transfer-matrix method along with channel decomposition. The nanocontact is modeled with pyramidal fcc(100) tips and 1 to 5 gold atoms between the tips. Upon elongation of the contact by adding gold atoms between the tips, the conductance at Fermi energy E_F evolves from G ~ 3 G_0 to G ~ 1 G_0 (G_0 = 2e/h^2). Formation of a true one-atom point contact, with G ~ 1 G_0 and only one open channel, requires at least one atom with coordination number 2 in the wire. Tips that share a common vertex atom or tips with touching vertex atoms have three partially open conductance channels at E_F, and the symmetries of the channels are governed by the wave functions of the tips. The long 5-atom contact develops conductance oscillations and conductance gaps in the studied energy range -3 < E-E_F < 5 eV, which reflects oscillations in the local density of electron states in the 5-atom linear "gold molecule" between the electrodes, and a weak coupling of this "molecule" to the tips.

We address the problem of the construction of quantum walks on Cayley graphs. Our main motivation is the relationship between quantum algorithms and quantum walks. In particular, we discuss the choice of the dimension of the local Hilbert space and consider various classes of graphs on which the structure of quantum walks may differ. We completely characterise quantum walks on free groups and present partial results on more general cases. Some examples are given, including a family of quantum walks on the hypercube involving a Clifford Algebra., Comment: J. Phys. A (accepted for publication)