We study pseudogap behavior in a metal near a spin density wave (SDW) instability due to thermal magnetic fluctuations. We consider the $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model on a square lattice at a finite doping, at intermediate coupling strength, and analyze the thermal evolution of the electron spectral function between a SDW ordered state at low temperatures and a normal Fermi liquid at high temperatures. We argue that for proper description of the pseudogap one needs to sum up infinite series of diagrams for both the fermionic self-energy and the SDW order parameter in the SDW state or the magnetic correlation length in the paramagnetic state. We use the eikonal approach to sum up an infinite series of diagrammatic contributions from thermal fluctuations. Earlier studies found that in the SDW state the spectral function ${A}_{\mathbit{k}}(\ensuremath{\omega})$ of a hot fermion at a finite
T is exponentially small below the energy scale $\mathrm{\ensuremath{\Delta}}(T)$, which scales with SDW order and vanishes at the ordering temperature
TN, and has a hump at a larger frequency ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{PG}}$, comparable to the zero-temperature SDW gap $\mathrm{\ensuremath{\Delta}}(T=0)$. We argue that the hump, which we associate with the pseudogap, survives in some
T range above
TN. We show that this range is split by regions of strong and weak pseudogap behavior. In the first region, ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{PG}}$ is weakly temperature dependent, despite the fact that it comes from thermal fluctuations. Such a behavior has been seen in numerical studies of the Hubbard model. We show that to obtain it one needs to go beyond the one-loop approximation and sum up the infinite series of diagrams. In the second regime, ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{PG}}$ decreases with increasing
T and eventually vanishes. We further argue that a magnetic pseudogap at a finite
T emerges only if the ground state is magnetically ordered. We present the phase diagram and apply the results to high-
Tc cuprates.
Abstract In this paper, we theoretically investigate the effect of temperature on spin correlations in an unpolarized quasi-one-dimensional electron gas (Q1DEG). The correlations are treated dynamically within quantum version of the self-consistent mean-field approach of Singwi et al Numerical results for the ↑↑ and ↑↓ components of static structure factor and pair-correlation function, and the wave vector dependent static spin and charge susceptibilities are presented over a wide range of temperature T and electron coupling r s . We find that the recently reported (2020 J. Phys.: Condens. Matter. 32 335403) non-monotonic T -dependence of the contact pair-correlation function g ( r = 0; T ) is driven primarily by an interplay between ↑↓ correlations and thermal effects. At a given temperature, the dynamics of both ↑↑ and ↑↓ correlations is found to become significant with increasing coupling r s , manifesting unambiguously as pronounced peak at 3.5 k F (periodic oscillations) in the corresponding components of the structure factor (pair-correlation function). Analysis of static spin and charge susceptibilities reveals that an imbalance between ↑↑ and ↑↓ correlations may induce a transition to a spin-density wave (SDW) phase of wave vector ∼3.5 k F above a critical coupling for a sufficiently high T , while to a long-wavelength SDW phase at a low T . Higher the temperature, higher is the predicted critical coupling for the SDW phase. Interestingly, transition to the SDW phase is found to precede the recently predicted Wigner crystal instability in the finite- T Q1DEG. Further, if one starts with partially spin-polarized electrons, the SDW instability is found to shift to somewhat higher τ and r s . In addition, we have presented results for the free exchange-correlation energy, free correlation energy, and excess kinetic energy for the unpolarized and fully spin-polarized phases of the finite- T Q1DEG. Wherever interesting, we have compared our results with the predictions of the static version of the mean-field approach.
We calculate the fermionic spectral function ${A}_{k}(\ensuremath{\omega})$ in the spiral spin density wave (SDW) state of the Hubbard model on a quasi-2D triangular lattice at small but finite temperature
T. The spiral SDW order $\mathrm{\ensuremath{\Delta}}(T)$ develops below
T=TN and has momentum $\mathbf{K}=(4\ensuremath{\pi}/3,0)$. We pay special attention to fermions with momenta
k, for which
k and
k+K are close to Fermi surface in the absence of SDW. At the mean-field level, ${A}_{k}(\ensuremath{\omega})$ for such fermions has peaks at $\ensuremath{\omega}=\ifmmode\pm\else\textpm\fi{}\mathrm{\ensuremath{\Delta}}(T)$ at
T<TN and displays a conventional Fermi liquid behavior at
T>TN. We show that this behavior changes qualitatively beyond mean field due to singular self-energy contributions from thermal fluctuations in a quasi-2D system. We use a nonperturbative eikonal approach and sum up infinite series of thermal self-energy terms. We show that ${A}_{k}(\ensuremath{\omega})$ shows peak/dip/hump features at
T<TN, with the peak position at $\mathrm{\ensuremath{\Delta}}(T)$ and hump position at $\mathrm{\ensuremath{\Delta}}(T=0)$. Above
TN, the hump survives up to
T=Tp>TN, and in between
TN and
Tp the spectral function displays the pseudogap behavior. We show that the difference between
Tp and
TN is controlled by the ratio of in-plane and out-of-plane static spin susceptibilities, which determines the combinatoric factors in the diagrammatic series for the self-energy. For certain values of this ratio,
Tp=TN, i.e., the pseudogap region collapses. In this last case, thermal fluctuations are logarithmically singular, yet they do not give rise to pseudogap behavior. Our computational method can be used to study pseudogap physics due to thermal fluctuations in other systems.
We study the phase diagram of electronic nematic instability in the presence of
xy anisotropy. While a second-order transition cannot occur in this case, mean-field theory predicts that a first-order transition occurs near Van Hove filling and its phase boundary forms a wing structure, which we term a Griffiths wing, referring to his original work of ${\mathrm{He}}^{3}\ensuremath{-}{\mathrm{He}}^{4}$ mixtures. When crossing the wing, the anisotropy of the electronic system exhibits a discontinuous change, leading to a metanematic transition, i.e., the analog to a metamagnetic transition in a magnetic system. The upper edge of the wing corresponds to a critical end line. It shows a nonmonotonic temperature dependence as a function of the external anisotropy and vanishes at a quantum critical end point for a strong anisotropy. The mean-field phase diagram is found to be very sensitive to fluctuations of the nematic order parameter, yielding a topologically different phase diagram. The Griffiths wing is broken into two pieces. A tiny wing appears close to zero anisotropy and the other is realized for a strong anisotropy. Consequently three quantum critical end points are realized. We discuss that these results can be related to various materials including a cold atom system.
We analyze a model of itinerant electrons interacting through a quadrupole density-density repulsion in three dimensions. At the mean-field level, the interaction drives a continuous Pomeranchuk instability towards
d-wave, spin-triplet nematic order, which simultaneously breaks the SU(2) spin-rotation and spatial-rotation symmetries. This order is characterized by spin-antisymmetric, elliptical deformations of the Fermi surfaces of up and down spins. We show that the effects of quantum fluctuations are similar to those in metallic ferromagnets, rendering the nematic transition first order at low temperatures. Using the fermionic quantum order-by-disorder approach to self-consistently calculate fluctuations around possible modulated states, we show that the first-order transition is preempted by the formation of a helical spin-triplet
d-density wave. Such a state is closely related to
d-wave bond density wave order in square-lattice systems. Moreover, we show that it may coexist with a modulated,
p-wave superconducting state.
Interactions in Fermi systems can generate a Pomeranchuk instability leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations and exhibits enhanced collective fluctuations. We analyze fluctuation effects in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. Density correlations with a d-wave form factor and the dynamical forward scattering interaction diverge near the instability. The singular forward scattering leads to large self-energy contributions, which destroy Fermi liquid behavior over the whole Fermi surface except at “cold spots” on the Brillouin zone diagonal. The decay rate of single-particle excitations, which is related to the width of the peaks in the spectral function, exceeds the excitation energy in the low-energy limit. The dispersion of the spectra flattens strongly near those portions of the Fermi surface which are remote from the zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots. We discuss the possible relevance of d-wave Fermi surface fluctuations for the “strange metal” behavior observed in the normal phase of cuprates.