Solutions for the <i>T</i> = 0 quantum spin glass transition in a metallic model with spin‐charge coupling

Oppermann, R.H.; Binderberger, M.

doi:10.1002/andp.19945060607

Cited by 14 publications

(22 citation statements)

References 19 publications

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“…Up to a slight deviation due to different model definitions this critical value quantitatively agrees with the results obtained in [3] for the case of a semi-elliptic free energy band. In the zero-temperature disordered phase, i.e.…”

Section: The Limit Of Zero Temperaturesupporting

confidence: 87%

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Dynamical CPA approach to an itinerant fermionic spin glass model

Bechmann

Oppermann

2003

The European Physical Journal B - Condensed Matter

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Abstract. We study a fermionic version of the Sherrington-Kirkpatrick model including nearest-neighbor hopping on a ∞-dimensional simple cubic lattices. The problem is reduced to one of free fermions moving in a dynamical effective random medium. By means of a CPA method we derive a set of self-consistency equations for the spin glass order parameter and for the Fourier components of the local spin susceptibility. In order to solve these equations numerically we employ an approximation scheme which restricts the dynamics to a feasible number of the leading Fourier components. From a sequence of systematically improved dynamical approximations we estimate the location of the quantum critical point.PACS. 75.10.Nr Spin glass and other random models -75.40.Cx Dynamic properties -71.10.Fd Lattice fermion models

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Section: The Limit Of Zero Temperaturesupporting

confidence: 87%

“…We present numerical solutions for all temperatures including T = 0. The spin-static T = 0 critical point well agrees with the results for an earlier model version [3].…”

Section: Introductionsupporting

confidence: 85%

Dynamical CPA approach to an itinerant fermionic spin glass model

Bechmann

Oppermann

2003

The European Physical Journal B - Condensed Matter

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“…Recently Miller and Huse [188] and Ye, Sachdev and Read [299] focused on the zero-temperature critical behavior and calculated the critical exponents γ = 1/2 (with multiplicative logarithmic corrections), β = 1 and zν = 1/2. Interestingly it seems that this quantum SK-model seems to fall into the same universality class as an infinite range metallic spin glass model incorporating itinerant electrons, which was investigated recently by Oppermann [214]. Another proposition for a mean-field quantum spin glass that is exactly solvable was made by Nieuwenhuizen [196] via the introduction of a quantum description of spherical spins.…”

Section: Quantum Spin Glassesmentioning

confidence: 89%

Monte Carlo Studies of Ising Spin Glasses and Random Field Systems

Rieger

1995

Annual Reviews of Computational Physics II

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We review recent numerical progress in the study of finite dimensional strongly disordered magnetic systems like spin glasses and random field systems. In particular we report in some details results for the critical properties and the non-equilibrium dynamics of Ising spin glasses. Furthermore we present an overview over recent investigations on the random field Ising model and finally of quantum spin glasses.

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“…40,41 Under the assumption of this order of critical points, a renormalizationgroup analysis, 42 based on a quantum-dynamic Ginzburg-Landau functional, was applied subsequently. Only above the upper critical dimension eight was a stable ͑Gaussian͒ fixed point obtained.…”

Section: E Combining Results On the Pseudogap With Previous Studies mentioning

confidence: 99%

Fermionic Sherrington-Kirkpatrick models with Hubbard interaction: Magnetism and electronic structure

Oppermann

Sherrington

2003

Phys. Rev. B

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Models with range-free frustrated Ising spin interaction and additional Hubbard interaction are treated exactly by means of the discrete time slicing method of Grassmann-field theory. Critical and tricritical points, spin and charge correlations, and the fermion propagator are derived as a function of temperature and chemical potential , of the Hubbard coupling U and the spin-glass energy J. U is allowed to be either repulsive (U Ͼ0) or attractive (UϽ0). Cuts through the multidimensional phase diagram are obtained. Analytical and numerical evaluations take important replica symmetry-breaking ͑RSB͒ effects into account. Results for the ordered phase are given at least in a one-step approximation ͑1RSB͒, and for Tϭ0 we report the first two-, three-, and four-step calculations ͑4RSB͒ for fermionic spin glasses. The use of exact relations and invariances under RSB together with 2RSB calculations for all fillings and 4RSB solutions for half filling allow to model exact solutions by interpolation. For Tϭ0, our numerical results provide strong evidence that the exact spin-glass pseudogap obeys (E)ϭc 1 ͉EϪE F ͉ for energies close to the Fermi level with c 1 Ϸ0.13. Rapid convergence of Ј(E F ) under increasing orders of RSB is observed and Љ(E) is evaluated to estimate subleading powers. Over a wide range of the pseudogap and after a small transient regime (E) regains a linear shape with a larger slope and a small S-like perturbation. The leading term resembles the Efros-Shklovskii Coulomb pseudogap of two-dimensional localized disordered fermionic systems. Beyond half filling we obtain a Ϫ1ϳ(ϪU) 2 , уU dependence of the fermion filling factor . We find a half filling transition between a phase for UϾ, where the Fermi level lies inside the Hubbard gap, into a phase where (ϾU) is located at the center of the upper spin-glass ͑SG͒ pseudogap ͑SG gap͒. For ϾU the Hubbard gap combines with the lower one of two SG gaps ͑phase I͒, while for ϽU it joins the sole SG gap which exists in this half-filling regime ͑phase II͒. Shoulders of the combined gaps are shaped by RSB due to spin-glass order. We predict scaling behavior at the half-filling transition which becomes continuous due to ϱRSB. Implications of the half-filling transition between the deeper insulating phase II and phase I for the eventual delocalization by additional hopping processes in itinerant model extensions are discussed. Possible metalinsulator transition scenarios are described. Generalizations to random Hubbard coupling and alloy models as well as frustrated magnetic interactions with ferro-or antiferromagnetic components are discussed.

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Solutions for the T = 0 quantum spin glass transition in a metallic model with spin‐charge coupling

Cited by 14 publications

References 19 publications

Dynamical CPA approach to an itinerant fermionic spin glass model

Dynamical CPA approach to an itinerant fermionic spin glass model

Monte Carlo Studies of Ising Spin Glasses and Random Field Systems

Fermionic Sherrington-Kirkpatrick models with Hubbard interaction: Magnetism and electronic structure

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