The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, Q N , connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from Q N is given by χ − 1 ∝ | Δ q | . Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a χ − 1 ∝ | Δ q | 2 dependence yields a robust finite- T scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the ( t − t ′ ) Hubbard model and found that at large U / t > 5.5 before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by χ − 1 ∝ | Δ q | 2 . Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state. Published by the American Physical Society 2024
The spin-fermion (SF) model postulates that the dominant coupling between low-energy fermions in near critical metals is mediated by collective spin fluctuations (paramagnons) peaked at the Néel wave vector, Q N , connecting hot spots on opposite sides of the Fermi surface. It has been argued that strong correlations at hot spots lead to a Fermi surface deformation (FSD) featuring flat regions and increased nesting. This conjecture was confirmed in the perturbative self-consistent calculations when the paramagnon propagator dependence on momentum deviation from Q N is given by χ − 1 ∝ | Δ q | . Using diagrammatic Monte Carlo (diagMC) technique we show that such a dependence holds only at temperatures orders of magnitude smaller than any other energy scale in the problem, indicating that a different mechanism may be at play. Instead, we find that a χ − 1 ∝ | Δ q | 2 dependence yields a robust finite- T scenario for achieving FSD. To link phenomenological and microscopic descriptions, we applied the connected determinant diagMC method to the ( t − t ′ ) Hubbard model and found that at large U / t > 5.5 before the formation of electron and hole pockets (i) the FSD defined as a maximum of the spectral function is not very pronounced; instead, it is the lines of zeros of the renormalized dispersion relation that deforms toward nesting, and (ii) the static spin susceptibility is well described by χ − 1 ∝ | Δ q | 2 . Flat FS regions yield a nontrivial scenario for realizing a non-Fermi liquid state. Published by the American Physical Society 2024
Many correlated materials display a quantum-critical point between a paramagnetic and a spin-density wave (SDW) state. The SDW wave vector connects points, so-called hot spots, on opposite sides of the Fermi surface. The Fermi velocities at these pairs of points are in general not parallel. Here, we consider the case where pairs of hot spots coalesce, and the wave vector $(\ensuremath{\pi},\ensuremath{\pi})$ of the SDW connects hot spots with parallel Fermi velocities. Using the specific example of electron-doped cuprates, we first show that Kanamori screening and generic features of the Lindhard function make this case experimentally relevant. The temperature dependence of the correlation length, the spin susceptibility, and the self-energy at the hot spots are found using the two-particle self-consistent theory and specific numerical examples worked out for band and interaction parameters characteristic of the electron-doped cuprates. While the curvature of the Fermi surface at the hot spots leads to deviations from perfect nesting, the pseudonesting conditions lead to drastic modifications of the temperature dependence of these physical observables: Neglecting logarithmic corrections, the correlation length $\ensuremath{\xi}$ scales like 1/T, namely, z=1 instead of the naive z=2, the $(\ensuremath{\pi},\ensuremath{\pi})$ static spin susceptibility $\ensuremath{\chi}$ like 1/T, and the imaginary part of the self-energy at the hot spots like T3/2. The correction ${T}_{1}^{\ensuremath{-}1}\ensuremath{\sim}{T}^{3/2}$ to the Korringa NMR relaxation rate is subdominant. We also consider this problem at zero temperature, or for frequencies larger than temperature, using a field-theoretical model of gapless collective bosonic modes (SDW fluctuations) interacting with fermions. The imaginary part of the retarded fermionic self-energy close to the hot spots scales as $\ensuremath{-}{\ensuremath{\omega}}^{3/2}\mathrm{ln}\ensuremath{\omega}$. This is less singular than earlier predictions of the form $\ensuremath{-}\ensuremath{\omega}\mathrm{ln}\ensuremath{\omega}$. The difference arises from the effects of umklapp terms that were not included in previous studies.
Exact diagrammatic quantum Monte Carlo (DiagMC) results for the nearest-neighbor Hubbard model motivate a closer study of the pseudogap. Using the improved two-particle self-consistent approach (TPSC+), we analyze Energy (EDC) and Momentum Distribution Curves (MDC) simultaneously. We show that Fermi-liquid terminology breaks down in the pseudogap regime, requiring a distinction between true and false Fermi surfaces and zero-energy quasiparticle (ZEQ) lines. A false Fermi surface has a momentum-space spectral maximum but a frequency-space depression at zero energy, while a false ZEQ line violates the standard quasiparticle condition ∂Σ′(k,ω)/∂ω∣ω=0<0.The pseudogap is driven by critical thermal spin fluctuations, which occur in two dimensions because of the Mermin-Wagner theorem. Commensurate fluctuations first open an antinodal pseudogap, leaving true Fermi arcs. With decreasing temperature, the Fermi surface evolves into hole- and electron-like false Fermi surfaces. Incommensurate fluctuations generate hot spots near the diagonal, where the pseudogap persists to the quantum critical point (QCP), whereas at kAN it disappears before the QCP doping. There, the spectrum has two precursor antiferromagnetic (AFM) bands, both in the unoccupied (ω>0) region. We benchmark TPSC+ against DiagMC results for the Matsubara spectral proxy −Im[G(k,iπT)]/π. TPSC+ underestimates pseudogap suppression in the strong-interaction regime, reproducing DiagMC behavior at lower temperatures or doping. This proxy is equivalent to the spectral function with thermal broadening η=πT, which obscures features when πT is not the smallest energy scale. Using A(k,0), we find that hole-like Fermi surfaces emerge at any interaction strength at low temperature, even at weak coupling.
We analyze quantum fluctuation effects at the onset of incommensurate 2 k F charge- or spin-density-wave order in two-dimensional metals for a model in which the ordering wave vector Q connects a single pair of hot spots on the Fermi surface with a vanishing Fermi surface curvature. The tangential momentum dependence of the bare dispersion near the hot spots is proportional to | k t | α with α > 2 . We first compute the order parameter susceptibility and the fermion self-energy in a random phase approximation (RPA). Logarithmic divergences are subsequently treated by a renormalization-group analysis. The coupling between the order parameter fluctuations and the fermions vanishes logarithmically in the low-energy limit. As a consequence, the logarithmic divergences found in the RPA do not sum up to anomalous power laws. Instead, only logarithmic corrections to Fermi liquid behavior are obtained. In particular, the quasiparticle weight and the Fermi velocity vanish logarithmically at the hot spots. Published by the American Physical Society 2024
We present a renormalization group (RG) analysis of a fermionic ``hot-spot'' model of interacting electrons on the square lattice. We truncate the Fermi-surface excitations to linearly dispersing quasiparticles in the vicinity of eight hot spots on the Fermi surface, with each hot spot separated from another by the wave vector $(\ensuremath{\pi},\ensuremath{\pi})$. This is motivated by the importance of these Fermi-surface locations to the onset of antiferromagnetic order; however, we allow for all possible quartic interactions between the fermions, and also for all possible ordering instabilities. We compute the RG equations for our model, which depend on whether or not the hot spots are perfectly nested, and relate our results to earlier models. We also compute the RG flow of the relevant order parameters for both Hubbard and J,V interactions, and present our results for the dominant instabilities in the nested and non-nested cases. In particular, we find that non-nested hot spots with J,V interactions have competing singlet ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting and d-form factor incommensurate density wave instabilities. We also investigate the enhancement of incommensurate density waves near experimentally observed wave vectors, and find dominant d-form factor enhancement for a range of couplings.
In this thesis we try to understand the unconventional superconducting mechanism on cuprates and organic superconductors (or sodium cobaltates) which can be modeled by a two-dimensional square- and triangular-lattice Hubbard model respectively. The formation of the superconducting dome requires explanations of feasible scenarios. Generally speaking, pairing strength is provided by magnetic fl_x001D_uctuations in the strongly correlated region and the structure of the Fermi surface in this region will favor superconducting pairings with a certain type of symmetry. For the cuprate physics, a superconducting dome composed of d-wave pairings has been identified experimentally. We study the Hubbard model on square lattices and _x001C_find that the pairing strength is originated from anti-ferromagnetic instabilities, and the nearly nested Fermi surface with the square symmetry further supports the d-wave pairing. Moreover, our results show there is a quantum critical point (QCP) beneath the superconducting dome. The QCP is a zero-temperature instability which separates the Fermi liquid and pseudogap regions and exhibits the quantum _x001D_fluctuations which may lead to a high superconducting transition temperature. Above the QCP, a V-shape marginal Fermi liquid region associated with the quantum critical phenomena is also identi_x001C_fied. Using next-nearest-neighbor hopping, chemical potential, and temperature as control parameters, there is a line of Lifshitz transition associated with the change of topology of the Fermi surface. Along the Lifshitz line with t'<=0, the marginal Fermi liquid region prevails, the peak of density of states crosses the Fermi level, and the bare d-wave pairing susceptibility shows a universal scaling with the exponent consistent with theoretical proposals. For the triangular-lattice Hubbard model in the strongly correlated region, we _x001C_find a d+id superconducting pairing on the hole-doped side of the phase diagram. Here the pairing strength comes from the instabilities of the anti-ferromagnetic order (120-degree-spin structure), and the nested hexagon-deformed Fermi surface with the triangular symmetry further boosts the d+id symmetry. Due to the strong competition between electronic interactions and geometric frustrations, the superconductivity and other novel features of the system equal to or above half fi_x001C_lling requires future studies. The numerical tool we apply to study these systems is the dynamical cluster approximation with continuous-time quantum Monte Carlo as the solver. Our approach includes nonlocal correlations embedded in a mean _x001C_field host and is a most up-to-date and reliable approach in dealing with the above mentioned strongly correlated systems valid in the thermodynamic limit. Our _x001C_findings shine light on future investigations of the nature
While many-body effects in flat-band systems are receiving renewed hot interest in condensed-matter physics for superconducting and topological properties as well as for magnetism, studies have primarily been restricted to multiband systems (with coexisting flat and dispersive bands). Here we focus on one-band systems where a band is ``partially flat,'' comprising flat and dispersive portions in k space to reveal whether intriguing correlation effects can already arise on the simplest possible one-band level. For that, the two-dimensional repulsive Hubbard model is studied for two models having different flat areas in an intermediate-coupling regime with the dynamical mean-field theory combined with the fluctuation exchange approximation. We have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied and this triggers, for the model with a wider flat portion, a triplet-pair superconductivity favored over an unusually wide filling region, which is taken over by a sharply growing singlet pairing. For the model with a narrower flat portion, TC against filling exhibits an unusual double-peaked TC dome, associated with different numbers of nodes in the gap function having remarkably extended pairs in real space. We identify these as a manifestation of the physics outside the conventional nesting physics where only the pair scattering across the Fermi surface in designated (hot) spots is relevant. Another correlation effect arising from the flattened band is found in a non-Fermi-liquid behavior as detected in the momentum distribution function, frequency dependence of the self-energy, and spectral function. These indicate that unusual correlation physics can indeed occur in flat-band systems.