Insulating spin liquid in the lightly doped two-dimensional Hubbard model

Abstract

We calculate the charge compressibility and uniform spin susceptibility for the two-dimensional (2D) Hubbard model slightly away from half-filling within a two-loop renormalization group scheme. We find numerically that both those quantities flow to zero as we increase the initial interaction strength from weak to intermediate couplings. This result implies gap openings in both charge and spin excitation spectra for the latter interaction regime. When this occurs, the ground state of the lightly doped 2D Hubbard model may be interpreted as an insulating spin liquid as opposed to a Mott insulating state.PACS numbers: 71.10. Hf, 71.10.Pm, 71.27.+a After two decades of intensive research on the highTc superconductors, physicists are still puzzled by some of their very unusual electronic properties 1 . The prominent example is given by the cuprates. At zero doping, despite the fact that their highest occupied band is halffilled, they are charge insulators, and display antiferromagnetic long-range order. For this reason, they are said to be Mott insulators. As soon as one starts doping those compounds with holes, the long-range magnetic order becomes rapidly suppressed, and there are experimental evidences of an emergence of a spin gap in their corresponding excitation spectra 2 . A charge gap is also observed by ARPES experiments in such lightly-doped systems 3 . Moreover, at finite temperatures, they turn themselves into poor conductors with electronic properties differing considerably from the predictions of Landau's Fermi liquid theory. This scenario configures the so-called pseudogap regime. Although this phase continues to be not well understood, it is widely acknowledged to play a fundamental role in the underlying microscopic mechanism of such high-Tc superconductors. Indeed, upon some further doping, those poor metals become superconducting with d-wave symmetry up to relatively high temperatures around the optimal doping level.From the theoretical viewpoint, it is widely accepted that the appropriate model for describing such systems is the two-dimensional (2D) Hubbard model (HM), since it is known to have a Mott insulating phase at half-filling, and is expected to become a d-wave superconductor at larger doping 4 . However, its intermediate doping regime, which could provide some insight to understand the physical nature of the pseudogap state, still remains elusive to this date. In this Letter we intend to address this question using renormalization group (RG) techniques in order to infer about the ground state of such model for electron densities slightly away from the half-filling limit.Our considerations here will be based on a complete two-loop RG calculation of the uniform charge (CS) and spin (SS) susceptibilities of the 2D HM, taking into account simultaneously both the renormalization of the couplings, and the self-energy effects. (The CS is also called the charge compressibility of the system.) To best of our knowledge, it is the first time that such a full two-loop RG calculation is performed ...

Renormalization group calculation of the uniform susceptibilities in low-dimensional systems

“…Notice that, for moderate initial couplings with Z going to zero, the susceptibilities become strongly suppressed in the same lowenergy limit in markedly contrast to the 1D case, where they remain finite. Therefore, our result adds further support to the interpretation that the low-energy effective theory for those cases should be a fully gapped state in both charge and spin excitation spectra [14]. Since such an effective theory has only gapful excitations present, it cannot be related to any spontaneously broken symmetry state.…”

“…This result means that those systems belong to the same universality class of a strongly coupled theory, whose detailed information must be determined from a consistent RG calculation of other quantities such as the uniform susceptibilities as we have done explicitly for the 1D HM case. In fact, we will see here that the suppression of the quasiparticle weight of the system will produce interesting effects in the RG flows of those quantities [14].…”

“…To compute the RG flow equations of these response functions, one needs to recall that the bare parameters are independent of the renormalization scale ω. Thus, using the RG condition ωdT α /dω = 0, we obtain [14]…”