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arXiv:cond-mat/9910119 · Physical review. B, Condensed matter

Self-organized three-band structure of the doped fermionic Ising spin glass

Heiko Feldmann, R. Oppermann

Published Oct 1, 2000• 6 citations
arXivHTMLPDF

Abstract

The fermionic Ising spin glass is analyzed for arbitrary filling and for all temperatures. A self-organized three-band structure of the model is obtained in the magnetically ordered phase. Deviation from half-filling generates a central nonmagnetic band, which becomes sharply separated at $T=0$ by (pseudo)gaps from upper and lower magnetic bands. Replica symmetry breaking effects are derived for several observables and correlations. They determine the shape of the three-band density of states, and, for given chemical potential, influence the fermion filling strongly in the low-temperature regime.

DOI
10.1103/physrevb.62.9030

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The fermionic Ising spin glass is analyzed for arbitrary filling and for all temperatures. A self-organized three-band structure of the model is obtained in the magnetically ordered phase. Deviation from half-filling generates a central nonmagnetic band, which becomes sharply separated at T=0T=0T=0 by (pseudo)gaps from upper and lower magnetic bands. Replica symmetry breaking effects are derived for several observables and correlations. They determine the shape of the three-band density of states, and, for given chemical potential, influence the fermion filling strongly in the low-temperature regime.
We report progress in understanding the fermionic Ising spin glass with arbitrary filling. A crossover from a magnetically disordered single band phase via two intermediate bands just below the freezing temperature to a 3-band structure at still lower temperatures - beyond an almost random field instability - is shown to emerge in the magnetic phase. An attempt is made to explain the exact solution in terms of a quantum Parisi phase. A central nonmagnetic band\nis found and seen to become sharply separated at T = 0 by gaps from upper and lower magnetic bands. The gap sizes tend towards zero as the number of replica symmetry breaking steps increases towards infinity. In an extended model, the competition between local pairing superconductivity and spin glass order is discussed.
We present details of the phase diagrams of fermionic systems with random and frustrated interactions, emphasizing the important role of the chemical potential. The insulating fermionic Ising spin glass model is shown to reveal different entangled magnetic instabilities and phase transitions. We review tricritical phenomena related to the strong correspondence between charge and spin fluctuations, being controlled by quantum statistics. We compare the spin density diluted Sherrington-Kirkpatrick spin glass with classical spin 1 models such as the BEG model. We analyse in detail the infinite range model and show that spin glass order must decay discontinuously as the chemical potential exceeds a critical value, provided the temperature is below the tricritical one, and that the T=0 transition is of classical type. Parisi replica permutation symmetry breaking (RPSB) governs the thermal spin glass transitions and fermionic modifications of the SK-models AT-line emerge. RPSB takes place everywhere within the fermionic spin glass phase. Although the critical field theory of the quantum paramagnet to spin glass transition in metallic systems remains replica--symmetric at T=0, with only small corrections at low T from RPSB, the phase diagram is affected at O(T^0) by RPSB. Generalizing our results for the fermionic Ising spin glass we consider aspects of models with additional spin and charge quantum--dynamics such as metallic spin glasses.
We analyze the infinite range Ising spin glass in a transverse-field $\ensuremath{\Gamma}$ below the critical temperature by a one step replica symmetry breaking theory. The set of nnn replicas is divided in rrr blocks of mmm replicas each. We present results for different values of the block-size parameter mmm. The spin operators are represented by bilinear combinations of fermionic fields and we compare the results of two models: In the four-states (4-S) model the diagonal Siz{S}_{i}^{z}Siz​ operator has two unphysical vanishing eigenvalues, that are suppressed by a restraint in the two-states (2-S) model. In the static approximation we obtain qualitatively similar results for both models. They both exhibit a critical temperature ${T}_{c}(\ensuremath{\Gamma})$ that decreases when $\ensuremath{\Gamma}$ increases, until it reaches a quantum critical point at the same value of ${\ensuremath{\Gamma}}_{c}$ and they are both unstable under replica symmetry breaking in the whole spin glass phase. Below the critical temperature we present results for the order parameters and free energy.
We solve the fermionic version of the Ising spin glass for arbitrary filling µ and temperature T taking into account replica symmetry breaking. Using a simple exact mapping from µ to the anisotropy parameter D , we also obtain the solution of the S = 1 Sherrington-Kirkpatrick model. An analytic expression for T = 0 gives an improved critical value for the first-order phase transition. We revisit the question of stability against replica-diagonal fluctuations and find that the appearance of complex eigenvalues of the Almeida-Thouless matrix is not an artefact of the replica-symmetric approximation.
We have studied numerically the states reached in a quench from various temperatures in the one-dimensional fully-connected Kotliar, Anderson and Stein Ising spin glass model. This is a model where there are long-range interactions between the spins which falls off as a power σ\sigmaσ of their separation. We have made a detailed study in particular of th e energies of the states reached in a quench from infinite temperature and their overlaps, including the spin glass susceptibility. In the regime where σ≤1/2\sigma \le 1/2σ≤1/2, where the model is similar to the Sherrington-Kirkpatrick model, we find that the spin glass susceptibility diverges logarithmically with increasing NNN, the number of spins in the syste m, whereas for σ>1/2\sigma> 1/2σ>1/2 it remains finite. We attribute the behavior for σ≤1/2\sigma \le 1/2σ≤1/2 to \emph {self-organized critical behavior}, where the system after the quench is cl ose to the transition between states which have trivial overlaps and those with the non-trivial overlaps associated with replica symmetry breaking.
We characterize numerically the properties of the phase transition of the three-dimensional Ising spin glass with Gaussian couplings and of the low-temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three-dimensional spin glasses.