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arXiv:2403.07620

Strong Local Bosonic Fluctuation: The Key to Understanding Strongly Correlated Metals

Syed R. Hassan, Gopal Prakash, N. S. Vidhyadhiraja, T. V. Ramakrishnan

Published Mar 12, 2024• 0 citations
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Abstract

In this paper, we present a theoretical framework for understanding the Extremely Correlated Fermi Liquid (ECFL) phenomenon within the $U=\infty$ Hubbard model. Our approach involves deriving equations of motion for the single-particle Green's function $G$ and its associated self-energy $Σ$, which involves the product of the bosonic correlation function comprising both density ($D_N$) and spin ($D_S$) correlations with $G$. By solving these equations self-consistently, we explore the behavior of $G$, $D_N$, and $D_S$ as functions of frequency, temperature, and hole concentration. Our results reveal distinct coherent and incoherent Fermi liquid regimes characterized by the presence or absence of quasiparticle excitations. Additionally, we analyze the intrinsic dc resistivity $ρ(T)$, observing a crossover from $T^2$ to linear behavior with increasing temperature. Our findings delineate Fermi liquid, quantum incoherent, and `classical' regimes in strongly correlated systems, emphasizing the importance of quantum diffusive local charge and spin fluctuations.

DOI
10.48550/arxiv.2403.07620

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In this paper, we present a theoretical framework for understanding the extremely correlated Fermi liquid (ECFL) phenomenon within the $U=\ensuremath{\infty}$ Hubbard model. Our approach involves deriving equations of motion for the single-particle Green's function $G$ and its associated self-energy $\mathrm{\ensuremath{\Sigma}}$, which involves the product of the bosonic correlation function comprising both density $({D}_{N})$ and spin $({D}_{S})$ correlations with $G$. By solving these equations self-consistently, we explore the behavior of $G$, ${D}_{N}$, and ${D}_{S}$ as functions of frequency, temperature, and hole concentration. Our results reveal distinct coherent and incoherent Fermi liquid regimes characterized by the presence or absence of quasiparticle excitations. Additionally, we analyze the intrinsic dc resistivity $\ensuremath{\rho}(T)$, observing a crossover from ${T}^{2}$ to linear behavior with increasing temperature. Our findings delineate Fermi liquid, quantum incoherent, and ``classical'' regimes in strongly correlated systems, emphasizing the importance of quantum diffusive local charge and spin fluctuations.

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In this paper, we present a theoretical framework for understanding the Extremely Correlated Fermi Liquid (ECFL) phenomenon within the U=∞U=\inftyU=∞ Hubbard model. Our approach involves deriving equations of motion for the single-particle Green's function GGG and its associated self-energy ΣΣΣ, which involves the product of the bosonic correlation function comprising both density (DND_NDN​) and spin (DSD_SDS​) correlations with GGG. By solving these equations self-consistently, we explore the behavior of GGG, DND_NDN​, and DSD_SDS​ as functions of frequency, temperature, and hole concentration. Our results reveal distinct coherent and incoherent Fermi liquid regimes characterized by the presence or absence of quasiparticle excitations. Additionally, we analyze the intrinsic dc resistivity ρ(T)ρ(T)ρ(T), observing a crossover from T2T^2T2 to linear behavior with increasing temperature. Our findings delineate Fermi liquid, quantum incoherent, and `classical' regimes in strongly correlated systems, emphasizing the importance of quantum diffusive local charge and spin fluctuations.
In this paper, we present a theoretical framework for understanding the extremely correlated Fermi liquid (ECFL) phenomenon within the $U=\ensuremath{\infty}$ Hubbard model. Our approach involves deriving equations of motion for the single-particle Green's function GGG and its associated self-energy $\mathrm{\ensuremath{\Sigma}}$, which involves the product of the bosonic correlation function comprising both density (DN)({D}_{N})(DN​) and spin (DS)({D}_{S})(DS​) correlations with GGG. By solving these equations self-consistently, we explore the behavior of GGG, DN{D}_{N}DN​, and DS{D}_{S}DS​ as functions of frequency, temperature, and hole concentration. Our results reveal distinct coherent and incoherent Fermi liquid regimes characterized by the presence or absence of quasiparticle excitations. Additionally, we analyze the intrinsic dc resistivity $\ensuremath{\rho}(T)$, observing a crossover from T2{T}^{2}T2 to linear behavior with increasing temperature. Our findings delineate Fermi liquid, quantum incoherent, and ``classical'' regimes in strongly correlated systems, emphasizing the importance of quantum diffusive local charge and spin fluctuations.
We have developed a semi-analytical framework formulated in the canonical fermion representation to investigate strongly correlated electron systems. We consider the U=∞\infty∞ Hubbard model and used the equation of motion method to calculate the fermion self-energy which has two parts: single and two-boson exchange processes. The emergent bosons here are self-generated local charge and spin-density fluctuations which become strongly time-dependent due to extreme correlations. The computed boson spectral density is a diffusive damped mode with a long tail. The electron self-energy at d=∞d=\inftyd=∞ is computed self-consistently. The corresponding fermionic spectral density displays a pronounced coherence peak at ω=0ω=0ω=0, while its frequency derivative develops a two-peak structure at finite ωωω. The resistivity shows a linear temperature dependence over a broad range, crossing over to coherent Fermi-liquid behavior at extremely low temperatures.
New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.
The Extremely Correlated Fermi Liquids (ECFL) theory is reviewed as a framework for understanding the ttt-JJJ model in metallic systems close to the Mott insulating limit. This overview presents the underlying ideas and the resulting equations in a form accessible to nonexperts. We compare theoretical results with all available resistivity data for single-layer High-Tc_{c}c​ systems, and with some spectral data. The highlighted results include a density dependent quasilinear T-dependence in resistivity, an unusually small quasiparticle weight, and distinct low-temperature emergent scales that dominate transport, thermodynamics and spectral properties of single-layer High Tc_cc​ systems. Suggestions are made for further experiments to probe the physics of these challenging quantum many-body systems.
We study the finite-temperature Fermi-liquid to non-Fermi-liquid crossover in the two-dimensional Hubbard model for a range of dopings using the self-consistent ladder dual fermion method. We consider relatively high temperatures where by comparing the single-particle self-energy and the two-particle spin susceptibility we identify a suppression of the density of states near the Fermi level caused by a quasi-antiferromagnetic behavior that is itself characterized by a long, but finite, correlation length scale which we extract. We compute the single-particle self-energy, and the charge/spin susceptibilities for the entire doping range at relatively high temperature, and also for the half-filled weak-coupling case at relatively low temperatures. We perform fluctuation diagnostics to decompose the single-particle self-energy into scattering qqq-vector and bosonic frequency contributions in the spin channel. Within this framework we find that the key contributions to the single-particle self-energy that give non-Fermi-liquid character show complicated dependence on zero, positive, and negative frequency bosonic modes. We find that for a nominal choice of ${t}^{\ensuremath{'}}$ that electron- and hole-doped systems with similar Fermi-liquid character have distinct spin and charge susceptibility and distinct spin-fluctuation diagnostics spectra.
Extreme correlations arise as the limit of strong correlations, when the local interaction constant UUU goes to infinity. This singular limit transforms canonical fermions to noncanonical Hubbard-type operators with a specific graded Lie algebra replacing the standard anticommutators. We are forced to deal with a fundamentally different and more complex lattice field theory. We study the $t\text{\ensuremath{-}}J$ model, embodying such extreme correlations. We formulate the picture of an extremely correlated electron liquid, generalizing the standard Fermi liquid. This quantum liquid breaks no symmetries, and has specific signatures in various physical properties, such as the Fermi-surface volume and the narrowing of electronic bands by spin- and density-correlation functions. We use Schwinger's source field idea to generate equations for the Green's function for the Hubbard operators. A local (matrix) scale transformation in the time domain to a quasiparticle Green's function is found to be optimal. This transformation allows us to generate vertex functions that are guaranteed to reduce to the bare values for high frequencies, i.e., are ``asymptotically free.'' The quasiparticles are fractionally charged objects, and we find an exact Schwinger-Dyson equation for their Green's function, i.e., the self-energy is given explicitly in terms of the singlet and triplet particle-hole vertex functions. We find a hierarchy of equations for the vertex functions, and further we obtain Ward identities so that systematic approximations are feasible. An expansion in terms of the density of holes measured from the Mott Hubbard insulating state follows from the nature of the theory. A systematic presentation of the formalism is followed by some preliminary explicit calculations. We find a ddd-wave superconducting instability at low TTT that formally resembles that found in the resonating valence-bond theory, but with a much reduced Tc{T}_{c}Tc​.