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arXiv:1703.02206 · Physical review. B./Physical review. B

Strange metal from Gutzwiller correlations in infinite dimensions

Wenxin Ding, Rok Žitko, Peizhi Mai, Edward Perepelitsky, B. Sriram Shastry

Published Aug 18, 2017• 13 citations
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Abstract

Recent progress in extremely correlated Fermi liquid theory (ECFL) and the dynamical mean field theory (DMFT) enables us to accurately compute in the $d\ensuremath{\rightarrow}\ensuremath{\infty}$ limit the resistivity of the $t\ensuremath{-}J$ model after setting $J\ensuremath{\rightarrow}0$. This is also the $U=\ensuremath{\infty}$ Hubbard model. Since $J$ is set to zero, our study isolates the dynamical effects of the single occupation constraint enforced by the projection operator originally introduced by Gutzwiller. We study three densities $n=.75,.8,.85$ that correspond to a range between the overdoped and optimally doped Mott insulating state. We delineate four distinct regimes separated by three crossovers, which are characterized by different behaviors of the resistivity $\ensuremath{\rho}$. We find at the lowest temperature $T$ a Gutzwiller correlated Fermi liquid regime with $\ensuremath{\rho}\ensuremath{\propto}{T}^{2}$ extending up to an effective Fermi temperature that is dramatically suppressed from the noninteracting value by the proximity to half filling, $n\ensuremath{\sim}1$. This is followed by a Gutzwiller correlated strange metal regime with $\ensuremath{\rho}\ensuremath{\propto}(T\ensuremath{-}{T}_{0})$, i.e., a linear resistivity extrapolating back to $\ensuremath{\rho}=0$ at a positive ${T}_{0}$. At a higher temperature scale this crosses over into the bad metal regime with $\ensuremath{\rho}\ensuremath{\propto}(T+{T}_{1})$, i.e., a linear resistivity extrapolating back to a finite resistivity at $T=0$ and passing through the Ioffe-Regel-Mott value where the mean free path is a few lattice constants. This regime finally gives way to the high $T$ metal regime, where we find $\ensuremath{\rho}\ensuremath{\propto}T$, i.e., a linear resistivity extrapolating back to zero at $T=0$. The present work emphasizes the first two, i.e., the two lowest temperature regimes, where the availability of an analytical ECFL theory is of help in identifying the changes in related variables entering the resistivity formula that accompanies the onset of linear resistivity, and the numerically exact DMFT helps to validate the results. We also examine thermodynamical variables such as the magnetic susceptibility, compressibility, heat capacity, and entropy and correlate changes in these with the change in resistivity. This exercise casts valuable light on the nature of charge and spin correlations in the Gutzwiller correlated strange metal regime, which has features in common with the physically relevant strange metal phase seen in strongly correlated matter.

DOI
10.1103/physrevb.96.054114

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Recent progress in extremely correlated Fermi liquid theory (ECFL) and the dynamical mean field theory (DMFT) enables us to accurately compute in the d\ensuremath→\ensuremath∞d\ensuremath{\rightarrow}\ensuremath{\infty}d\ensuremath→\ensuremath∞ limit the resistivity of the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model after setting J\ensuremath→0J\ensuremath{\rightarrow}0J\ensuremath→0. This is also the U=\ensuremath∞U=\ensuremath{\infty}U=\ensuremath∞ Hubbard model. Since JJJ is set to zero, our study isolates the dynamical effects of the single occupation constraint enforced by the projection operator originally introduced by Gutzwiller. We study three densities n=.75,.8,.85n=.75,.8,.85n=.75,.8,.85 that correspond to a range between the overdoped and optimally doped Mott insulating state. We delineate four distinct regimes separated by three crossovers, which are characterized by different behaviors of the resistivity \ensuremathρ\ensuremath{\rho}\ensuremathρ. We find at the lowest temperature TTT a Gutzwiller correlated Fermi liquid regime with \ensuremathρ\ensuremath∝T2\ensuremath{\rho}\ensuremath{\propto}{T}^{2}\ensuremathρ\ensuremath∝T2 extending up to an effective Fermi temperature that is dramatically suppressed from the noninteracting value by the proximity to half filling, n\ensuremath∼1n\ensuremath{\sim}1n\ensuremath∼1. This is followed by a Gutzwiller correlated strange metal regime with \ensuremathρ\ensuremath∝(T\ensuremath−T0)\ensuremath{\rho}\ensuremath{\propto}(T\ensuremath{-}{T}_{0})\ensuremathρ\ensuremath∝(T\ensuremath−T0​), i.e., a linear resistivity extrapolating back to \ensuremathρ=0\ensuremath{\rho}=0\ensuremathρ=0 at a positive T0{T}_{0}T0​. At a higher temperature scale this crosses over into the bad metal regime with \ensuremathρ\ensuremath∝(T+T1)\ensuremath{\rho}\ensuremath{\propto}(T+{T}_{1})\ensuremathρ\ensuremath∝(T+T1​), i.e., a linear resistivity extrapolating back to a finite resistivity at T=0T=0T=0 and passing through the Ioffe-Regel-Mott value where the mean free path is a few lattice constants. This regime finally gives way to the high TTT metal regime, where we find \ensuremathρ\ensuremath∝T\ensuremath{\rho}\ensuremath{\propto}T\ensuremathρ\ensuremath∝T, i.e., a linear resistivity extrapolating back to zero at T=0T=0T=0. The present work emphasizes the first two, i.e., the two lowest temperature regimes, where the availability of an analytical ECFL theory is of help in identifying the changes in related variables entering the resistivity formula that accompanies the onset of linear resistivity, and the numerically exact DMFT helps to validate the results. We also examine thermodynamical variables such as the magnetic susceptibility, compressibility, heat capacity, and entropy and correlate changes in these with the change in resistivity. This exercise casts valuable light on the nature of charge and spin correlations in the Gutzwiller correlated strange metal regime, which has features in common with the physically relevant strange metal phase seen in strongly correlated matter.
Using two approaches to strongly correlated systems, the extremely correlated Fermi liquid theory and the dynamical mean field theory, we compute the transverse transport coefficients, namely, the Hall constants RH{R}_{H}RH​ and Hall angles ${\ensuremath{\theta}}_{H}$, and the longitudinal and transverse optical response of the $U=\ensuremath{\infty}$ Hubbard model in the limit of infinite dimensions. We focus on two successive low-temperature regimes, the Gutzwiller-correlated Fermi liquid (GCFL) and the Gutzwiller-correlated strange metal (GCSM). We find that the Hall angle $cot{\ensuremath{\theta}}_{H}$ is proportional to T2{T}^{2}T2 in the GCFL regime, while upon warming into the GCSM regime it first passes through a downward bend and then continues as T2{T}^{2}T2. Equivalently, RH{R}_{H}RH​ is weakly temperature dependent in the GCFL regime, but becomes strongly temperature dependent in the GCSM regime. Drude peaks are found for both the longitudinal optical conductivity ${\ensuremath{\sigma}}_{xx}(\ensuremath{\omega})$ and the optical Hall angles $tan{\ensuremath{\theta}}_{H}(\ensuremath{\omega})$ below certain characteristic energy scales. By comparing the relaxation rates extracted from fitting to the Drude formula, we find that in the GCFL regime there is a single relaxation rate controlling both longitudinal and transverse transport, while in the GCSM regime two different relaxation rates emerge. We trace the origin of this behavior to the dynamical particle-hole asymmetry of the Dyson self-energy, arguably a generic feature of doped Mott insulators.
Strange or bad metallic transport, defined by incompatibility with the conventional quasiparticle picture, is a theme common to many strongly correlated materials, including high-temperature superconductors. The Hubbard model represents a minimal starting point for modeling strongly correlated systems. Here we demonstrate strange metallic transport in the doped two-dimensional Hubbard model using determinantal quantum Monte Carlo calculations. Over a wide range of doping, we observe resistivities exceeding the Mott-Ioffe-Regel limit with linear temperature dependence. The temperatures of our calculations extend to as low as 1/40 of the noninteracting bandwidth, placing our findings in the degenerate regime relevant to experimental observations of strange metallicity. Our results provide a foundation for connecting theories of strange metals to models of strongly correlated materials.
We present the $O({\ensuremath{\lambda}}^{3})$ results from the $\ensuremath{\lambda}$ expansion in the extremely correlated Fermi-liquid theory applied to the infinite-dimensional $t\ensuremath{-}J$ model (with J=0J=0J=0) and compare the results with the earlier $O({\ensuremath{\lambda}}^{2})$ results as well as the results from the dynamical mean-field theory. We focus attention on the TTT dependence of the resistivity $\ensuremath{\rho}(T)$, the Dyson self-energy, and the quasiparticle weight ZZZ at various densities. The comparison shows that all the methods display quadratic-in-TTT resistivity followed by a quasilinear-in-TTT resistivity characterizing a strange metal and gives an estimate of the different scales of these variables relative to the exact results.
Metallic quantum states coined strange metal (SM), with robust linear-TTT resistivity, have been widely observed in many quantum materials under strong electron correlations, ranging from high-Tc{T}_{c}Tc​ cuprate superconductors and organic superconductors to twisted multilayer graphene and MoTe2/WSe2{\mathrm{MoTe}}_{2}/{\mathrm{WSe}}_{2}MoTe2​/WSe2​ superlattices. Despite decades of intensive studies, the mystery of SM still defies any sensible theoretical explanation and has been a key puzzle in modern condensed matter physics. Here, we solve a doped Mott insulator model called an Ising-Kondo lattice, which includes static spin fluctuation. With Monte Carlo simulation, the Ising-Kondo lattice unambiguously exhibits SM phenomena accompanied with quantum critical scaling in observables, e.g., resistivity, susceptibility, and specific heat. A closer look at SM reveals the breakdown of Landau's Fermi liquid theory without any symmetry breaking, i.e., the violation of Luttinger theorem. Our paper reveals that the long-overlooked static fluctuations in literature may play an essential role in non-Fermi liquid behaviors in correlated electron systems.
Bad metals exhibit approximately TTT-linear dc resistivity beyond the Ioffe--Regel limit. That this behavior occurs in systems with radically different ground states suggests it is a generic manifestation of strong local correlations. We test this hypothesis in the infinite-UUU Hubbard model with small hole densities using exact diagonalization to compute thermodynamic and transport properties of finite clusters. Upon cooling, we find an intermediate temperature range, an electronic analogue of the ``semi-quantum regime'' of liquid helium, in which quantum effects produce a roughly TTT-independent compressibility, yet the resistivity is TTT-linear and exceeds the Ioffe--Regel limit. Entry into this regime is accompanied by the formation of quasi-local ferromagnetic ``spin cages'' around doped holes, regions that facilitate local quantum motion embedded in a fluctuating spin background, analogous to the transient crystalline cages thought to control incoherent transport in semi-quantum liquid helium. Remarkably, despite the simplicity of the model, the bad metal behavior found here resembles that seen in various material platforms.
The strange metal is an enigma within the field of many-body quantum physics, as it defies the standard Fermi liquid theory of metals due to the absence of well-defined, electron-like quasiparticles. It has been presumed that strange metal behavior arises due to strong correlations between electrons that are not present in ordinary Fermi liquids, but the exact nature of these correlations is unknown. To this end, this thesis aims to address the fundamental question: What, precisely, is so strongly correlated about charge in the strange metal? This question is tackled by experimentally measuring the dynamic charge response function, which directly encodes charge correlations in momentum and energy, using the technique of Momentum-resolved Electron Energy-loss Spectroscopy (M-EELS). In particular, two prototypical members of the cuprate and ruthenate strange metal families are studied: Bi-2212 and Sr2_22​RuO4_44​. By studying Bi-2212 at optimal doping, it is found that the charge response of the strange metal is characterized by a broad continuum of fluctuations that are momentum and energy independent over a large range of parameter space, unlike Fermi liquid charge correlations which exhibit propagating density waves of charge with well defined energy and momentum (i.e. plasmons). We argue that, in essence, the charge correlations of the strange metal are highly localized in both space and time, unlike the Fermi Liquid where they are localized in momentum and energy instead. To understand how charge correlations change as one leaves the strange metal regime, the M-EELS response of Bi-2212 is mapped out as a function of doping and temperature. At high temperature, it is found that the continuum is largely doping independent. However, upon cooling, very large changes in spectral weight are observed over a range of energy scales nearly two orders of magnitude larger than the thermal scale kBTk_B TkB​T. Moreover, this change in spectral weight undergoes a sign reversal as a function of doping, with spectral weight enhancement on the underdoped side, suppression in the overdoped regime, and no change at optimal doping. These changes in spectral weight are completely unlike the case of the Fermi liquid, where doping only acts to rigidly shift the plasmon energy and no significant changes occur as a function of temperature. Finally, we venture further and ask whether strange metal and Fermi liquid charge correlations can simultaneously coexist in a material. To explore this possibility, we measured the M-EELS response of Sr2_22​RuO4_44​, a material which exhibits strange and bad metal behavior at high temperature, but transitions to a well-defined Fermi liquid at low temperature. Surprisingly, in the strange metal regime, Sr2_22​RuO4_44​ exhibits both a broad continuum similar to Bi-2212 and a propagating Fermi liquid collective mode at low-energies and momentum. Upon cooling, low-energy spectral weight is suppressed in the strange metal continuum and the Fermi liquid collective mode velocity is strongly renormalized. These findings confirm the strange metal and Fermi liquid can coexist and demonstrate that Sr2_22​RuO4_44​ exhibits charge correlations with strange metal character at high energies and short length scales and Fermi liquid character at low energies and long wavelengths.