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arXiv:cond-mat/9801004 · Physical review. B, Condensed matter

Marginal Fermi liquid in a lattice of three-body bound states

A. F. Ho, Piers Coleman

Published Aug 15, 1998• 6 citations
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Abstract

We study a lattice model for marginal Fermi-liquid behavior, involving a gas of electrons coupled to a dense lattice of three-body bound states. The presence of the bound states changes the phase space for electron-electron scattering and induces a marginal self-energy among the electron gas. When the three-body bound states are weakly coupled to the electron gas, there is a substantial window for marginal Fermi-liquid behavior and in this regime, the model displays the presence of two relaxation times, one linear, one quadratic in the temperature. At low temperatures the bound states develop coherence, leading to a crossover to conventional Fermi-liquid behavior. At strong coupling, marginal Fermi-liquid behavior is preempted by a pairing or magnetic instability, and it is not possible to produce a linear scattering rate comparable with the temperature. We discuss the low-temperature instabilities of this model and compare it to the Hubbard model at half filling.

DOI
10.1103/physrevb.58.4418

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We study a lattice model for marginal Fermi-liquid behavior, involving a gas of electrons coupled to a dense lattice of three-body bound states. The presence of the bound states changes the phase space for electron-electron scattering and induces a marginal self-energy among the electron gas. When the three-body bound states are weakly coupled to the electron gas, there is a substantial window for marginal Fermi-liquid behavior and in this regime, the model displays the presence of two relaxation times, one linear, one quadratic in the temperature. At low temperatures the bound states develop coherence, leading to a crossover to conventional Fermi-liquid behavior. At strong coupling, marginal Fermi-liquid behavior is preempted by a pairing or magnetic instability, and it is not possible to produce a linear scattering rate comparable with the temperature. We discuss the low-temperature instabilities of this model and compare it to the Hubbard model at half filling.
We present a numerical study on the non-Fermi liquid behavior of a three-dimensional strongly correlated system. The Hubbard model in a simple cubic lattice is simulated by the dynamical cluster approximation; in particular, the quasi-particle weight is calculated at finite dopings for a range of temperatures. By fitting the quasi-particle weight to the marginal Fermi liquid form at finite doping near the putative quantum critical point, we find evidence of a separatrix between Fermi liquid and non-Fermi liquid regions. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point exist in the non-symmetry broken solution of the three-dimensional interacting electron systems. We also calculate the spectral function, close to the half-filling, and we obtain evidence of pseudogap.
We construct examples of translationally invariant solvable models of strongly correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi-liquid behavior. In the marginal-Fermi-liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi surfaces. The self-energy has a singular frequency dependence but lacks momentum dependence, reminiscent of a dynamical mean-field-theory-like behavior but in dimensions d < ∞. In the low-temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi surface in the non-Fermi-liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse-grained descriptions of a class of intermediate-scale non-Fermi-liquid behavior in generic correlated metals.
We investigate quantitatively the effects of strong electron-electron coupling onto the dynamics of lattice electrons. To that purpose the self-consistent version of the bubble-chain approximation at zero temperature and half filling of the Anderson (Hubbard) model is used. Special attention is paid to a critical region of an electron-hole correlation function shaping the transition from weak to strong interaction. We find an analytic solution with Fermi-liquid properties on the weak-coupling side of the critical region around the two-particle pole. It is shown that Fermi-liquid theory does not lead to a consistent behavior of the self-consistent solution on the strong-coupling side of the critical region.
We study the dilute-gas expansion for a two-dimensional Fermi system with arbitrary short-range repulsive interactions. In contrast with the three-dimensional case, we find an unusual pole in the vertex part in the particle-particle channel, for all center-of-mass momenta q2kF{\mathit{k}}_{\mathit{F}}kF​. We show that this represents an excitation consisting of bound hole pairs, which disperses down to zero energy at q=2kF{\mathit{k}}_{\mathit{F}}kF​. We study the effect of these bound states on the single-particle self-energy and find that the quasiparticles are well defined. Thus in the low-density regime, there is no breakdown of Fermi-liquid theory. In the Appendix we discuss the two-particle phase shift in the dilute Fermi gas, its connection with bound states, and the analogy with the potential scattering phase shift.
We find marginal-Fermi-liquid- (MFL) like behavior in the Hubbard model on a square lattice for a range of hole doping and on-site interaction parameter U. Thereby we use a self-consistent projection operator method. It enables us to compute the momentum and frequency dependence of the single-particle excitations with high resolution. The Fermi surface is found to be holelike in the underdoped regime and electronlike in the overdoped regime. Our calculations concern normal state properties of the system. When a comparison is possible, we find consistency with finite temperature quantum Monte Carlo results. We also find a discontinuous change with doping concentration from a MFL to a Fermi-liquid behavior resulting from a collapse of the lower Hubbard band. This renders Luttinger's theorem inapplicable in the underdoped regime.
We investigate quantitatively the effects of strong electron - electron coupling on the dynamics of lattice electrons. For this purpose the self-consistent version of the bubble-chain approximation at zero temperature and half filling of the Anderson (Hubbard) model is used. Special attention is paid to a critical region of an electron - hole correlation function shaping the transition from weak to strong interaction. We find an analytic solution with Fermi-liquid properties on the weak-coupling side of the critical region around the two-particle pole. It is shown that Fermi-liquid theory does not lead to a consistent behaviour of the self-consistent solution on the strong-coupling side of the critical region.