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arXiv:0804.2393

One-electron scattering rate and normal-state linear-$T$ resistivity of the cuprates

J. M. P. Carmelo

Published Apr 15, 2008• 0 citations
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Abstract

Here we use a description of the electronic correlations contained in the Hubbard model on the square-lattice perturbed by very weak three-dimensional uniaxial anisotropy in terms of the residual interactions of charge $c$ fermions and spin-neutral composite two-spinon $s1$ fermions. Excellent quantitative agreement with the anisotropic linear-$ω$ one-electron scattering rate and normal-state linear-$T$ resistivity observed in experiments on hole-doped cuprates with critical concentrations $x_c\approx 0.05$ and $x_*\approx 0.27$ is achieved. Our results provide strong evidence that the normal-state linear-$T$ resistivity is a manifestation of low-temperature scale-invariant physics.

DOI
10.48550/arxiv.0804.2393

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A description of the electronic correlations contained in the Hubbard model on the square-lattice perturbed by very weak three-dimensional uniaxial anisotropy in terms of the residual interactions of charge $c$ fermions and spin-neutral composite two-spinon $s1$ fermions is used to access further information on the origin of quantum critical behavior in the hole-doped cuprate superconductors. Excellent quantitative agreement with their anisotropic linear-$ω$ one-electron scattering rate and normal-state linear-$T$ resistivity is achieved. Our results provide strong evidence that the normal-state linear-$T$ resistivity is indeed a manifestation of low-temperature scale-invariant physics.

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Effects of the residual interactions of the square-lattice quantum-liquid $c$ and $s1$ fermions: Superconductivity as a side effect of the short-range spin order

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Evidence is found that for zero spin density $m=0$ and the range $0<x<x_c$ of finite hole concentrations of the short-range spin ordered phase where $x_c=1/\pi$ for $U/4t\to\infty$ and $x_c=0.27$ for $U/4t\approx 1.525$ the ground state of the Hubbard model on the square lattice is superconducting. Superconductivity emerges naturally from the effects of the residual interactions of the square-lattice quantum-liquid $c$ and $s1$ fermions and as a side product of the short-range spin correlations. The investigations of this paper rely on a description of that quantum problem in terms of objects which arise from a suitable electron - rotated-electron unitary transformation. Occupancy configurations of such objects generate the energy eigenstates and correspond to the representations of the $[SO(4)\times U(1)]/Z_2$ group which was found recently to refer to the model global symmetry. The studies of this paper focus on the effects of the residual interactions of the $c$ and $s1$ fermions of the square-lattice quantum liquid which emerges from the model in the subspace spanned by the ground state and the excited states generated by application onto it of one- and two-electron operators. An excellent overall agreement is reached for the magnitudes of all energy scales of four representative systems of the hole-doped cuprates: Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+\delta}$, Tl$_2$Ba$_2$CuO$_{6+\delta}$, YBa$_2$Cu$_3$O$_{6+\delta}$, and La$_{2-x}$Sr$_x$CuO$_4$.

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d-wave superconductivity in Hubbard model on the square lattice perturbed by weak 3D uniaxial anisotropy

J. M. P. Carmelo

The Hubbard model on a square lattice is one of the most studied condensed-matter quantum problems.Here we find evidence that for intermediate $U/4t$ values and a hole-concentration range $x\in (x_c,x_*)$ the ground state of the Hubbard model on the square lattice perturbed by weak three-dimensional (3D) uniaxial anisotropy has long-range d-wave superconducting order. Here $t$ is the effective nearest-neighbor transfer integral and $U$ the effective on-site repulsion. The lower critical concentration $x_c$ involves the Ginzburg number Gi and is approximately given by $x_c\approx {\rm Gi}+x_0\approx 0.05$. Here $x_0

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Superconductivity and magnetism in strongly correlated electronic systems

M. J. Sampaio

In this thesis, symmetry and related transformation laws under a suitable unitary transformation are used in the study of the superconducting and magnetic properties of strongly correlated electronic systems. Such a study profits from a recently found global SO(3)×SO(3)×U(1) = [SO(4)×U(1)]/Z2 symmetry in the Hubbard model on a bipartite lattice. The introduction of the square-lattice quantum liquid relies on a general description of the Hubbard model consistent with its exact global SO(3) × SO(3) × U(1) symmetry. Such a quantum liquid is expected to play the same role for many-electron problems with short-range interactions on a square lattice, as a Fermi liquid for three-dimensional isotropic metals. It refers to the Hubbard model on the square lattice in the subspace spanned by the ground state, and the excited states generated by application onto it of one- and two-electron operators. For such a square-lattice quantum liquid only the charge c fermions and spin-neutral two-spinon s1 fermions play an active role. Part of the studies of this thesis use an effective superconductivity theory according to which, for zero spin density m = 0 and the range 0 < x < x∗ of finite hole concentrations of a short-range spin ordered phase, the ground state of the square-lattice quantum liquid of c and s1 fermions with residual interactions is superconducting. (For U/4t > ui ≈ 3/4 the critical hole concentration x∗ increases continuously upon increasing the U/4t value from x∗ = 1/√2 ≈ 0.225 at U/4t = ui to x∗ = 1/ ≈ 0.318 for U/4t → ∞.) Superconductivity emerges naturally from the effects of the residual interactions of the c and s1 fermions and as a side product of the short-range spin correlations. The phase of the c fermion pairs reads = 0 + 1 where the fluctuations of the phases 0 and 1 become large for x → 0 and x → x∗, respectively. For 0 < x < x∗ and x = 0, the symmetry of the action for the phase is a global superconducting U(1) symmetry and a local compact gauge symmetry, respectively. The former U(1) symmetry is identified with the U(1) symmetry of the Hubbard-model global SO(3) × SO(3) × U(1) = [SO(4) × U(1)]/Z2 symmetry. The amplitudes g = g0 g1, g0 = |heiθ0i|, and g1 = |heiθ1i|, their zero-temperature values ˘g ≈ (x/x∗)(1−x/x∗), ˘g0 ≈ (x/x∗), and ˘g1 ≈ (1−x/x∗) and the fluctuations of the phase , play an important role in the physics of the square-lattice quantum liquid. Together with the energy scale 2 0, which gives the maximum magnitude of the s1 fermion spinon pairing energy, they fully control the order parameters of both the short-range spin and long-range superconducting correlations. Indeed, for temperatures T < Tc, the short-range spin ordered phase has both a macroscopic quantum phase-coherent pair superconducting order so that |heiθi| > 0, and a short-range spin order, whereas for Tc < T < T∗ only the latter order prevails yet there remain c fermion pairing correlations such that |heiθ1i| > 0 but heiθ0i = 0. Here the critical temperature Tc and the crossover pseudogap temperature T∗ are fully controlled by the absolute value of the order parameters of the two above orders, respectively. However, the square-lattice quantum liquid alone does not describe quantitatively the unusual properties of the hole-doped cuprates. To fulfill such a goal we profit from a suitable theory according to which the interplay of electronic correlations described by the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions with intrinsic disorder, is behind the unusual properties of the holedoped hight-temperature cuprate superconductors. By profiting from such an interplay, an excellent quantitative agreement with experiments for the physical quantities of several families of hole-doped cuprates is reached. That includes universal properties such as a dome-like critical-temperature hole-concentration dependence and normal-state linear-T resistivity near optimal doping, extending over a wide temperature window. The results confirm a coexisting two-gap scenario associated with an incoherent two-spinon pairing and a coherent twoc- fermion pairing, respectively. While most of our studies focus on the superconducting and magnetic properties of the square-lattice quantum liquid associated with the Hubbard model on the square lattice, the magnetic properties of a related model – the periodic Anderson model – are also addressed, on the cubic lattice.

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Peizhi Mai, Nathan Nichols, Seher Karakuzu +4 more

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arXiv:2210.14930•Nature Communications•May 20, 2023•13 citations
One-electron scattering rate and normal-state linear-TTT resistivity of the cuprates
Here we use a description of the electronic correlations contained in the Hubbard model on the square-lattice perturbed by very weak three-dimensional uniaxial anisotropy in terms of the residual interactions of charge ccc fermions and spin-neutral composite two-spinon s1s1s1 fermions. Excellent quantitative agreement with the anisotropic linear-ωωω one-electron scattering rate and normal-state linear-TTT resistivity observed in experiments on hole-doped cuprates with critical concentrations xc≈0.05x_c\approx 0.05xc​≈0.05 and x∗≈0.27x_*\approx 0.27x∗​≈0.27 is achieved. Our results provide strong evidence that the normal-state linear-TTT resistivity is a manifestation of low-temperature scale-invariant physics.
A description of the electronic correlations contained in the Hubbard model on the square-lattice perturbed by very weak three-dimensional uniaxial anisotropy in terms of the residual interactions of charge ccc fermions and spin-neutral composite two-spinon s1s1s1 fermions is used to access further information on the origin of quantum critical behavior in the hole-doped cuprate superconductors. Excellent quantitative agreement with their anisotropic linear-ωωω one-electron scattering rate and normal-state linear-TTT resistivity is achieved. Our results provide strong evidence that the normal-state linear-TTT resistivity is indeed a manifestation of low-temperature scale-invariant physics.
We find evidence that for zero spin density m=0m=0m=0, intermediate U/4tU/4tU/4t values, and a range x∈(xc,x∗)x\in (x_c,x_*)x∈(xc​,x∗​) of finite hole concentrations the ground state of the virtual-electron pair quantum liquid obtained from perturbing the square-lattice quantum liquid of Ref. \cite{companion2} by weak three-dimensional (3D) uniaxial anisotropy and intrinsic disorder has long-range d-wave superconducting order. Here ttt is the effective nearest-neighbor transfer integral and UUU the effective on-site repulsion. The long-range d-wave superconducting order emerges below a critical temperature TcT_cTc​ for a hole concentration range centered at xop=(xc+x∗)/2x_{op}= (x_c+x_*)/2xop​=(xc​+x∗​)/2. It results from the effects of the residual interactions of the charge ccc fermions and spin-neutral two-spinon s1s1s1 fermions of Ref. \cite{companion2}, as a by-product of the short-range spin correlations. Rather than the U(1) symmetry contained in the ηηη-spin SU(2) symmetry of the SO(4)=[SU(2)×SU(2)]/Z2SO(4) = [SU(2)\times SU(2)]/Z_2SO(4)=[SU(2)×SU(2)]/Z2​ symmetry, the U(1) symmetry broken at TcT_cTc​ is the ccc fermion U(1) symmetry of Ref. \cite{bipartite}. It is contained in the extended global SO(3)×SO(3)×U(1)=[SO(4)×U(1)]/Z2SO(3)\times SO(3)\times U(1)=[SO(4)\times U(1)]/Z_2SO(3)×SO(3)×U(1)=[SO(4)×U(1)]/Z2​ symmetry of the Hubbard model on the square lattice. Our preliminary results seem to indicate that combining the electronic correlations described by the square-lattice quantum liquid perturbed by 3D uniaxial anisotropy with the very weak effects of intrinsic disorder or superfluid-density anisotropy leads for the hole-concentration range x∈(xc,x∗)x\in (x_c,x_*)x∈(xc​,x∗​) to a successful description of the universal properties of the hole-doped cuprate superconductors.
Effects of the residual interactions of the square-lattice quantum-liquid ccc and s1s1s1 fermions: Superconductivity as a side effect of the short-range spin order
Evidence is found that for zero spin density m=0m=0m=0 and the range 0<x<xc0<x<x_c0<x<xc​ of finite hole concentrations of the short-range spin ordered phase where xc=1/πx_c=1/\pixc​=1/π for U/4t→∞U/4t\to\inftyU/4t→∞ and xc=0.27x_c=0.27xc​=0.27 for U/4t≈1.525U/4t\approx 1.525U/4t≈1.525 the ground state of the Hubbard model on the square lattice is superconducting. Superconductivity emerges naturally from the effects of the residual interactions of the square-lattice quantum-liquid ccc and s1s1s1 fermions and as a side product of the short-range spin correlations. The investigations of this paper rely on a description of that quantum problem in terms of objects which arise from a suitable electron - rotated-electron unitary transformation. Occupancy configurations of such objects generate the energy eigenstates and correspond to the representations of the [SO(4)×U(1)]/Z2[SO(4)\times U(1)]/Z_2[SO(4)×U(1)]/Z2​ group which was found recently to refer to the model global symmetry. The studies of this paper focus on the effects of the residual interactions of the ccc and s1s1s1 fermions of the square-lattice quantum liquid which emerges from the model in the subspace spanned by the ground state and the excited states generated by application onto it of one- and two-electron operators. An excellent overall agreement is reached for the magnitudes of all energy scales of four representative systems of the hole-doped cuprates: Bi2_{2}2​Sr2_22​CaCu2_22​O8+δ_{8+\delta}8+δ​, Tl2_22​Ba2_22​CuO6+δ_{6+\delta}6+δ​, YBa2_22​Cu3_33​O6+δ_{6+\delta}6+δ​, and La2−x_{2-x}2−x​Srx_xx​CuO4_44​.
The Hubbard model on a square lattice is one of the most studied condensed-matter quantum problems.Here we find evidence that for intermediate U/4tU/4tU/4t values and a hole-concentration range x∈(xc,x∗)x\in (x_c,x_*)x∈(xc​,x∗​) the ground state of the Hubbard model on the square lattice perturbed by weak three-dimensional (3D) uniaxial anisotropy has long-range d-wave superconducting order. Here ttt is the effective nearest-neighbor transfer integral and UUU the effective on-site repulsion. The lower critical concentration xcx_cxc​ involves the Ginzburg number Gi and is approximately given by xc≈Gi+x0≈0.05x_c\approx {\rm Gi}+x_0\approx 0.05xc​≈Gi+x0​≈0.05. Here $x_0
In this thesis, symmetry and related transformation laws under a suitable unitary transformation are used in the study of the superconducting and magnetic properties of strongly correlated electronic systems. Such a study profits from a recently found global SO(3)×SO(3)×U(1) = [SO(4)×U(1)]/Z2 symmetry in the Hubbard model on a bipartite lattice. The introduction of the square-lattice quantum liquid relies on a general description of the Hubbard model consistent with its exact global SO(3) × SO(3) × U(1) symmetry. Such a quantum liquid is expected to play the same role for many-electron problems with short-range interactions on a square lattice, as a Fermi liquid for three-dimensional isotropic metals. It refers to the Hubbard model on the square lattice in the subspace spanned by the ground state, and the excited states generated by application onto it of one- and two-electron operators. For such a square-lattice quantum liquid only the charge c fermions and spin-neutral two-spinon s1 fermions play an active role. Part of the studies of this thesis use an effective superconductivity theory according to which, for zero spin density m = 0 and the range 0 < x < x∗ of finite hole concentrations of a short-range spin ordered phase, the ground state of the square-lattice quantum liquid of c and s1 fermions with residual interactions is superconducting. (For U/4t > ui ≈ 3/4 the critical hole concentration x∗ increases continuously upon increasing the U/4t value from x∗ = 1/√2 ≈ 0.225 at U/4t = ui to x∗ = 1/ ≈ 0.318 for U/4t → ∞.) Superconductivity emerges naturally from the effects of the residual interactions of the c and s1 fermions and as a side product of the short-range spin correlations. The phase of the c fermion pairs reads = 0 + 1 where the fluctuations of the phases 0 and 1 become large for x → 0 and x → x∗, respectively. For 0 < x < x∗ and x = 0, the symmetry of the action for the phase is a global superconducting U(1) symmetry and a local compact gauge symmetry, respectively. The former U(1) symmetry is identified with the U(1) symmetry of the Hubbard-model global SO(3) × SO(3) × U(1) = [SO(4) × U(1)]/Z2 symmetry. The amplitudes g = g0 g1, g0 = |heiθ0i|, and g1 = |heiθ1i|, their zero-temperature values ˘g ≈ (x/x∗)(1−x/x∗), ˘g0 ≈ (x/x∗), and ˘g1 ≈ (1−x/x∗) and the fluctuations of the phase , play an important role in the physics of the square-lattice quantum liquid. Together with the energy scale 2 0, which gives the maximum magnitude of the s1 fermion spinon pairing energy, they fully control the order parameters of both the short-range spin and long-range superconducting correlations. Indeed, for temperatures T < Tc, the short-range spin ordered phase has both a macroscopic quantum phase-coherent pair superconducting order so that |heiθi| > 0, and a short-range spin order, whereas for Tc < T < T∗ only the latter order prevails yet there remain c fermion pairing correlations such that |heiθ1i| > 0 but heiθ0i = 0. Here the critical temperature Tc and the crossover pseudogap temperature T∗ are fully controlled by the absolute value of the order parameters of the two above orders, respectively. However, the square-lattice quantum liquid alone does not describe quantitatively the unusual properties of the hole-doped cuprates. To fulfill such a goal we profit from a suitable theory according to which the interplay of electronic correlations described by the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions with intrinsic disorder, is behind the unusual properties of the holedoped hight-temperature cuprate superconductors. By profiting from such an interplay, an excellent quantitative agreement with experiments for the physical quantities of several families of hole-doped cuprates is reached. That includes universal properties such as a dome-like critical-temperature hole-concentration dependence and normal-state linear-T resistivity near optimal doping, extending over a wide temperature window. The results confirm a coexisting two-gap scenario associated with an incoherent two-spinon pairing and a coherent twoc- fermion pairing, respectively. While most of our studies focus on the superconducting and magnetic properties of the square-lattice quantum liquid associated with the Hubbard model on the square lattice, the magnetic properties of a related model – the periodic Anderson model – are also addressed, on the cubic lattice.
There is growing evidence that the hole-doped single-band Hubbard and t - J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.