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| Quantum criticality | |
|---|---|
| Name | Quantum criticality |
| Field | Condensed matter physics |
| Related | Quantum phase transition; Critical point; Renormalization group |
Quantum criticality is the behavior of matter at a zero-temperature continuous transition driven by non-thermal tuning parameters, where quantum fluctuations dominate and classical thermal criticality is replaced by scale-invariant quantum dynamics. It unifies ideas from Kenneth G. Wilson's scaling theory, Philip W. Anderson's ideas on correlations, and concepts developed in studies by Subir Sachdev and John Cardy, and it underpins research across experimental platforms such as heavy-fermion metals, cuprate superconductors, and ultracold atomic gases.
Quantum criticality occurs at a quantum critical point (QCP) where a control parameter like pressure, composition, or magnetic field tunes a ground state between distinct phases such as antiferromagnetism and superconductivity; influential studies include experiments on CeCu6-xAux, YbRh2Si2, and the cuprate La2-xSrxCuO4. The phenomenon connects to theoretical frameworks pioneered by Richard Feynman's path integrals and Leo Kadanoff's block-spin ideas and has implications for exotic phases explored at institutions like MIT and CERN.
The theoretical foundation rests on mapping d-dimensional quantum problems to (d+z)-dimensional classical problems using dynamical critical exponent z, an approach formalized in work by John Hertz and elaborated by Andrew J. Millis; renormalization-group flows were advanced by Kenneth G. Wilson and many collaborators. Models central to the theory include the transverse-field Ising model studied in the context of the Ising model and the Kondo lattice model motivated by experiments on CeCoIn5, with analytical and numerical methods developed at centers like Los Alamos National Laboratory and Lawrence Berkeley National Laboratory. Field-theory treatments often reference techniques from Alexander Polyakov's conformal field theory and lattice quantum Monte Carlo methods championed by groups at Harvard University and University of Cambridge.
Quantum phase transitions appear in itinerant electron systems such as the ferromagnetic-to-paramagnetic transition explored in MnSi under pressure and in localized moment systems like the Kondo breakdown studied in YbRh2Si2. Topological quantum phase transitions were emphasized in work on Brian David Josephson-related junction arrays and in studies of the quantum Hall plateau transitions exemplified by André Geim's graphene experiments. Transitions in low-dimensional magnets and chains have been addressed in materials like SrCu2(BO3)2 and by theoretical analysis from groups affiliated with Max Planck Institute for Solid State Research.
Probes include neutron scattering performed at facilities such as the Institut Laue-Langevin, muon spin rotation at instruments developed by Z. Salman's collaborations, and angle-resolved photoemission spectroscopy (ARPES) used by teams including Zhi-Xun Shen. Transport anomalies—non-Fermi liquid resistivity observed in CeCoIn5 and linear-in-temperature resistivity in Bi2Sr2CaCu2O8+x—have been linked to QCPs; thermodynamic signatures involve divergent Grüneisen ratios measured in studies at Max Planck Society facilities. Cold-atom quantum simulators built at JILA and MIT-Harvard Center for Ultracold Atoms provide controllable probes of quantum critical dynamics, while scanning tunneling microscopy by groups like STM pioneer Gerd Binnig's collaborators reveals local density of states variations.
Scaling hypotheses derive from the work of Leo Kadanoff and Kenneth G. Wilson with universality classes classified by symmetries and dimensionality; quantum critical scaling functions incorporate dynamic exponent z as emphasized in analyses by Subir Sachdev and John Cardy. Universality has been tested in systems ranging from heavy-fermion compounds studied at ETH Zurich to cold-atom lattices investigated at Institute for Quantum Optics and Quantum Information laboratories. Advanced numerical renormalization techniques such as density-matrix renormalization group (DMRG) developed by Steven R. White and quantum Monte Carlo methods by groups at Princeton University provide quantitative checks of scaling predictions.
Prominent materials include heavy-fermion metals like CeCu6-xAux, YbRh2Si2, CeCoIn5, iron pnictides such as BaFe2As2, and cuprates like YBa2Cu3O7 and La2-xSrxCuO4. Low-dimensional magnets showing criticality include SrCu2(BO3)2 and KCuF3, while quantum Hall systems studied in Bell Labs and graphene researched by Andre Geim and Konstantin Novoselov’s teams reveal topological critical points. Artificial systems—optical lattices at JILA, Josephson junction arrays explored by groups at University of Illinois Urbana-Champaign, and engineered quantum dots made in facilities at Bell Labs—serve as tunable platforms to study QCP phenomena.
Quantum criticality provides routes to unconventional superconductivity as proposed for CeCoIn5 and the cuprate family studied at Brookhaven National Laboratory and Argonne National Laboratory, and informs proposals for quantum devices exploiting critical entanglement in platforms pursued by IBM and Google. The interplay of quantum critical fluctuations with topology underlies ideas advanced by researchers at Perimeter Institute and Institute for Advanced Study, with potential impact on materials design initiatives at DARPA and advanced spectroscopy programs at National Institute of Standards and Technology.