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Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Abstract

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau’s Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit ‘strange metal’ behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal—the ‘d-wave metal’. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian—the usual t–J model with electron kinetic energy t and two-spin exchange J supplemented with a frustrated electron ‘ring-exchange’ term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.

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Figure 1: Schematic of the t–J–K model Hamiltonian.
Figure 2: Picture of the parton bands for the d -wave metal phase.
Figure 3: Phase diagram of the t–J–K electron ring-exchange model at electron density ρ = 1/3 on the two-leg ladder.
Figure 4: DMRG measurements in the conventional Luttinger liquid phase at J/t = 2 and K/t = 0.5.
Figure 5: DMRG measurements in the unconventional d -wave metal phase at J/t = 2 and K/t = 1.8.
Figure 6: Evolution of singular wavevectors in the d -wave metal phase.
Figure 7: Central charge c as a function of interaction K/t.

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Acknowledgements

We thank T. Senthil, R. Kaul, L. Balents, S. Sachdev, A. Vishwanath and P. Lee for discussions. This work was supported by the NSF under the KITP grant PHY05-51164 and the MRSEC programme under award number DMR-1121053 (H.-C.J.), the NSF under grants DMR-1101912 (M.S.B., R.V.M., J.R.G. and M.P.A.F.), DMR-1056536 (M.S.B.), DMR-0906816 and DMR-1205734 (D.N.S.), DMR-0907145 (O.I.M.), and by the Caltech Institute of Quantum Information and Matter, an NSF Physics Frontiers Center with the support of the Gordon and Betty Moore Foundation (O.I.M. and M.P.A.F.). We also acknowledge support from the Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC award (DMR-1121053), and an NSF grant (CNS-0960316).

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Correspondence to Ryan V. Mishmash.

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Jiang, HC., Block, M., Mishmash, R. et al. Non-Fermi-liquid d-wave metal phase of strongly interacting electrons. Nature 493, 39–44 (2013). https://doi.org/10.1038/nature11732

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