Cluster Dynamical Mean-Field Theory of the density-driven Mott transition in the one-dimensional Hubbard model

The one-dimensional Hubbard model is investigated by means of two different cluster schemes suited to introduce short-range spatial correlations beyond the single-site Dynamical Mean-Field Theory, namely the Cluster-Dynamical Mean-Field Theory and its periodized version. It is shown that both cluster schemes are able to describe with extreme accuracy the evolution of the density as a function of the chemical potential from the Mott insulator to the metallic state. Using exact diagonalization to solve the cluster impurity model, we discuss the role of the truncation of the Hilbert space of the bath, and propose an algorithm that gives higher weights to the low frequency hybridization matrix elements and improves the speed of the convergence of the algorithm.Comment: 6 pages, 4 figures, minor corrections in v

Pseudogap induced by short-range spin correlations in a doped Mott insulator

We study the evolution of a Mott-Hubbard insulator into a correlated metal upon doping in the two-dimensional Hubbard model using the Cellular Dynamical Mean Field Theory. Short-range spin correlations create two additional bands apart from the familiar Hubbard bands in the spectral function. Even a tiny doping into this insulator causes a jump of the Fermi energy to one of these additional bands and an immediate momentum dependent suppression of the spectral weight at this Fermi energy. The pseudogap is closely tied to the existence of these bands. This suggests a strong-coupling mechanism that arises from short-range spin correlations and large scattering rates for the pseudogap phenomenon seen in several cuprates.Comment: 6 pages, 6 figure

Sequence-Selection-Based Constellation Shaping for Nonlinear Channels

Probabilistic shaping is, nowadays, a pragmatic and popular approach to improve the performance of coherent optical fiber communication systems. In the linear regime, the potential of probabilistic shaping in terms of shaping gain and rate granularity is well known, and its practical implementation has been mostly mastered. In the nonlinear regime, the advantages offered by probabilistic shaping remain not only valid, but might also increase thanks to the appealing opportunity to use the same technique to mitigate nonlinear effects and obtain an additional nonlinear shaping gain. Unfortunately, despite the recent research efforts, the optimization of conventional shaping techniques, such as probabilistic amplitude shaping (PAS), yields a relevant nonlinear shaping gain only in particular scenarios of limited practical interest, e.g., in the absence of carrier phase recovery. Recently, a more theoretical approach, referred to as sequence selection, has been proposed to understand the performance and limitation of nonlinear constellation shaping. Sequence selection shapes the distribution of the transmitted symbols by selecting or discarding the sequences generated by a certain source according to a metric that measures their quality. In this manuscript, after a brief review of conventional probabilistic shaping, we use sequence selection to investigate through simulations the potential, opportunities, and challenges offered by probabilistic shaping for nonlinear channels. First, we show that ideal sequence selection is able to provide up to 0.13 b/s/Hz additional gain with respect to PAS with an optimized blocklength. However, this additional gain is obtained only if the selection metric accounts for the signs of the symbols, ruling out the possibility of using one of the simple recently proposed sign-independent metrics. We also show that, while the signs must be known to compute the selection metric, there is no need to shape them, since nearly the same gain can be obtained by properly selecting the amplitudes (with a sign-dependent metric) and leaving the signs uniform i.i.d. Furthermore, we show that the selection depends in a non-critical way on the symbol rate and link length: the sequences selected for a certain scenario still provide a relevant gain if the link length or baud rate are modified (within a reasonable range). Then, we analyze and compare several practical implementations of sequence selection by taking into account interaction with forward error correction (FEC), information loss due to selection, and complexity. Overall, we conclude that the single block and the multi block FEC-independent bit scrambling are the best options for the practical implementation of sequence selection, with a gain up to 0.08 b/s/Hz. The main challenge and limitation to their practical implementation remains the evaluation of the metric, whose complexity is currently too high. Finally, we show that the nonlinear shaping gain provided by sequence selection persists when carrier phase recovery is included, in contrast to the nonlinear shaping gain offered by optimizing the blocklength of conventional PAS techniques

Unconventional high-energy-state contribution to the Cooper pairing in under-doped copper-oxide superconductor HgBa2_2Ca2_2Cu3_3O8+δ_{8+\delta}

We study the temperature-dependent electronic B1g Raman response of a slightly under-doped single crystal HgBa$_2$Ca$_2$Cu$_3$O$_{8+\delta}$ with a superconducting critical temperature Tc=122 K. Our main finding is that the superconducting pair-breaking peak is associated with a dip on its higher-energy side, disappearing together at Tc. This result hints at an unconventional pairing mechanism, whereas spectral weight lost in the dip is transferred to the pair-breaking peak at lower energies. This conclusion is supported by cellular dynamical mean-field theory on the Hubbard model, which is able to reproduce all the main features of the B1g Raman response and explain the peak-dip behavior in terms of a nontrivial relationship between the superconducting and the pseudo gaps.Comment: 7 pages 4 figure

Nodal/Antinodal Dichotomy and the Two Gaps of a Superconducting Doped Mott Insulator

We study the superconducting state of the hole-doped two-dimensional Hubbard model using Cellular Dynamical Mean Field Theory, with the Lanczos method as impurity solver. In the under-doped regime, we find a natural decomposition of the one-particle (photoemission) energy-gap into two components. The gap in the nodal regions, stemming from the anomalous self-energy, decreases with decreasing doping. The antinodal gap has an additional contribution from the normal component of the self-energy, inherited from the normal-state pseudogap, and it increases as the Mott insulating phase is approached.Comment: Corrected typos, 4.5 pages, 4 figure

On the Nonlinear Shaping Gain with Probabilistic Shaping and Carrier Phase Recovery

The performance of different probabilistic amplitude shaping (PAS)techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques—namely, sphere shaping, shell mapping with different number of shells, and constant composition DM—and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations ($1\times 180$ km, $15\times 80$ km, and $27\times 80$ km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm

Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators

Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step towards a quantitative theory of the competition between antiferromagnetism (AFM) and d-wave superconductivity (SC) in the cuprates, we use Cellular Dynamical Mean Field Theory to compute zero temperature properties of the two-dimensional square lattice Hubbard model. The d-wave order parameter is found to scale like the superexchange coupling J for on-site interaction U comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second-neighbor hopping t', the zero temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third-neighbor hopping t'' improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs T_{c}/T_{c}^{max} phase diagram of the cuprates is universal. The calculated ARPES spectrum displays the observed electron-hole asymmetry. Our calculations reproduce important features of d-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard BCS approach.Comment: 13 pages, 7 figure