arXiv subjects

G. Sordi

Publications and source records attributed to G. Sordi.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics of superconducting pairs in the two-dimensional Hubbard model

The frequency structure of the superconducting correlations in cuprates gives insights on the pairing mechanism. Here we present an exhaustive study of this problem in the two-dimensional Hubbard model with cellular dynamical mean-field theory. To this end, we systematically quantify the dependence on doping $δ$ and interaction strength $U$ of the superconducting gap, of the frequency scales where $d$-wave pairing occurs, and of their relative contribution to pairing. For all values of $U$ and $δ$, we find pair-forming processes confined to frequencies set by the superexchange interaction and followed by pair-breaking processes, ruling out both pair-forming and pair-breaking processes on the scale of $U$. This suggests that at high frequencies, the effect of $U$ is eliminated by the $d$-wave paring, and that at small frequencies, $U$ generates the superexchange interaction that leads to low-frequency pair-forming processes providing the net contribution to pairing.

cond-mat.str-el↗

arXiv2025

Charge gap and charge redistribution among copper and oxygen orbitals in the normal state of the Emery model

Unraveling the behavior of the electrons in the copper-oxygen planes of cuprate superconductors remains a challenge. Here we examine the electronic charge redistribution among planar copper and oxygen orbitals and the charge gap using the Emery model in the normal state, solved with cellular dynamical mean-field theory at finite temperature. We quantify the charge redistribution as a function of the onsite Coulomb repulsion on the copper orbitals, the bare copper-oxygen energy difference, and the hole or electron doping. We find that the position relative to the metal to insulator boundary of the Zaanen-Sawatzky-Allen diagram determines the charge redistribution among copper and oxygen orbitals. For a fixed bare Cu-O energy difference, an increase in the Cu electron repulsion leads to a transfer of the electronic charge from Cu to O orbitals. For a fixed charge gap size of the undoped state, as the system evolves from a charge-transfer to a Mott-Hubbard regime, the electronic charge is transferred from Cu to O orbitals. Our findings posit the Coulomb repulsion and the bare charge-transfer energy as key drivers of the microscopic process of charge redistribution in the CuO$_2$ plane. They quantify the anticorrelation between the charge gap size and oxygen hole content. They show that for fixed band-structure parameters, the charge gap and the charge redistribution between Cu and O orbitals provide a way to understand observed trends in cuprates.

cond-mat.str-el↗

arXiv2025

Ambipolar doping of a charge-transfer insulator in the Emery model

Understanding the similarities and differences between adding or removing electrons from a charge-transfer insulator may provide insights about the origin of the electron-hole asymmetry found in cuprates. Here we study with cellular dynamical mean-field theory the Emery model set in the charge-transfer insulator regime, and dope it with either electrons or holes. We consider the normal state only and focus on the doping evolution of the orbital character of the dopants and on the nature of the doping driven transition. Regarding the orbital character of the dopants, we found an electron-hole asymmetry: doped electrons mostly enter the copper orbitals, whereas doped holes mostly enter the oxygen orbitals. Regarding the nature of the doping driven transition, we found no qualitative electron-hole asymmetry: upon either electron or hole doping, there is a two-stage transition from a charge-transfer insulator to a strongly correlated pseudogap and then to a metal. This shows that a strongly correlated pseudogap is an emergent feature of doped correlated insulators in two dimensions, in qualitative agreement with recent experiments on ambipolar Sr$_{1-x}$La$_{x}$CuO$_{2+y}$ cuprate films. Our results indicate that merely doping with holes or electrons a charge-transfer insulator is not sufficient for explaining the electron-hole asymmetry observed in the normal state phase diagram of cuprates. Our work reinforces the view that actual hole-doped cuprates are more correlated than their electron-doped counterparts.

cond-mat.str-el↗

arXiv2024

Introducing the concept of the Widom line in the QCD phase diagram

Critical phenomena emerging from the critical end point of a first-order transition are ubiquitous in nature. Here we bring the concept of a supercritical crossover, the Widom line, initially developed in the context of fluids, into the interacting matter described by quantum chromodynamics (QCD). We show that the existence of the putative critical end point between hadron gas and quark-gluon plasma in the temperature versus chemical potential of the QCD phase diagram implies the existence of a Widom line emerging from it in the supercritical region. We survey the thermodynamic anomalies already identified in simplified theoretical models of QCD exhibiting a critical end point, to show that they can be interpreted in terms of a Widom line. Then we suggest possible directions where the Widom line concept could provide new light on the QCD phase diagram.

hep-ph↗

arXiv2023

Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: a quantum impurity model analysis

Doping a Mott insulator gives rise to unconventional superconducting correlations. Here we address the interplay between d-wave superconductivity and Mott physics using the two-dimensional Hubbard model with cellular dynamical mean-field theory on a $2\times2$ plaquette. Our approach is to study superconducting correlations from the perspective of a cluster quantum impurity model embedded in a self-consistent bath. At the level of the cluster, we calculate the probabilities of the possible cluster electrons configurations. Upon condensation we find an increased probability that cluster electrons occupy a four-electron singlet configuration, enabling us to identify this type of short-range spin correlations as key to superconducting pairing. The increased probability of this four-electron singlet comes at the expense of a reduced probability of a four-electron triplet with no significant probability redistribution of fluctuations of charges. This allows us to establish that superconductivity at the level of the cluster primarily involves a reorganisation of short-range spin correlations rather than charge correlations. We gain information about the bath by studying the spectral weight of the hybridization function. Upon condensation, we find a transfer of spectral weight leading to the opening of a superconducting gap. We use these insights to interpret the signatures of superconducting correlations in the density of states of the system and in the zero-frequency spin susceptibility.

cond-mat.str-el↗

arXiv2022

Prediction of anomalies in the velocity of sound for the pseudogap of hole-doped cuprates

We predict sound anomalies at the doping $δ_{p}$ where the pseudogap ends in the normal state of hole-doped cuprates. Our prediction is based on the two-dimensional compressible Hubbard model using cluster dynamical mean-field theory. We find sharp anomalies (dips) in the velocity of sound as a function of doping and interaction. These dips are a signature of supercritical phenomena, stemming from an electronic transition without symmetry breaking below the superconducting dome. If experimentally verified, these signatures may help to solve the fundamental question of the nature of the pseudogap -- pinpointing its origin as due to Mott physics and resulting short-range correlations.

cond-mat.str-el↗

arXiv2021

Information-theoretic measures of superconductivity in a two-dimensional doped Mott insulator

A key open issue in condensed matter physics is how quantum and classical correlations emerge in an unconventional superconductor from the underlying normal state. We study this problem in a doped Mott insulator with information theory tools on the two-dimensional Hubbard model at finite temperature with cluster dynamical mean-field theory. We find that the local entropy detects the superconducting state and that the difference in the local entropy between the superconducting and normal states follows the same difference in the potential energy. We find that the thermodynamic entropy is suppressed in the superconducting state and monotonically decreases with decreasing doping. The maximum in entropy found in the normal state above the overdoped region of the superconducting dome is obliterated by superconductivity. The total mutual information, which quantifies quantum and classical correlations, is amplified in the superconducting state of the doped Mott insulator for all doping levels, and shows a broad peak versus doping, as a result of competing quantum and classical effects.

cond-mat.str-el↗

arXiv2020

Entanglement and classical correlations at the doping-driven Mott transition in the two-dimensional Hubbard model

Tools of quantum information theory offer a new perspective to characterize phases and phase transitions in interacting many-body quantum systems. The Hubbard model is the archetypal model of such systems and can explain rich phenomena of quantum matter with minimal assumptions. Recent measurements of entanglement-related properties of this model using ultracold atoms in optical lattices hint that entanglement could provide the key to understanding open questions of the doped Hubbard model, including the remarkable properties of the pseudogap phase. These experimental findings call for a theoretical framework and new predictions. Here we approach the doped Hubbard model in two dimensions from the perspective of quantum information theory. We study the local entropy and the total mutual information across the doping-driven Mott transition within plaquette cellular dynamical mean-field theory. We find that upon varying doping these two entanglement-related properties detect the Mott insulating phase, the strongly correlated pseudogap phase, and the metallic phase. Imprinted in the entanglement-related properties we also find the pseudogap to correlated metal first-order transition, its finite temperature critical endpoint, and its supercritical crossovers. Through this footprint we reveal an unexpected interplay of quantum and classical correlations. Our work shows that sharp variation in the entanglement-related properties and not broken symmetry phases characterizes the onset of the pseudogap phase at finite temperature.

cond-mat.str-el↗

arXiv2020

Mott transition and high-temperature crossovers at half-filling

The interaction-driven Mott transition in the half-filled Hubbard model is a first-order phase transition that terminates at a critical point $(T_\mathrm{c},U_\mathrm{c})$ in the temperature-interaction plane $T-U$. A number of crossovers occur along lines that extend for some range above $(T_\mathrm{c},U_\mathrm{c})$. Asymptotically close to $(T_\mathrm{c},U_\mathrm{c})$, these lines coalesce into the so-called Widom line. The existence of $(T_\mathrm{c},U_\mathrm{c})$ and of the associated crossovers becomes unclear when long-wavelength fluctuations or long-range order occur above $(T_\mathrm{c},U_\mathrm{c})$. We study this problem using continuous-time quantum Monte Carlo methods as impurity solvers for both Dynamical Mean-Field Theory (DMFT) and Cellular Dynamical Mean-Field Theory (CDMFT). We contrast the cases of the square lattice, where antiferromagnetic fluctuations dominate in the vicinity of the Mott transition, and the triangular lattice where they do not. The inflexion points and maxima found near the Widom line for the square lattice can serve as proxy for the triangular lattice case. But the only crossover observable in all cases at sufficiently high temperature is that associated with the opening of the Mott gap. The same physics also controls an analog crossover in the resistivity called the "Quantum Widom line".

cond-mat.str-el↗

arXiv2019

Specific heat maximum as a signature of Mott physics in the two-dimensional Hubbard model

Recent experiments on cuprates show that as a function of doping, the normal-state specific heat sharply peaks at the doping $δ^*$, where the pseudogap ends at low temperature. This finding is taken as the thermodynamic signature of a quantum critical point, whose nature has not yet been identified. Here we present calculations for the two-dimensional Hubbard model in the doped Mott insulator regime, which indicate that the specific heat anomaly can arise from the finite temperature critical endpoint of a first-order transition between a pseudogap phase with dominant singlet correlations and a metal. As a function of doping at the temperature of the endpoint, the specific heat diverges. Upon increasing temperature, the peak becomes broader. The diverging correlation length is associated with uniform density fluctuations. No broken symmetries are needed. These anomalies also occur at half-filling as a function of interaction strength, and are relevant for organic superconductors and ultracold atoms.

cond-mat.str-el↗

arXiv2019

Critical Opalescence across the Doping Driven Mott Transition in Optical Lattices of Ultracold Atoms

Phase transitions and their associated crossovers are imprinted in the behavior of fluctuations. Motivated by recent experiments on ultracold atoms in optical lattices, we compute the thermodynamic density fluctuations $δN^2$ of the two-dimensional fermionic Hubbard model with plaquette cellular dynamical mean-field theory. To understand the length scale of these fluctuations, we separate the local from the nonlocal contributions to $δN^2$. We determine the effects of particle statistics, interaction strength $U$, temperature $T$ and density $n$. At high temperature, our theoretical framework reproduces the experimental observations in the doping-driven crossover regime between metal and Mott insulator. At low temperature, there is an increase of thermodynamic density fluctuations, analog to critical opalescence, accompanied by a surprising reduction of the absolute value of their nonlocal contributions. This is a precursory sign of an underlying phase transition between a pseudogap phase and a metallic phase in doped Mott insulators, which should play an important role in the cuprate high-temperature superconductors. Predictions for ultracold atom experiments are made.

cond-mat.quant-gas↗

arXiv2018

Thermodynamic and information-theoretic description of the Mott transition in the two-dimensional Hubbard model

At the Mott transition, electron-electron interaction changes a metal, in which electrons are itinerant, to an insulator, in which electrons are localized. This phenomenon is central to quantum materials. Here we contribute to its understanding by studying the two-dimensional Hubbard model at finite temperature with plaquette cellular dynamical mean-field theory. We provide an exhaustive thermodynamic description of the correlation-driven Mott transition of the half-filled model by calculating pressure, charge compressibility, entropy, kinetic energy, potential energy and free energy across the first-order Mott transition and its high-temperature crossover (Widom line). The entropy is extracted from the Gibbs-Duhem relation and shows complex behavior near the transition, marked by discontinuous jumps at the first-order boundary, singular behavior at the Mott endpoint and inflections marking sharp variations in the supercritical region. The free energy allows us to identify the thermodynamic phase boundary, to discuss phases stability and metastability, and to touch upon nucleation and spinodal decomposition mechanisms for the transition. We complement this thermodynamic description of the Mott transition by an information-theoretic description. We achieve this by calculating the local entropy, which is a measure of entanglement, and the single-site total mutual information, which quantifies quantum and classical correlations. These information-theoretic measures exhibit characteristic behaviors that allow us to identify the first-order coexistence regions, the Mott critical endpoint and the crossovers along the Widom line in the supercritical region.

cond-mat.str-el↗

arXiv2018

Entanglement entropy and mutual information across the Mott transition in the two-dimensional Hubbard model

Entanglement and information are powerful lenses to probe phases transitions in many-body systems. Motivated by recent cold atom experiments, which are now able to measure the corresponding information-theoretic quantities, we study the Mott transition in the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory, and focus on two key measures of quantum correlations: entanglement entropy and mutual information. We show that they detect the first-order nature of the transition, the universality class of the endpoint, and the crossover emanating from the endpoint.

cond-mat.str-el↗

arXiv2017

Effects of interaction strength, doping, and frustration on the antiferromagnetic phase of the two-dimensional Hubbard model

Recent quantum-gas microscopy of ultracold atoms and scanning tunneling microscopy of the cuprates reveal new detailed information about doped Mott antiferromagnets, which can be compared with calculations. Using cellular dynamical mean-field theory, we map out the antiferromagnetic (AF) phase of the two-dimensional Hubbard model as a function of interaction strength $U$, hole doping $δ$ and temperature $T$. The Néel phase boundary is non-monotonic as a function of $U$ and $δ$. Frustration induced by second-neighbor hopping reduces Néel order more effectively at small $U$. The doped AF is stabilized at large $U$ by kinetic energy and at small $U$ by potential energy. The transition between the AF insulator and the doped metallic AF is continuous. At large $U$, we find in-gap states similar to those observed in scanning tunneling microscopy. We predict that, contrary to the Hubbard bands, these states are only slightly spin polarized.

cond-mat.str-el↗

arXiv2017

Signatures of the Mott transition in the antiferromagnetic state of the two-dimensional Hubbard model

The properties of a phase with large correlation length can be strongly influenced by the underlying normal phase. We illustrate this by studying the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory with continuous-time quantum Monte Carlo. Sharp crossovers in the mechanism that favors antiferromagnetic correlations and in the corresponding local density of states are observed. These crossovers occur at values of the interaction strength $U$ and temperature $T$ that are controlled by the underlying normal-state Mott transition.

cond-mat.str-el↗

arXiv2016

Antagonistic effects of nearest-neighbor repulsion on the superconducting pairing dynamics in the doped Mott insulator regime

The nearest-neighbor superexchange-mediated mechanism for d_{x^2-y^2}-wave superconductivity in the one-band Hubbard model faces the challenge that nearest-neighbor Coulomb repulsion can be larger than superexchange. To answer this question, we use cellular dynamical mean-field theory (CDMFT) with a continuous-time quantum Monte Carlo solver to determine the superconducting phase diagram as a function of temperature and doping for on-site repulsion $U=9t$ and nearest-neighbor repulsion $V=0,2t,4t$. In the underdoped regime, $V$ increases the CDMFT superconducting transition temperature $T_c^d$ even though it decreases the superconducting order parameter at low temperature for all dopings. However, $V$ decreases $T_c^d$ in the overdoped regime. We gain insight into these paradoxical results through a detailed study of the frequency dependence of the anomalous spectral function, extracted at finite temperature via the MaxEntAux method for analytic continuation. A systematic study of dynamical positive and negative contributions to pairing reveals that even though $V$ has a high-frequency depairing contribution, it also has a low frequency pairing contribution since it can reinforce superexchange through $J=4t^2/(U-V)$. Retardation is thus crucial to understand pairing in doped Mott insulators, as suggested by previous zero-temperature studies. We also comment on the tendency to charge order for large $V$ and on the persistence of d-wave superconductivity over extended-$s$ or s+d-wave.

cond-mat.supr-con↗

arXiv2016

Pseudogap and superconductivity in two-dimensional doped charge-transfer insulators

High-temperature superconductivity emerges in the CuO$_2$ plane upon doping a Mott insulator. To ascertain the influence of Mott physics plus short-range correlations, we solve a three-band copper-oxide model in the charge-transfer regime using cellular dynamical mean-field theory with continuous-time quantum Monte Carlo as an impurity solver. We report the normal and superconducting phase diagram of this model as a function of doping, interaction strength and temperature. Upon hole doping of the charge-transfer insulator, the phase boundary between pseudogap and correlated metal consists of a first-order transition line at finite doping ending at a critical point, as in the one-band model. Beyond the endpoint, the phase boundary continues as a Widom crossover line, across which thermodynamic quantities peak. This phase boundary determines changes in the pairing mechanism and is an emergent phenomenon characteristic of doped Mott insulators, independent of many microscopic details. Broader implications are discussed.

cond-mat.str-el↗

arXiv2016

An organizing principle for two-dimensional strongly correlated superconductivity

Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature $T_c^d$, the maximum of the condensation energy as a function of doping, the correlation between maximum $T_c^d$ and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.

cond-mat.str-el↗