arXiv subjects

A. -M. S. Tremblay

Publications and source records attributed to A. -M. S. Tremblay.

At least 19 recordsLinked to original sources

arXiv2026

The role of the apical oxygen in cuprate high-temperature superconductors

Scanning tunneling microscopy measurements exploiting the natural superstructure modulation of the cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212) have revealed a possible correlation between the Cu-apical-O distance $δ_{\mathrm{api}}$ and the superconducting order parameter $m_{\mathrm{SC}}$, as reported recently by O'Mahony et al. (Proc. Natl. Acad. Sci. 119, e2207449119 (2022)). These observations were interpreted as evidence for a direct link between superconductivity and the charge-transfer gap, and more broadly revived the long-standing question of the role of apical oxygens in cuprate superconductivity. Using a combination of density-functional theory and cluster dynamical mean-field theory, we compute from first principles the variations of $m_{\mathrm{SC}}$ induced solely by apical oxygen displacement in Bi$_2$Sr$_2$CuO$_{6+δ}$, Bi-2212, and HgBa$_2$CuO$_{4+δ}$. The quantitative agreement between our calculations and experiments allows us to unambiguously attribute the observed variations of $m_{\mathrm{SC}}$ to changes in $δ_{\mathrm{api}}$. We demonstrate, however, that these variations of $m_{\mathrm{SC}}$ originate predominantly from changes in the effective hole-doping of the CuO$_2$ planes, with negligible effect on the charge-transfer gap. The modest magnitude of the $m_{\mathrm{SC}}$ modulation induced by apical-oxygen displacement alone therefore warrants caution in interpreting correlations between $T_c$ and $δ_{\mathrm{api}}$ inferred from comparisons across different cuprate compounds. Our work demonstrates that the present ab initio framework can quantitatively resolve the influence of specific structural degrees of freedom on superconductivity in correlated oxides.

cond-mat.str-el↗

arXiv2026

Resilient strange metal at an unconventional quantum critical point in $d=2$

Properties of the two-dimensional Hubbard model with nearest-neighbor hopping are under scrutiny in cold-atom experiments and diagrammatic quantum Monte Carlo. Given the controlled nature of these approaches, it is timely to make predictions about strange-metal behavior and its relation to quantum-critical properties. Even for interaction strengths below the Mott transition, several peculiarities occur at the quantum critical point separating Fermi liquid and incommensurate spin-density wave order. Here, we predict, using the non-perturbative improved two-particle self-consistent approach, that for correlation lengths ranging from about one to one hundred lattice spacings, Kohn anomalies on the underlying Fermi surface lead to unconventional critical exponents. The temperature dependence of the single-particle self-energy acquires strong momentum dependence along the Fermi surface with no clear evidence of Landau quasiparticles. Nevertheless, we observe strange-metal behavior, namely, resistivity that scales linearly with temperature as $T\rightarrow{0}$. Our work shows that a linear temperature dependence of resistivity arises without a linear-in-temperature self-energy along the Fermi surface, as is often assumed.

cond-mat.str-el↗

arXiv2026

Pseudogap, Fermi liquid, Van Hove singularity and maxima of the compressibility and of the Knight shift as a function of doping in the two-dimensional Hubbard model

Qualitative changes in thermodynamic and single-particle properties characterize the transition between the pseudogapped electronic liquid and the Fermi liquid. Recent cold-atom experiments on a Hubbard model simulator with nearest-neighbor hoppings \cite{kendrick2025pseudogap} showed that the isothermal compressibility $κ(δ)$ has a maximum as a function of doping $δ$. Here we use the two-particle self-consistent plus (TPSC+) approach to explain these experiments and connect the maximum in $κ(δ)$ to the single-particle spectrum transformation from the pseudogapped to the metallic regime, elucidating the nature of the pseudogap (PG). The maximum in $κ(δ)$ practically coincides with the doping where the precursor of the lower $(π,π)$ spin density wave (SDW) band at the antinodal point crosses zero frequency $ω=0$. The Knight shift, $χ_{sp}(0,0)(δ)$, should also exhibit a maximum versus doping. Additionally, TPSC+ correctly predicts a maximum in the temperature dependence of the Knight shift, $χ_{sp}(0,0)(T)$, consistent with recent ultracold atom experiments \cite{chalopin2026observation}.These maxima should exist at low temperatures ($T$) in both the intermediate $U \approx U_{Mott}$ and weak $U < U_{Mott}$ interaction limits due to critical thermal SDW fluctuations. At the antinodal pseudogap, the correlation length at $δ_{max}(T)$ can be small, controlled by dynamic rather than static critical thermal fluctuations. The SDW fluctuations are incommensurate at $δ=δ_{max}$. At low $T$, multiple peaks in the incommensurate spin susceptibility lead to more than two SDW precursor peaks in the spectral function and density of states. By accessing parameter regimes relevant to cuprates, including further-neighbor hopping ($t', t''$) and low temperatures, our work provides a high-impact tool for further studies.

cond-mat.str-el↗

arXiv2026

Correlation of maximum superconducting critical temperature with copper-oxygen energy distance and oxygen hole content in the Emery model

Identifying microscopic parameters that optimize the maximum superconducting critical temperature $T_c^{\rm max}$ in the canonical model of the copper-oxygen plane of cuprates, the Emery model, remains challenging. Using cellular dynamical mean-field theory at finite temperature, we find that for a fixed charge gap size in the parent charge-transfer insulating state, $T_c^{\rm max}$ unexpectedly increases with increasing the copper-oxygen energy distance, as this favors the transfer of electrons from oxygen to copper orbitals. We show that these findings emerge naturally in the Zaanen-Sawatzky-Allen scheme and capture observed trends in hole-doped cuprates. Overall, our study uncovers that $T_c^{\rm max}$ is optimized in the Emery model under three conditions: upon doping a charge-transfer insulator, close to the charge-transfer insulator to metal boundary, and deep into the charge-transfer regime. This finding indicates new paths for optimizing $T_c^{\rm max}$.

cond-mat.str-el↗

arXiv2026

Charge-transfer gap size and oxygen hole content as two mechanisms controlling $T_c$ in the Emery model

Investigating the drivers of superconducting critical temperature trends in cuprates is crucial for uncovering the mechanism of high-temperature superconductivity. Here we study this problem in the canonical model of the copper-oxygen plane, the Emery model, with cellular dynamical mean-field theory. Using the Zaanen-Sawatzky-Allen diagram as a guiding framework, we systematically quantify how the maximum superconducting critical temperature $T_c^{\rm max}$ depends on the copper-oxygen energy distance and on the local repulsion on the copper orbital. Unexpectedly, $T_c^{\rm max}$ is optimized not only near the charge-transfer insulator to metal boundary, consistent with previous findings, but also deep in the charge-transfer regime, revealing an unexplored mechanism. Then we link model parameters to physical observables, identifying the charge-transfer gap size and the oxygen hole content as two mechanisms controlling $T_c^{\rm max}$. $T_c^{\rm max}$ increases monotonically as the oxygen hole content increases and the charge gap size decreases. The oxygen hole content is the dominant variable in varying $T_c^{\rm max}$. Our work provides predictions for proposed realizations of the Emery model with ultracold atoms and a theoretical framework for understanding key experimental trends in hole-doped cuprates.

cond-mat.str-el↗

arXiv2026

Magnetic phases of the anisotropic triangular Hubbard model from the ghost-Gutzwiller approximation in the rotating spin-frame

We investigate the magnetic phase diagram of the half-filled Hubbard model on the anisotropic triangular lattice using the Gutzwiller approximation (GA) and its ghost generalization (ghost-GA). By combining a rotating spin-frame formulation with high-resolution momentum grids, we determine magnetic ground states through direct total-energy minimization over the ordering wavevector. We benchmark standard GA and ghost-GA against dynamical mean-field theory (DMFT) and dual-fermion results. We show that GA already captures the qualitative structure of the phase diagram, but systematically overestimates the stability of magnetic order due to the absence of dynamical fluctuations. We find that introducing a small number of auxiliary ''ghost'' orbitals is sufficient to recover most dynamical effects and significantly improves quantitative agreement with DMFT. Exploring the full Brillouin zone, we obtain a phase diagram comprising paramagnetic and various magnetic phases. In contrast to ladder dual-fermion susceptibility-based predictions, we find that the one-dimensional antiferromagnetic phase is never stabilized, despite being the leading instability in certain regimes. Our results establish ghost-GA as an efficient and systematically improvable framework for studying magnetism in frustrated systems, capable of achieving near-DMFT accuracy at a fraction of the computational cost. They also highlight that standard GA performs qualitatively well for capturing the general phase diagram, enabling the investigation of incommensurate magnetic orders in more complex systems.

cond-mat.str-el↗

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↗

arXiv2026

The Frenkel line and the pseudogap: an analogy between classical and electronic fluids

Asymptotically close to critical end-points of first-order transitions, maxima in thermodynamic quantities occur along a line called the Widom line, a concept first introduced in classical fluids. This concept has been extended to strongly correlated electronic fluids in the context of the Mott transition. Namely, upon increasing interaction strength in the Hubbard model at half-filling, one finds a first-order Mott metal-insulator transition with a critical endpoint at high temperature, above which several crossover lines are observable. Using the dynamical cluster approximation for the triangular-lattice Hubbard model, we compute a new crossover line, the Frenkel line, a concept borrowed from classical fluids that is useful for defining a sharp crossover between the pseudogap and the correlated Fermi liquid. The Frenkel line in the electron fluid is defined by the appearance of back-scattering upon entering the pseudogap. The signature of back-scattering is the existence of a negative value in the time-domain optical conductivity. The Frenkel line extends to high temperatures.

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

Antiferromagnetic pseudogap in the two-dimensional Hubbard model deep in the renormalized classical regime

Long-wavelength spin fluctuations prohibit antiferromagnetic long-range order at finite temperature in two dimensions. Nevertheless, the correlation length starts to grow rapidly at a crossover temperature, leading to critical slowing down and to a renormalized-classical regime over a wide range of temperature, between a fraction of the mean-field transition temperature and the zero-temperature ordered state. This leads to a single-particle pseudogap of the kind observed in electron-doped cuprates. Very few theoretical methods can claim an accurate description of this regime. The challenge is that in this regime Fermi-liquid quasiparticles are already destroyed and new quasiparticles of the ordered state are not fully formed yet. Here, we study this problem for the two-dimensional Hubbard model by first generalizing the two-particle self-consistent approach. Using a special algorithm, spin fluctuations are treated in the thermodynamic limit even for large correlation lengths. The effects of Kanamori-Brückner screening, of classical and of quantum fluctuations are taken into account. Results are presented at half-filling for the one-band Hubbard model with nearest-neighbor hopping. They agree well with available benchmark diagrammatic quantum Monte Carlo at high temperature where the pseudogap opens up. In addition to temperature-dependent spectral properties, we find quantum corrections to the zero-temperature renormalized mean-field antiferromagnetic gap. Finally, analytic continuation of the Matsubara results for spectral functions show that the pseudogap opens up at significantly higher temperature than was previously identified based on the Matsubara data only.

cond-mat.str-el↗

arXiv2024

Cluster dynamical mean field study of intra-unit-cell charge nematicity in hole-doped cuprates

Recent scanning-tunneling microscopy on hole-doped Bi$_2$Sr$_2$CaCu$_2$O$_8$, one of the materials of the cuprate family, finds a long-range ordered spontaneous splitting of the energy levels of oxygen orbitals inside the CuO$_2$ unit cells [S. Wang et al., Nat. Mat. 23, 492-498 (2024)]. This spontaneous intra-unit-cell orbital ordering, also known as electronic nematicity, breaks $C_4$ symmetry and is thought to arise from the Coulomb interaction (denoted by $V_{pp}$) between oxygen $p_x$ and $p_y$ electrons. In this work, we study the spontaneous emergence of electronic nematicity within the three-band Hubbard (aka the Emery-VSA model), using cluster dynamical mean field theory. This method incorporates short-range electronic correlations and gives us access to the density of states, a quantity that is directly probed in experiments. We argue that there is a delicate competition between $V_{pp}$ and $V_{pd}$ (the latter being the Coulomb interaction between copper $d_{x^2-y^2}$ and oxygen $p_{x,y}$ electrons) that must be taken into account in order to find a Zhang-Rice singlet band well-resolved from the upper Hubbard band, and a splitting of the charge-transfer band (one of the signatures of charge nematicity) by roughly 50 meV, as observed recently.

cond-mat.str-el↗

arXiv2024

Doping the Mott insulating state of the triangular-lattice Hubbard model reveals the Sordi transition

It has been reported that upon doping a Mott insulator, there can be a crossover to a pseudogaped metallic phase followed by a first-order transition to another thermodynamically stable metallic phase. We call this first-order metal-metal transition the Sordi transition. It was argued that the initial reports of Sordi transitions at finite temperature could be explained by finite size effects and biases related to the model and method used. In this work, we report the Sordi transition on larger clusters at finite temperature on a triangular lattice, where long-range antiferromagnetic fluctuations are frustrated, using a different method, the dynamical cluster approximation instead of the cellular dynamical mean-field theory. This demonstrates that this first-order transition is a directly observable transition in doped Mott insulators and that it is relevant for experiments on candidate spin-liquid organic materials.

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↗

arXiv2024

Spin Hall conductivity in the Kane-Mele-Hubbard model at finite temperature

The Kane-Mele model is known to show a quantized spin Hall conductivity at zero temperature. Including Hubbard interactions at each site leads to a quantum phase transition to an XY antiferromagnet at sufficiently high interaction strength. Here, we use the two-particle self-consistent approach (TPSC), which we extend to include spin-orbit coupling, to investigate the Kane-Mele-Hubbard model at finite temperature and half-filling. TPSC is a weak to intermediate coupling approach capable of calculating a frequency- and momentum-dependent self-energy from spin and charge fluctuations. We present results for the spin Hall conductivity and correlation lengths for antiferromagnetic spin fluctuations for different values of temperature, spin-orbit coupling and Hubbard interaction. The vertex corrections, which here are analogues of Maki-Thompson contributions, show a strong momentum dependence and give a large contribution in the vicinity of the phase transition at all temperatures. Their inclusion is necessary to observe the quantization of the spin Hall conductivity for the interacting system in the zero temperature limit. At finite temperature, increasing the Hubbard interaction leads to a decrease of the spin Hall conductivity. This decrease can be explained by band-gap renormalization from scattering of electrons on antiferromagnetic spin fluctuations.

cond-mat.str-el↗

arXiv2023

Strontium Ferrite Under Pressure: Potential Analogue to Strontium Ruthenate

Despite the significant attention it has garnered over the last thirty years, the paradigmatic material strontium ruthenate remains the focus of critical questions regarding strongly correlated materials. As an alternative platform to unravel some of its perplexing characteristics, we propose to study the isostructural and more correlated material strontium ferrite. Using density functional theory combined with dynamical mean-field theory, we attribute the experimentally observed insulating behavior at zero pressure to strong local electronic correlations generated by Mott and Hund's physics. At high pressure, our simulations reproduce the reported insulator-to-metal transition around 18 GPa. Along with distinctive features of a Hund's metal, the resulting metallic state is found to display an electronic structure analogous to that of strontium ruthenate, suggesting that it could exhibit similar low-energy properties.

cond-mat.str-el↗

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↗

arXiv2023

The Two-Particle Self-Consistent Approach for Multiorbital models: application to the Emery model

The Emery model, or three-band Hubbard model, is a Hamiltonian that is thought to contain much of the physics of cuprate superconductors. This model includes two noninteracting $p$ orbitals and one interacting $d$ orbital per unit cell. Few methods that can solve multiorbital interacting Hamiltonians reliably and efficiently exist. Here, we introduce an application of the two particle self-consistent (TPSC) approach to the Emery model. We construct this method within the framework of the TPSC+DMFT method, which can be seen as a way to introduce nonlocal corrections to dynamical mean-field theory (DMFT). We show that interacting orbital densities, rather than the noninteracting ones, must be used in the calculations. For the Emery model, we find that at constant bare interaction $U$, the vertex for spin fluctuations, $U_{sp}$, decreases rapidly with filling. This may be one of the factors that contributes to electron-doped cuprates appearing less correlated than hole-doped ones. More generally, our work opens the road to the application of the TPSC approach to spin fluctuations in multiorbital models.

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