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We revisit the somewhat less studied problem of Yang-Lee zeros of the Ising antiferromagnet. For this purpose, we study two models, the nearest-neighbor model on a square lattice, and the more tractable mean-field model corresponding to infinite-ranged coupling between all sites. In the high-temperature limit, we show that the logarithm of the Yang-Lee zeros can be written as a series in half odd integer powers of the inverse temperature, $k$, with the leading term $\sim k^{1/2}$. This result is true in any dimension and for arbitrary lattices. We also show that the coefficients of the expansion satisfy simple identities (akin to sum rules) for the nearest-neighbor case. These new identities are verified numerically by computing the exact partition function for a 2D square lattice of size $16\times16$. For the mean-field model, we write down the partition function (termed the mean-field polynomials) for the ferromagnetic (FM) and antiferromagnetic (AFM) cases, and derive from them the mean-field equations. We analytically show that at high temperatures the zeros of the AFM mean-field polynomial scale as $\sim k^{1/2}$ as well. Using a simple numerical method, we find the roots lie on certain curves (the root curves), in the thermodynamic limit for the mean-field polynomials for the AFM case as well as for the FM one. Our results show a new root curve, that was not found earlier. Our results also clearly illustrate the phase transition expected for the FM and AFM cases, in the language of Yang-Lee zeros. Moreover, for the AFM case, we observe that the root curves separate two distinct phases of zero and non-zero complex staggered magnetization, and thus depict a complex phase boundary.

Motivated by recent experiments, we append long ranged Coulomb interactions to dominant strong local correlations and study the resulting $t$-$J$-$V_C$ model for the 2-dimensional cuprate materials. This model includes the effect of short ranged Hubbard-Gutzwiller-Kanamori type correlations and long ranged Coulomb interactions on tight binding electrons. We calculate the $ \{\vec{q},\omega\}$ dependent charge density fluctuations in this model using the extremely correlated fermi liquid theory, characterized by quasiparticles with very small weight $Z$. We develop a novel set of formulae to represent the dynamical charge susceptibility and the dielectric function, using a version of the charge-current continuity equation for a band system valid for arbitrary $\vec{q}$. Combining these ingredients, we present results for the dynamical charge susceptibility $\widetilde{\chi}_{\rho\rho}(\vec{q},\omega)$, (longitudinal) dielectric function $\varepsilon(\vec{q},\omega)$, current susceptibility $\widetilde{\chi}_{J J}(\vec{q},\omega)$, conductivity $\sigma(\vec{q},\omega)$, and the plasma frequency for any $\vec{q}$. We also present calculations for the first moment of the structure function and discuss a characteristic energy scale $\Omega_p(\vec{q})$, which locates a peak in $\Im m \, \widetilde{\chi}_{\rho\rho}(\vec{q},\omega)$., Comment: 40 pages, 18 figures

Superconductivity in the t-J model is studied by extending the recently introduced extremely correlated fermi liquid theory. Exact equations for the Greens functions are obtained by generalizing Gor'kov's equations to include extremely strong local repulsion between electrons of opposite spin. These equation are expanded in a parameter $\lambda$ representing the fraction of double occupancy, and the lowest order equations are further simplified near $T_c$, resulting in an approximate integral equation for the superconducting gap. The condition for $T_c$ is studied using a model spectral function embodying a reduced quasiparticle weight $Z$ near half-filling, yielding an approximate analytical formula for $T_c$. This formula is evaluated using parameters representative of single layer High-$T_c$ systems. In a narrow range of electron densities that is necessarily separated from the Mott-Hubbard insulator at half filling, we find superconductivity with a typical $T_c$$\sim$$10^2$K., Comment: 31 pages, 5 figures

We present an explicit solution of the eigen-spectrum Toeplitz matrix $C_{ij}= e^{- \kappa |i-j|}$ with $0\leq i,j \leq N$ and apply it to find analytically the plasma modes of a layered assembly of 2-dimensional electron gas. The solution is found by elementary means that bypass the Wiener-Hopf technique usually used for this class of problems. It rests on the observation that the inverse of $C_{ij}$ is effectively a nearest neighbor hopping model with a specific onsite energies which can in turn be diagonalized easily. Extensions to a combination of a Toeplitz and Hankel matrix, and to a generalization of $C_{ij}$, are discussed at the end of the paper., Comment: 12 pages, 1 figure

Planar normal state resistivity data taken from three families of cuprate superconductors are compared with theoretical calculations from the recent extremely correlated Fermi liquid theory (ECFL). The two hole doped cuprate materials $LSCO$ and $BSLCO$ and the electron doped material $LCCO$ have yielded rich data sets at several densities $\delta$ and temperatures T, thereby enabling a systematic comparison with theory. The recent ECFL resistivity calculations for the highly correlated $t$-$t'$-$J$ model by us give the resistivity for a wide set of model parameters. After using X-ray diffraction and angle resolved photoemission data to fix parameters appearing in the theoretical resistivity, only one parameter, the magnitude of the hopping $t$, remains undetermined. For each data set, the slope of the experimental resistivity at a single temperature-density point is sufficient to determine $t$, and hence the resistivity on absolute scale at all remaining densities and temperatures. This procedure is shown to give a fair account of the entire data., Comment: 27 pages, 6 Figures, With extended discussion of theory and added references

There is considerable recent interest in the phenomenon of anisotropic electroresistivity of correlated metals. While some interesting work has been done on the iron-based superconducting systems, not much is known for the cuprate materials. Here we study the anisotropy of elastoresistivity for cuprates in the normal state. We present theoretical results for the effect of strain on resistivity, and additionally on the optical weight and local density of states. We use the recently developed extremely strongly correlated Fermi liquid theory in two dimensions, which accounts quantitatively for the unstrained resistivities for three families of single-layer cuprates. The strained hoppings of a tight-binding model are roughly modeled analogously to strained transition metals. The strained resistivity for a two-dimensional $t$-$t'$-$J$ model are then obtained, using the equations developed in recent work. Our quantitative predictions for these quantities have the prospect of experimental tests in the near future, for strongly correlated materials such as the hole-doped and electron-doped high-$T_c$ materials.

The change of a material's electrical resistance (R) in response to an external magnetic field (B) provides subtle information for the characterization of its electronic properties and has found applications in sensor and storage related technologies. In good metals, Boltzmann's theory predicts a quadratic growth in magnetoresistance (MR) at low B, and saturation at high fields. On the other hand, a number of nonmagnetic materials with weak electronic correlation and low carrier concentration for metallicity, such as inhomogeneous conductors, semimetals, narrow gap semiconductors and topological insulators, two-dimensional electron gas (2DEG) show positive, non-saturating linear magnetoresistance (LMR). However, observation of LMR in single crystals of a good metal is rare. Here we present low-temperature, angle dependent magnetotransport in single crystals of the antiferromagnetic metal, TmB4. We observe large, positive and anisotropic MR(B), which can be tuned from quadratic to linear by changing the direction of the applied field. In view of the fact that isotropic, single crystalline metals with large Fermi surface (FS) are not expected to exhibit LMR, we attribute our observations to the anisotropic FS topology of TmB4. Furthermore, the linear MR is found to be temperature-independent, suggestive of quantum mechanical origin., Comment: 14 pages, 5 figures, Accepted version of PRB

We study the two-dimensional $t$-$J$ model with second neighbor hopping parameter $t'$ and in a broad range of doping $\delta$ using a closed set of equations from the {\em Extremely Correlated Fermi Liquid} (ECFL) theory. We obtain asymmetric energy distribution curves and symmetric momentum distribution curves of the spectral function, consistent with experimental data. We further explore the Fermi surface and local density of states for different parameter sets. Using the spectral function, we calculate the resistivity, Hall number and spin susceptibility. The curvature change in the resistivity curves with varying $\delta$ is presented and connected to intensity loss in Angle Resolved Photoemission Spectroscopy (ARPES) experiments. We also discuss the role of the super-exchange $J$ in the spectral function and the resistivity in the optimal to overdoped density regimes.

Three Fermion sumrules for interacting systems are derived at T=0, involving the number expectation $\bar{N}(\mu)$, canonical chemical potentials $\mu(m)$, a logarithmic time derivative of the Greens function $\gamma_{\vec{k} \sigma}$ and the static Greens function. In essence we establish at zero temperature the sumrules linking: $$ \bar{N}(\mu) \leftrightarrow \sum_{m} \Theta(\mu- \mu(m)) \leftrightarrow \sum_{\vec{k},\sigma} \Theta\left(\gamma_{\vec{k} \sigma}\right) \leftrightarrow \sum_{\vec{k},\sigma} \Theta\left(G_\sigma(\vec{k},0)\right). $$ Connecting them across leads to the Luttinger and Ward sumrule, originally proved perturbatively for Fermi liquids. Our sumrules are nonperturbative in character and valid in a considerably broader setting that additionally includes non-canonical Fermions and Tomonaga-Luttinger models. Generalizations are given for singlet-paired superconductors, where one of the sumrules requires a testable assumption of particle-hole symmetry at all couplings. The sumrules are found by requiring a continuous evolution from the Fermi gas, and by assuming a monotonic increase of $\mu(m)$ with particle number m. At finite T a pseudo-Fermi surface, accessible to angle resolved photoemission, is defined using the zero crossings of the first frequency moment of a weighted spectral function., Comment: Total 29 pages ; Enlarged discussion from earlier version

We study the particle-hole asymmetry of the scattering rate in strongly correlated electron systems by examining the cubic $\omega^3$ and $\omega T^2$ terms in the imaginary part of the self-energy of the Anderson impurity model. We show that the sign is opposite in the weak-coupling and strong-coupling limits, explaining the differences found in theoretical approaches taking the respective limits as the starting points. The sign change in fact precisely delineates the cross-over between the weak and strong correlation regimes of the model. For weak interaction $U$ the sign reversal occurs for small values of the doping $\delta=1-n$, while for interaction of order $U \approx 2 \Gamma$, $\Gamma$ being the hybridization strength, the cross-over curve rapidly shifts to the large-doping range. This curve based on the impurity dynamics is genuinely different from other cross-over curves defined through impurity thermodynamic and static properties., Comment: 4 pages, 5 figures

We address the problem of resistivity saturation observed in materials such as the A-15 compounds. To do so, we calculate the resistivity for the Hubbard-Holstein model in infinite spatial dimensions to second order in on-site repulsion $U\leq D$ and to first order in (dimensionless) electron-phonon coupling strength $\lambda\leq0.5$, where $D$ is the half-bandwidth. We identify a unique mechanism to obtain two parallel quantum conducting channels: low-energy and band-edge high-energy quasi-particles. We identify the source of the hitherto unremarked high-energy quasi-particles as a positive slope in the frequency-dependence of the real part of the electron self-energy. In the presence of phonons, the self-energy grows linearly with the temperature at high-$T$, causing the resistivity to saturate. As $U$ is increased, the saturation temperature is pushed to higher values, offering a mechanism by which electron-correlations destroy saturation., Comment: 8 pages, 15 figures

We present theoretical results for the optical conductivity and the non-resonant Raman susceptibilities for three principal polarization geometries relevant to the square lattice. The susceptibilities are obtained using the recently developed extremely correlated Fermi liquid theory for the two-dimensional t-t'-J model, where t and t' are the nearest and second neighbor hopping. Our results are sensitively depending on t, t'. By studying this quartet of related dynamical susceptibilities, and their dependence on t, t', doping and temperature, we provide a useful framework for interpreting and planning future Raman experiments on the strongly correlated matter.

We study the one dimensional t-t'-J model for generic couplings using two complementary theories, the extremely correlated Fermi liquid theory and time-dependent density matrix renormalization group over a broad energy scale. The two methods provide a unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as a Tomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation, i.e. the splitting of Landau quasiparticles of higher dimensions into two constituents, driven by strong quantum fluctuations inherent in one dimension. The momentum distribution function, the spectral function, and the excitation dispersion of these two methods also compare well.

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 $R_H$ and Hall angles $\theta_H$, and also the longitudinal and transverse optical response of the $U=\infty$ 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 angles $\cot \theta_H \propto T^2$ in the GCFL regime, on warming into the strange metal regime, it passes through a downward bend and continues as $T^2$. Equivalently, $R_H$ is weakly temperature dependent in the GCFL regime, and becomes strongly $T$-dependent in the GCSM regime. Drude peaks are found for both the longitudinal optical conductivity $\sigma_{xx}(\omega)$ and the optical Hall angles $\tan \theta_H(\omega)$ 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 independent 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., Comment: 12 pages, 10 figures

Low energy properties of the metallic state of the 2-dimensional tJ model are presented at various densities and temperatures for second neighbor hopping t', with signs that are negative or positive corresponding to hole or electron doping. The calculation employs a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory. These equations, when used in $d=\infty$ reproduce most of the known low energies features of the $U=\infty$ Hubbard model. In 2-dimensions we are able to study the variations due to the superexchange J. The resulting Dyson self energy is found to be momentum dependent as expected. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity and cotangent of the Hall angle in experimentally relevant units. These display significant thermal sensitivity for density n >~ 0.8, signifying an effective Fermi-liquid temperature scale which is two or three orders of magnitude below the bare bandwidth. Flipping the sign of the hopping t', i.e. studying hole versus electron doping, is found to induce a change in curvature of the temperature dependent resistivity from convex to concave at low temperatures. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter., Comment: 27 pages, 5 figures, Updated on 24 August 2017 with extended discussion and extra figures

Recent progress in extremely correlated Fermi liquid theory (ECFL) and dynamical mean field theory (DMFT) enables us to compute in the $d \to \infty$ limit the resistivity of the $t-J$ model after setting $J\to0$. This is also the $U=\infty$ Hubbard model. 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 characterized by different behaviors of the resistivity $\rho$. We find at the lowest $T$ a Gutzwiller Correlated Fermi Liquid regime with $\rho \propto T^2$ extending up to an effective Fermi temperature that is dramatically suppressed from the non-interacting value. This is followed by a Gutzwiller Correlated Strange Metal regime with $\rho \propto (T-T_0)$, i.e. a linear resistivity extrapolating back to $\rho=0$ at a positive $T_0$. At a higher $T$ scale, this crosses over into the Bad Metal regime with $\rho \propto (T+T_1)$ 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 $\rho \propto T$. The present work emphasizes the first two, where the availability of an analytical ECFL theory is of help in identifying the changes in related variables entering the resistivity formula that accompany the onset of linear resistivity, and the numerically exact DMFT helps to validate the results. We also examine thermodynamic 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 strange metal regime, which has features in common with the physically relevant strange metal phase seen in strongly correlated matters., Comment: 14 pages, 16 figures, accepted version

In $TmB_4$, localized electrons with a large magnetic moment interact with metallic electrons in boron-derived bands. We examine the nature of $TmB_4$ using full-relativistic ab-initio density functional theory calculations, approximate tight-binding Hamiltonian results, and the development of an effective Kondo-Ising model for this system. Features of the Fermi surface relating to the anisotropic conduction of charge are discussed. The observed magnetic moment $\sim 6 \, \mu_B$ is argued to require a subtle crystal field effect in metallic systems, involving a flipped sign of the effective charges surrounding a Tm ion. The role of on-site quantum dynamics in the resulting Kondo-Ising type "impurity" model are highlighted. From this model, elimination of the conduction electrons will lead to spin-spin (RKKY-type) interaction of Ising character required to understand the observed fractional magnetization plateaus in $TmB_4$.

We investigate the origin of ubiquitous low energy kinks found in Angle Resolved Photoemission (ARPES) experiments in a variety of correlated matter. Such kinks are unexpected from weakly interacting electrons and hence identifying their origin should lead to fundamental insights in strongly correlated matter. We devise a protocol for extracting the kink momentum and energy from the experimental data which relies solely on the two asymptotic tangents of each dispersion curve, away from the feature itself. It is thereby insensitive to the different shapes of the kinks as seen in experiments. The body of available data is then analyzed using this method. We proceed to discuss two alternate theoretical explanations of the origin of the kinks. Some theoretical proposals invoke local Bosonic excitations (Einstein phonons or other modes with spin or charge character), located exactly at the energy of observed kinks, leading to a momentum independent self energy of the electrons. A recent alternate is the theory of extremely correlated Fermi liquids (ECFL). This theory predicts kinks in the dispersion arising from a momentum dependent self energy of correlated electrons. We present the essential results from both classes of theories, and identify experimental features that can help distinguish between the two mechanisms. The ECFL theory is found to be consistent with currently available data on kinks in the nodal direction of cuprate superconductors, but conclusive tests require higher resolution energy distribution curve data.

We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the high-temperature series expansion. We consider generic dimension $d$ as well as the infinite-$d$ limit, arbitrary electron density $n$, and both finite and infinite repulsion $U$. We use moment-reconstruction methods to obtain the one-electron spectral function, the self-energy, and the optical conductivity. They are all smooth functions at high-temperature and, at large-$U$, they are featureless with characteristic widths of order the lattice hopping parameter $t$. In the infinite-$d$ limit we compare the series expansion results with accurate numerical renormalization group and interaction expansion quantum Monte-Carlo results. We find excellent agreement down to surprisingly low temperatures, throughout most of the bad-metal regime which applies for $T \gtrsim (1-n)D$, the Brinkman-Rice scale. The resistivity increases linearly in $T$ at high-temperature without saturation. This results from the $1/T$ behaviour of the compressibility or kinetic energy, which play the role of the effective carrier number. In contrast, the scattering time (or diffusion constant) saturate at high-$T$. We find that $\sigma(n,T) \approx (1-n)\sigma(n=0,T)$ to a very good approximation for all $n$, with $\sigma(n=0,T)\propto t/T$ at high temperatures. The saturation at small $n$ occurs due to a compensation between the density-dependence of the effective number of carriers and that of the scattering time. The $T$-dependence of the resistivity displays a knee-like feature which signals a cross-over to the intermediate-temperature regime where the diffusion constant (or scattering time) start increasing with decreasing $T$. At high-temperatures, the thermopower obeys the Heikes formula, while the Wiedemann-Franz law is violated with the Lorenz number vanishing as $1/T^2$., Comment: 38 pages, 16 figures

We present the results for the low energy properties of the infinite dimensional t-J model with $J=0$, using $O(\lambda^2)$ equations of the extremely correlated Fermi liquid formalism. The parameter $\lambda \in [0,1]$ is analogous to the inverse spin parameter $1/(2S)$ in quantum magnets. The present analytical scheme allows us to approach the physically most interesting regime near the Mott insulating state $n\lesssim 1$. It overcomes the limitation to low densities $n \lesssim .7$ of earlier calculations, by employing a variant of the skeleton graph expansion, and a high frequency cutoff that is essential for maintaining the known high-T entropy. The resulting quasiparticle weight $Z$, the low $\omega,T $ self energy and the resistivity are reported. These are quite close at all densities to the exact numerical results of the $U=\infty$ Hubbard model, obtained using the dynamical mean field theory. The present calculation offers the advantage of generalizing to finite $T$ rather easily, and allows the visualization of the loss of coherence of Fermi liquid quasiparticles by raising $T$. The present scheme is generalizable to finite dimensions and a non vanishing $J$., Comment: 15 pages, 12 figures

We study level statistics in ensembles of integrable $N\times N$ matrices linear in a real parameter $x$. The matrix $H(x)$ is considered integrable if it has a prescribed number $n>1$ of linearly independent commuting partners $H^i(x)$ (integrals of motion) $\left[H(x),H^i(x)\right] = 0$, $\left[H^i(x), H^j(x)\right]$ = 0, for all $x$. In a recent work, we developed a basis-independent construction of $H(x)$ for any $n$ from which we derived the probability density function, thereby determining how to choose a typical integrable matrix from the ensemble. Here, we find that typical integrable matrices have Poisson statistics in the $N\to\infty$ limit provided $n$ scales at least as $\log{N}$; otherwise, they exhibit level repulsion. Exceptions to the Poisson case occur at isolated coupling values $x=x_0$ or when correlations are introduced between typically independent matrix parameters. However, level statistics cross over to Poisson at $ \mathcal{O}(N^{-0.5})$ deviations from these exceptions, indicating that non-Poissonian statistics characterize only subsets of measure zero in the parameter space. Furthermore, we present strong numerical evidence that ensembles of integrable matrices are stationary and ergodic with respect to nearest neighbor level statistics., Comment: 18 pages, 26 figures, discussion on number variance added; published version

We present a calculation of the low energy Greens function in $1+\epsilon$ dimensions using the method of extended poor man's scaling, developed here. We compute the wave function renormalization $Z(\omega)$ and also the decay rate near the Fermi energy. Despite the lack of $\omega^2$ damping characteristic of 3-dimensional Fermi liquids, we show that quasiparticles do exist in $1+\epsilon$ dimensions, in the sense that the quasiparticle weight $Z$ is finite and that the damping rate is smaller than the energy. We explicitly compute the crossover from this behavior to a 1-dimensional type Tomonaga-Luttinger liquid behavior at higher energies.

We study TmB_4, a frustrated magnet on the Archimedean Shastry-Sutherland lattice, through magnetization and transport experiments. The lack of anisotropy in resistivity shows that TmB_4 is an electronically three-dimensional system. The magnetoresistance (MR) is hysteretic at low-temperature even though a corresponding hysteresis in magnetization is absent. The Hall resistivity shows unconventional anomalous Hall effect (AHE) and is linear above saturation despite a large MR. We propose that complex structures at magnetic domain walls may be responsible for the hysteretic MR and may also lead to the AHE.

We present the structural and magnetic properties of a new compound family, Mg$_2$RE$_3$Sb$_3$O$_{14}$ (RE = Gd, Dy, Er), with a hitherto unstudied frustrating lattice, the "tripod kagome" structure. Susceptibility (ac, dc) and specific heat exhibit features that are understood within a simple Luttinger-Tisza type theory. For RE = Gd, we found long ranged order (LRO) at 1.65 K, which is consistent with a 120 $^{\circ}$ structure, demonstrating the importance of diople interactions for this 2D Heisenberg system. For RE = Dy, LRO at 0.37 K is related to the "kagome spin ice (KSI)" physics for a 2D system. This result shows that the tripod kagome structure accelerates the transition to LRO predicted for the related pyrochlore systems. For RE = Er, two transitions, at 80 mK and 2.1 K are observed, suggesting the importance of quantum fluctuations for this putative XY system., Comment: 5 pages, 2 figures with supplemental material

We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -- a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M family of integrable matrices consists of exactly N-M independent commuting N-by-N matrices linear in a real parameter. We first develop a rotationally invariant parametrization of such matrices, previously only constructed in a preferred basis. For example, an arbitrary choice of a vector and two commuting Hermitian matrices defines a type-1 family and vice versa. Higher types similarly involve a random vector and two matrices. The basis-independent formulation allows us to derive the joint probability density for integrable matrices, in a manner similar to the construction of Gaussian ensembles in the RMT., Comment: 11 pages, 1 figure (added); published version

Anderson localization is known to be inevitable in one dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess "additional" integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction., Comment: 23 pages, 5 figures

The recently developed theory of extremely correlated Fermi liquids (ECFL), applicable to models involving the physics of Gutzwiller projected electrons, shows considerable promise in understanding the phenomena displayed by the $t$-$J$ model. Its formal equations for the Greens function are reformulated by a new procedure that is intuitively close to that used in the usual Feynman-Dyson theory. We provide a systematic procedure by which one can draw diagrams for the $\lambda$-expansion of the ECFL introduced in Ref. (9), where the parameter $\lambda \in (0,1)$ counts the order of the terms. In contrast to the Schwinger method originally used for this problem, we are able to write down the $n^{th}$ order diagrams ($O(\lambda^n)$) directly with the appropriate coefficients, without enumerating all the previous order terms. This is a considerable advantage since it thereby enables the possible implementation of Monte Carlo methods to evaluate the $\lambda$ series directly. The new procedure also provides a useful and intuitive alternative to the earlier methods., Comment: 39 pages, 41 figures

The t-J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson-Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitean quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further a transparent physical interpretation of the previously introduced auxiliary Greens functions and the caparison factor is obtained. The low energy electron spectral function in this theory with a strong intrinsic asymmetry, is summarized in terms of a few expansion coefficients. These include an important emergent energy scale $\Delta_0$ that shrinks to zero on approaching the insulating state, thereby making it difficult to access the underlying low energy Fermi liquid behavior. The scaled low frequency ECFL spectral function is related simply to the Fano line shape. The resulting energy dispersion (EDC or MDC) is a hybrid of a massive and a massless Dirac spectrum $ E^*_Q\sim \gamma\, Q- \sqrt{\Gamma_0^2 + Q^2} $, where the vanishing of $Q$, a momentum like variable, locates the kink. Therefore the quasiparticle velocity interpolates between $(\gamma \mp 1)$ over a width $\Gamma_0$ on the two sides of $Q=0$. The resulting kink strongly resembles a prominent low energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate materials. We also propose novel ways of analyzing the ARPES data to isolate the predicted asymmetry between particle and hole excitations., Comment: 27 pages, 1 Figure, Updated figure and discussion of the "kink" feature

We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically enabling us to carry out the expansion to the eighth order in powers of the hopping amplitude. We compute the finite-temperature Green's function analytically in the momentum and Matsubara frequency space as a function of the electron density. Employing Pade approximations, we study the equation of state, Kelvin thermopower, momentum distribution function, quasiparticle fraction, and quasiparticle lifetime of the system at temperatures lower than, or of the order of, the hopping amplitude. We also discuss several different approaches for obtaining the spectral functions through analytic continuation of the imaginary frequency Green's function, and show results for the system near half filling. We benchmark our results for the equation of state against those obtained from a numerical linked-cluster expansion carried out to the eleventh order., Comment: 15 pages, 11 figures, 1 table

We study the infinite spatial dimensionality limit of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory for the t-J model. We directly analyze the Schwinger equations of motion for the Gutzwiller projected electron Green's function. From simplifications arising in this limit, we are able to make several exact statements about the theory. The ECFL Green's function is shown to have a momentum independent Dyson (Mori) self energy. For practical calculations we introduce a partial projection parameter \lambda, and obtain the complete set of ECFL integral equations to second order in \lambda. In a related publication, these equations are compared in detail with the dynamical mean field theory for the large U Hubbard model. Paralleling the well known mapping for the Hubbard model, we find that the infinite dimensional t-J model can be mapped to the infinite-U Anderson impurity model with a self-consistently determined set of parameters. This mapping extends individually to the auxiliary Green's function and the caparison factor of the ECFL theory. Additionally, the optical conductivity is shown to be obtainable from the Green's function with negligibly small vertex corrections. These results are shown to hold to each order in \lambda., Comment: 13 pages, 0 figures, To be published in "Annals of Physics" (2013)

We consider a doped Mott insulator in the large dimensionality limit within both the recently developed Extremely Correlated Fermi Liquid (ECFL) theory and the Dynamical Mean-Field Theory (DMFT). We show that the general structure of the ECFL sheds light on the rich frequency-dependence of the DMFT self-energy. Using the leading Fermi-liquid form of the two key auxiliary functions introduced in the ECFL theory, we obtain an analytical ansatz which provides a good quantitative description of the DMFT self-energy down to hole doping level 0.2. In particular, the deviation from Fermi-liquid behavior and the corresponding particle-hole asymmetry developing at a low energy scale are well reproduced by this ansatz. The DMFT being exact at large dimensionality, our study also provides a benchmark of the ECFL in this limit. We find that the main features of the self-energy and spectral line-shape are well reproduced by the ECFL calculations in the O(\lambda^2) `minimal scheme', for not too low doping level >0.3. The DMFT calculations reported here are performed using a state-of-the-art numerical renormalization-group impurity solver, which yields accurate results down to an unprecedentedly small doping level 0.001., Comment: 21 pages, 18 figures

We apply the recently developed extremely correlated Fermi liquid theory to the Anderson impurity model, in the extreme correlation limit. We develop an expansion in a parameter \lambda, related to n_d, the average occupation of the localized orbital, and find analytic expressions for the Green's functions to O(\lambda^2). These yield the impurity spectral function and also the self-energy \Sigma(\omega) in terms of the two self energies of the ECFL formalism. The imaginary parts of the latter, have roughly symmetric low energy behaviour (~ \omega^2), as predicted by Fermi Liquid theory. However, the inferred impurity self energy \Sigma"(\omega) develops asymmetric corrections near n_d ~ 1, leading in turn to a strongly asymmetric impurity spectral function with a skew towards the occupied states. Within this approximation the Friedel sum rule is satisfied but we overestimate the quasiparticle weight z relative to the known exact results, resulting in an over broadening of the Kondo peak. Upon scaling the frequency by the quasiparticle weight z, the spectrum is found to be in reasonable agreement with numerical renormalization group results over a wide range of densities., Comment: 10 pages,5 figures

We study a recently proposed quantum integrable model defined on a lattice with N sites, with Fermions or Bosons populating each site, as a close relative of the well known spin-1/2 Gaudin model. This model has 2N arbitrary parameters, a linear dependence on an interaction type parameter x, and can be solved exactly. It has N known constants of motion that are linear in x. We display further constants of motion with higher Fermion content, that are are linearly independent of the known conservation laws. Our main result is that despite the existence of these higher conservation laws, the model has only N functionally independent conservation laws. Therefore we propose that N can be viewed as the number of degrees of freedom, in parallel to the classical definition of integrability., Comment: 5 pages

A strong-coupling series expansion for the Green's function and the extremely-correlated Fermi liquid (ECFL) theory are used to calculate the moments of the electronic spectral functions of the infinite-U Hubbard model. Results from these two complementary methods agree very well at both, low densities, where the ECFL solution is the most accurate, and at high to intermediate temperatures, where the series converge. We find that a modified first moment, which underestimates the contributions from the occupied states and is accessible in the series through the time-dependent Green's function, best describes the quasiparticle peak location in the strongly-correlated regime. This is examined by the ECFL results at low temperatures, where it is shown that the spectral function is largely skewed towards the occupied states., Comment: 5 pages, 3 figures

We present a software package DiracQ, for use in quantum many-body Physics. It is designed for helping with typical algebraic manipulations that arise in quantum Condensed Matter Physics and Nuclear Physics problems, and also in some subareas of Chemistry. DiracQ is invoked within a Mathematica session, and extends the symbolic capabilities of Mathematica by building in standard commutation and anticommutation rules for several objects relevant in many-body Physics. It enables the user to carry out computations such as evaluating the commutators of arbitrary combinations of spin, Bose and Fermi operators defined on a discrete lattice, or the position and momentum operators in the continuum. Some examples from popular systems, such as the Hubbard model, are provided to illustrate the capabilities of the package., Comment: Introduction (5 pages) and Examplebook_V0 (22 pages) included here. The package may be downloaded from http://DiracQ.org or from http://physics.ucsc.edu/~sriram/DiracQ

We present detailed results from a recent microscopic theory of extremely correlated Fermi liquids, applied to the t-J model in two dimensions. We use typical sets of band parameters relevant to the cuprate superconductors. The second order theory in the parameter \lambda is argued to be quantitatively valid in the overdoped regime for 0 < n < 0.75 (n is the particle density). The calculation involves the self consistent solution of equations for an auxiliary Fermi liquid type Greens function and an adaptive spectral weight, or caparison factor, described in recent papers by Shastry (Refs. (1) and (5)). We present the numerical results at low as well as high T at various low to intermediate densities in the normal phase with emphasis placed on features that are experimentally accessible. We display the momentum space occupation function m(k), various energy dispersions locating the peaks of spectral functions, the optical conductivity, relaxation rates for quasiparticles, and the electronic spectral functions along various directions in the Brillouin zone, and with typical additional elastic scattering. The line-shapes have an asymmetric shape and a broad background that is seen in experiments near and beyond optimal hole doping, and validate approximate recent recent versions of the theory. The results display features such as the high energy kink, and provide an in depth understanding of its origin and dependence on band parameters., Comment: 25 pages, 21 figures. Version with higher resolution figures available at: http://physics.ucsc.edu/~sriram/papers/paper_134.pdf

Electronic frustration and strong correlations may lead to large Seebeck coefficients. To understand this physics on general grounds, we compute the thermopower of the one-band Hubbard model on the 3-dimensional fcc lattice over the whole range of fillings for intermediate and large interaction strength. Dynamical mean-field theory shows that when the density approaches half-filling, the fcc lattice at strong coupling exhibits a large low temperature Seebeck coefficient $S$. The largest effect occurs as one approaches $n=1$ from dopings where electronic frustration is maximized. The high-frequency limit of the thermopower and the Kelvin limit are both used to provide physical insight as well as practical tools to estimate the thermopower. The high-frequency limit gives a reliable estimate of the DC limit at low temperature when the metal becomes coherent. By contrast, the Kelvin approach is useful in the strongly interacting case at high temperature when transport is incoherent. The latter result shows that in doped Mott insulators at high temperature and strong coupling the thermopower can be understood on entropic grounds., Comment: 9 pages, 5 figures. A discussion about the density dependence of the thermopower in the incoherent regime has been added, starting near the end of p.5

We present the detailed formalism of the extremely correlated Fermi liquid theory, developed for treating the physics of the t-J model. We start from the exact Schwinger equation of motion for the Greens function for projected electrons, and develop a systematic expansion in a parameter \lambda, relating to the double occupancy. The resulting Greens function has a canonical part arising from an effective Hamiltonian of the auxiliary electrons, and a caparison part, playing the role of a frequency dependent adaptive spectral weight. This adaptive weight balances the requirement at low \omega, of the invariance of the Fermi volume, and at high \omega, of decaying as c_0/(i \omega), with a correlation depleted c_0 <1. The effective Hamiltonian H_{eff} describing the auxiliary Fermions is given a natural interpretation with an effective interaction V_{eff} containing both the exchange J(ij), and the hopping parameters t(ij). It is made Hermitian by adding suitable terms that ultimately vanish, in the symmetrized theory developed in this paper. Simple but important shift invariances of the t-J model are noted with respect to translating its parameters uniformly. These play a crucial role in constraining the form of V_{eff} and also provide checks for further approximations. The auxiliary and physical Greens function satisfy two sum rules, and the Lagrange multipliers for these are identified. A complete set of expressions for the Greens functions to second order in \lambda is given, satisfying various invariances. A systematic iterative procedure for higher order approximations is detailed. A superconducting instability of the theory is noted at the simplest level with a high transition temperature., Comment: 33 pages, 6 figures, 4 tables