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  • Review Article
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Quantum phases driven by strong correlations

Abstract

It has long been thought that strongly correlated systems are adiabatically connected to their non-interacting counterpart. Recent developments have highlighted the fallacy of this traditional notion in a variety of settings. In this Review, we use a class of strongly correlated electron systems to illustrate the type of quantum phases and fluctuations that are created by strong correlations. Examples include quantum critical states that violate the Fermi liquid paradigm, unconventional superconductivity that goes beyond the Bardeen–Cooper–Schrieffer framework, and topological semimetals induced by the Kondo interaction. We assess the prospects for designing other exotic phases of matter by using alternative degrees of freedom or alternative interactions, and discuss the potential of these correlated states for quantum technology.

Key points

  • Quantum criticality accumulates entropy, turns quantum matter soft, and makes it prone to the development of exotic excitations and new emergent phases.

  • Strongly correlated electron systems can exhibit quantum critical points with fluctuations beyond those of the vanishing Landau order parameter, as exemplified by electronic localization–delocalization transitions associated with Kondo-destruction quantum criticality.

  • Quantum phases are enriched by the interplay between strong correlations, geometrical frustration, entwined degrees of freedom and hybrid interactions.

  • Strong correlations interplay with spin–orbit coupling and space-group symmetry to drive topological states of matter, as exemplified by Weyl–Kondo semimetals.

  • In quantum materials, we let nature work for us and reveal new physics that we might never have imagined. This leads to models and concepts that could then be studied in artificial settings such as ultracold atomic and photonic systems, and models for gravity.

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Fig. 1: Functionality of strongly correlated materials.
Fig. 2: Tuning correlation strength.
Fig. 3: Quantum criticality.
Fig. 4: Fermi-surface jump at a Kondo-destruction quantum critical point.
Fig. 5: Quantum critical scaling.
Fig. 6: Composite and boosted interactions.
Fig. 7: Weyl–Kondo semimetals.
Fig. 8: Electronic localization–delocalization and bad metal behaviour in correlated quantum matter.

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Acknowledgements

The authors thank the late Elihu Abrahams, and P. Aynajian, P. Blaha, A. Cai, P. Coleman, J. Dai, W. Ding, S. Dzsaber, G. Eguchi, S. Friedemann, P. Goswami, S. Grefe, K. Grube, K. Held, H. Hu, K. Ingersent, S. Kirchner, J. Kono, H.-H. Lai, C.-C. Liu, Y. Luo, V. Martelli, E. Morosan, A. Nevidomskyy, D. H. Nguyen, E. Nica, J. Pixley, L. Prochaska, A. Prokofiev, E. Schuberth, A. Severing, T. Shiroka, F. Steglich, O. Stockert, L. Sun, P. Sun, M. Taupin, J. D. Thompson, J. Tomczak, H. von Löhneysen, S. Wirth, J. Wu, Z. Xu, X. Yan, R. Yu, H. Yuan, J.-X. Zhu and D. Zocco for collaborations and/or discussions. The work has been supported in part by the Austrian Science Fund grants no. P29279-N27, P29296-N27 and DK W1243, the European Union’s Horizon 2020 Research and Innovation Programme grant EMP-824109 (S.P.), the US National Science Foundation (NSF) grant no. DMR-1920740 and the Robert A. Welch Foundation grant no. C-1411 (Q.S.). We acknowledge the hospitality of the Aspen Center for Physics, which is supported by NSF grant no. PHY-1607611.

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Supplementary information

Glossary

Sommerfeld–Wilson ratio

The ratio of the (Pauli paramagnetic, temperature-independent) magnetic susceptibility to the linear-in-temperature specific heat (Sommerfeld) coefficient γ.

Kadowaki–Woods ratio

The ratio of the quadratic-in-temperature electrical resistivity coefficient, A, to the square of the linear-in-temperature specific heat (Sommerfeld) coefficient γ.

Grüneisen ratio

A quantity that is proportional to the ratio of volume thermal expansion to specific heat and diverges at a quantum critical point.

Mott–Ioffe–Regel limit

The condition of maximal scattering in a metal, where the mean free path becomes comparable to the ratio of 2π to the Fermi wavevector kF.

de Haas–van Alphen (dHvA) frequencies

Characteristic frequencies in quantum oscillation measurements of the magnetic susceptibility that characterize information about the material’s Fermi surface.

ω/T scaling

The collapsing of the dependence on the energy ω (in units of the reduced Planck constant) and temperature T in terms of their ratio ω/T.

dangerously irrelevant variable

A term in the renormalization-group (RG) treatment of a many-body system, denoting a variable that is irrelevant in the RG sense but provides leading contributions to certain physical quantities of the system.

SU(4) spin–orbital-coupled Kondo effect

Entwined spin and orbital building blocks form an SU(4) local multiplet, which is coupled to the corresponding conduction electron degrees of freedom to form an SU(4) Kondo singlet.

Berry curvature

The gauge-invariant rank-two tensor that is associated with the Berry (or geometric) phase; for itinerant electrons, it acts as a fictitious magnetic field in momentum space and is singularly large around the nodes of a Weyl semimetal.

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Paschen, S., Si, Q. Quantum phases driven by strong correlations. Nat Rev Phys 3, 9–26 (2021). https://doi.org/10.1038/s42254-020-00262-6

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