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arXiv:1608.06927 · Physical Review X

Exact Critical Exponents for the Antiferromagnetic Quantum Critical Metal in Two Dimensions

Andrés Schlief, Peter Lunts, Sung-Sik Lee

Published Apr 20, 2017• 78 citations
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Abstract

Strange metals, which exhibit unusual changes in physical properties such as electrical resistance and heat capacity in response to temperature, are difficult to understand with current theoretical tools. A new analysis provides the exact solution to a theory that describes two-dimensional strange metals that arise as a metal transitions to a magnet.

DOI
10.1103/physrevx.7.021010

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Strange metals, which exhibit unusual changes in physical properties such as electrical resistance and heat capacity in response to temperature, are difficult to understand with current theoretical tools. A new analysis provides the exact solution to a theory that describes two-dimensional strange metals that arise as a metal transitions to a magnet.
In this thesis, we study the low-energy effective theory for the antiferromagnetic quantum critical metal in two dimensions. The theory has been the subject of intense study for more than twenty years, due to the novel physics of non-Fermi liquid metals and its potential relevance to high-temperature superconductors and heavy-fermion compounds. In the first part of the thesis, we present the perturbative study of the theory in 3 minus epsilon space dimensions by extending the earlier one-loop analysis to higher-loop orders. We show that the expansion is not organized by the standard loop expansion, and a two-loop graph becomes as important as one-loop graphs even in the small epsilon limit due to an infrared singularity caused by an emergent quasilocality. This qualitatively changes the nature of the infrared fixed point, and the epsilon expansion is controlled only after the two-loop effect is taken into account. Furthermore, we show that a ratio between velocities emerges as a small parameter, which suppresses a large class of diagrams. We show that the critical exponents do not receive quantum corrections beyond the linear order in epsilon in the limit that the ratio of velocities vanishes. In the second part of the thesis, we present a nonperturbative solution to the theory in two dimensions based on an ansatz that is inspired by the perturbative analysis. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by the ratio of velocities that dynamically flows to zero in the low-energy limit. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures.
We show that the anomalous temperature scaling of five distinct transport quantities in the strange metal regime of the cuprate superconductors can be reproduced with only two nontrivial critical exponents. The quantities are (i) the electrical resistivity, (ii) the Hall angle, (iii) the Hall-Lorenz ratio, (iv) the magnetoresistance, and (v) the thermopower. The exponents are the dynamical critical exponent z=4/3z=4/3z=4/3 and an anomalous scaling dimension $\ensuremath{\Phi}=\ensuremath{-}2/3$ for the charge density operator.
Strange metals—ubiquitous in correlated quantum materials—transport electrical charge at low temperatures but not by the individual electronic quasiparticle excitations, which carry charge in ordinary metals. In this work, we consider two-dimensional metals of fermions coupled to quantum critical scalars, the latter representing order parameters or fractionalized particles. We show that at low temperatures ( T ), such metals generically exhibit strange metal behavior with a T -linear resistivity arising from spatially random fluctuations in the fermion-scalar Yukawa couplings about a nonzero spatial average. We also find a T ln(1/ T ) specific heat and a rationale for the Planckian bound on the transport scattering time. These results are in agreement with observations and are obtained in the large N expansion of an ensemble of critical metals with N fermion flavors.