Starting from a generalization of Weyl's relations in finite dimension $N$, we show that the Heisenberg commutation relations can be satisfied in a specific $N-1$ dimensional subspace, and display a linear map for projecting operators to this subspace. This setup is used to construct a hierarchy of parameter-dependent commuting matrices in $N$ dimensions. This family of commuting matrices is then related to Type-1 matrices representing quantum integrable models. The commuting matrices find an interesting application in quantum computation, specifically in Grover's database search problem. Each member of the hierarchy serves as a candidate Hamiltonian for quantum adiabatic evolution and, in some cases, achieves higher fidelity than standard choices -- thus offering improved performance.

Planar normal state resistivity data from two families of hole doped single layer cuprate superconductors Bi2201 (Bi_2Sr_2CuO_6+x) and Tl2201 (Tl_2Ba_2CuO_6+x) are calculated using the extremely correlated Fermi liquid theory (ECFL). This theory was recently employed for understanding the three families of single layer cuprate superconductors LSCO, BSLCO and NCCO. Adding these two systems accounts for essentially all single layer compounds where data is available for a range of densities and temperatures. The added case of Bi2201 is of particular interest since it was the original system where the almost linear in temperature resistivity was reported in 1990, and has been followed up by a systematic doping analysis only recently in 2022. The Tl2201 system has two distinct set of band parameters that fit the same Fermi surface, providing new challenges and insights into the ECFL theory.

Planar normal state resistivity data from two families of hole doped single layer cuprate superconductors $Bi2201$ (Bi$_2$Sr$_2$CuO$_{6+x}$) and $Tl2201$ (Tl$_2$Ba$_2$CuO$_{6+x}$) are calculated using the extremely correlated Fermi liquid theory (ECFL). This theory was recently employed for understanding the three families of single layer cuprate superconductors LSCO, BSLCO and NCCO. Adding these two systems accounts for essentially all single layer compounds where data is available for a range of densities and temperatures. The added case of $Bi2201$ is of particular interest since it was the original system where the almost linear in temperature resistivity was reported in 1990, and has been followed up by a systematic doping analysis only recently in 2022. The $Tl2201$ system has two distinct set of band parameters that fit the same Fermi surface, providing new challenges and insights into the ECFL theory.

We present a method for calculating the Yang-Lee partition function zeros of a translationally invariant model of lattice fermions, exemplified by the Hubbard model. The method rests on a theorem involving the usual single-electron self-energy Σ_{σ}(k[over ⃗],iω_{n}|μ) with chemical potential μ, in the imaginary time Matsubara formulation. The theorem maps the Yang-Lee zeros to a set of wave vector and spin labeled virtual energies ξ_{k[over ⃗]σ}. These, thermodynamically derived virtual energies, are solutions of the set of equations ξ_{kσ}=ɛ_{σ}(k[over ⃗])-1/2U+Σ_{σ}(k[over ⃗],iπ/β|ξ_{kσ}+1/2U-iπ/β)=0. Examples of the method in simplified situations are provided.

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 ∼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 identities are verified numerically by computing the exact partition function for a two-dimensional square lattice of size 16×16. 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 ∼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 nonzero complex staggered magnetization, and thus depict a complex phase boundary.

A fundamental question about the nature of quantum materials such as high-Tc systems remains open to date: it is unclear whether they are (some variety of) Fermi liquids, or (some variety of) non Fermi liquids. A direct avenue to determine their nature is to study the (imaginary part of the) self-energy at low energies. Here we present a method to extract this low-w self-energy from experimentally derived spectral functions. The method seems suited for implementation with high-quality angle-resolved photoemission data. It is based on a helpful theorem proposed here, which assures us that the method has minimal (or vanishing) error at the lowest energies. We provide numerical examples showing that a few popular model systems yield distinguishably different low-energy self-energies.

We present the ${\cal O}(\lambda^3)$ results from the $\lambda$ expansion in the extremely correlated Fermi liquid theory applied to the infinite-dimensional $t$-$J$ model (with $J=0$), and compare the results with the earlier ${\cal O}(\lambda^2)$ results as well as the results from the dynamical mean field theory. We focus attention on the $T$ dependence of the resistivity $\rho(T)$, the Dyson self energy, and the quasiparticle weight $Z$ at various densities. The comparison shows that all the methods display quadratic in T resistivity followed by a quasi-linear in T resistivity characterizing a strange metal, and gives an estimate of the different scales of these variables relative to the exact results.

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 $\Im m \, \widetilde{\chi}_{\rho\rho}(\vec{q},\omega)$.

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.

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 re-pulsion between electrons of opposite spin. These equations 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 a typical T-c similar to 10(2) K. (C) 2021 The Author(s). Published by Elsevier Inc.

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.

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.

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, and two dimensional electron gas, show positive, nonsaturating linear magnetoresistance (LMR). However, observation of LMR in single crystals of a good metal is rare. Here we present low-temperature, angledependent 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. Disciplines Condensed Matter Physics | Quantum Physics Authors Sreemanta Mitra, Jeremy Goh Swee Kang, John Shin, Jin Quan Ng, Sai Swaroop Sunku, Tai Kong, Paul C. Canfield, B. Sriram Shastry, Pinaki Sengupta, and Christos Panagopoulos PHYSICAL REVIEW B 99, 045119 (2019) Quadratic to linear magnetoresistance tuning in TmB4 Sreemanta Mitra,1,* Jeremy Goh Swee Kang,1 John Shin,2 Jin Quan Ng,1 Sai Swaroop Sunku,1,† Tai Kong,3,‡ Paul C. Canfield,3 B. Sriram Shastry,2 Pinaki Sengupta,1 and Christos Panagopoulos1,§ 1Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21, Nanyang Link 637371, Singapore 2Department of Physics, University of California, Santa Cruz, California 95064, USA 3Ames Laboratory, U.S. DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA (Received 9 February 2018; revised manuscript received 5 September 2018; published 9 January 2019) 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, and two dimensional electron gas, show positive, nonsaturating 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. DOI: 10.1103/PhysRevB.99.045119

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, and two dimensional electron gas, show positive, nonsaturating 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.

Three Fermion sumrules for interacting systems are derived at T=0, involving the number expectation N̄(μ), canonical chemical potentials μ(m), a logarithmic time derivative of the Greens function γk→σ and the static Greens function. In essence we establish at zero temperature the sumrules linking: N̄(μ)↔∑mΘ(μ−μ(m))↔∑k→,σΘγk→σ↔∑k→,σΘGσ(k→,0). 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 μ(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.

Quadratic to linear magnetoresistance tuning in TmB4 Sreemanta Mitra,1,* Jeremy Goh Swee Kang,1 John Shin,2 Jin Quan Ng,1 Sai Swaroop Sunku,1,† Tai Kong,3,‡ Paul C. Canfield,3 B. Sriram Shastry,2 Pinaki Sengupta,1 and Christos Panagopoulos1,§ 1Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21, Nanyang Link 637371, Singapore 2Department of Physics, University of California, Santa Cruz, California 95064, USA 3Ames Laboratory, U.S. DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

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≤D and to first order in (dimensionless) electron-phonon coupling strength λ≤0.5, 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 quasiparticles 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.