Hyperscaling at the spin density wave quantum critical point in two dimensional metals

Abstract

The hyperscaling property implies that spatially isotropic critical quantum states in $d$ spatial dimensions have a specific heat which scales with temperature as $T^{d/z}$, and an optical conductivity which scales with frequency as ${\omega }^{(d-2)/z}$ for $\omega \gg T$, where $z$ is the dynamic critical exponent. We examine the spin-density-wave critical fixed point of metals in $d=2$ found by Sur and Lee (Phys. Rev. B 91, 125136 (2015)) in an expansion in $\epsilon =3-d$. We find that the contributions of the "hot spots" on the Fermi surface to the optical conductivity and specific heat obey hyperscaling (up to logarithms), and agree with the results of the large $N$ analysis of the optical conductivity by Hartnoll et al. (Phys. Rev. B 84, 125115 (2011)). With a small bare velocity of the boson associated with the spin density wave order, there is an intermediate energy regime where hyperscaling is violated with $d\to d_t$, where $d_t=1$ is the number of dimensions transverse to the Fermi surface. We also present a Boltzmann equation analysis which indicates that the hot spot contribution to the DC conductivity has the same scaling as the optical conductivity, with $T$ replacing $\omega$.

46 pages, 5 figures, To appear in Phys. Rev. B

References in corpus (20)

• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Quantum criticality
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Quantum Criticality
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Quantum critical transport in clean graphene
• Are non-Fermi-liquids stable to Cooper pairing?
• Momentum dissipation and effective theories of coherent and incoherent transport
• Quantum Critical Transport and the Hall Angle
• Memory matrix theory of magnetotransport in strange metals
• Dissecting holographic conductivities
• Absence of disorder-driven metal-insulator transitions in simple holographic models
• Anomalous dynamical scaling from nematic and U(1)-gauge field fluctuations in two dimensional metals
• DC resistivity at the onset of spin density wave order in two-dimensional metals
• Conductivity of a strange metal: from holography to memory functions
• Hydrodynamic transport in strongly coupled disordered quantum field theories
• Quasi-Local Strange Metal
• A controlled expansion for certain non-Fermi liquid metals
• Quantum kinetics of ultracold fermions coupled to an optical resonator
• Quantum criticality of reconstructing Fermi surfaces in antiferromagnetic metals

Cited by in corpus (40)

• Holographic quantum matter
• Memory matrix theory of magnetotransport in strange metals
• Bad Metals from Fluctuating Density Waves
• Hydrodynamic transport in strongly coupled disordered quantum field theories
• Quantum Electrodynamics in d=3 from the epsilon-expansion
• DC resistivity of quantum critical, charge density wave states from gauge-gravity duality
• Exact critical exponents for the antiferromagnetic quantum critical metal in two dimensions
• Optical response of correlated electron systems
• Hyperscaling violation at the Ising-nematic quantum critical point in two dimensional metals
• Anisotropic Non-Fermi Liquids
• Transport in the non-Fermi liquid phase of isotropic Luttinger semimetals
• Emergence of a control parameter for the antiferromagnetic quantum critical metal
• Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals
• Spin density wave order, topological order, and Fermi surface reconstruction
• Scaling behaviour and superconducting instability in anisotropic non-Fermi liquids
• Unparticles and Anomalous Dimensions in the Cuprates
• Universality in antiferromagnetic strange metals
• Non-Fermi liquid at the FFLO quantum critical point
• Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"
• Hydrodynamic flows of non-Fermi liquids: magnetotransport and bilayer drag
• Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions
• Raman response and shear viscosity in the non-Fermi liquid phase of Luttinger semimetals
• Noncommutativity between the low-energy limit and integer dimension limits in the $\mathbf{\epsilon }$-expansion: a case study of the antiferromagnetic quantum critical metal
• Memory matrix theory of the dc resistivity of a disordered antiferromagnetic metal with an effective composite operator
• Transport properties in non-Fermi liquid phases of nodal-point semimetals
• Incommensurate $2k_F$ density wave quantum criticality in two dimensional metals
• Space of non-Fermi liquids
• Fermi liquids beyond the forward scattering limit: the role of non-forward scatterings for scale invariance and instabilities
• Thermal and thermoelectric transport coefficients for a two-dimensional SDW metal with weak disorder: A memory matrix calculation
• Quenched disorder at antiferromagnetic quantum critical points in $2d$ metals
• Calculation of the magnetotransport for a spin-density-wave quantum critical theory in the presence of weak disorder
• Strange metallicity in an antiferromagnetic quantum critical model: A sign-problem-free quantum Monte-Carlo study
• Conductivity bounds in probe brane models
• Critical behavior of itinerant fermions - role of finite size effects
• Effects of general non-magnetic quenched disorder on a spin-density-wave quantum critical metallic system in two spatial dimension
• Emergence of curved momentum-spacetime and its effect on the cyclotron motion in the antiferromagnetic quantum critical metal
• Spin pumping effect in non-Fermi liquid metals
• Entanglement and Excitations in Gauge/Gravity Duality
• Anomalous quasiparticle lifetime in geometric quantum critical metals
• Dynamical kinetic energy quenching in the antiferromagnetic quantum critical metals