Abstract
We present a functional renormalization group analysis of a quantum critical point in two-dimensional metals involving Fermi surface reconstruction due to the onset of spin-density wave order. Its critical theory is controlled by a fixed point in which the order parameter and fermionic quasiparticles are strongly coupled and acquire spectral functions with a common dynamic critical exponent. We obtain results for critical exponents and for the variation in the quasiparticle spectral weight around the Fermi surface. Our analysis is implemented on a two-band variant of the spin-fermion model which will allow comparison with sign-problem-free quantum Monte Carlo simulations.
Highlights
Quantum phase transitions between two Fermi liquids, one of which spontaneously breaks translational symmetry and so reconstructs its Fermi surface, have been of long standing theoretical and experimental interest
To immediate relevance for a class of strongly correlated electron materials, the spin-fermion model has evolved into a minimal model for itinerant lattice electrons with strong, commensurate magnetic fluctuations that are believed to destroy the Fermi liquid behavior when tuned to the critical point
For the hot spot field theory at the onset of spin density wave order, no such critical theory appeared at the two-loop level
Summary
Quantum phase transitions between two Fermi liquids, one of which spontaneously breaks translational symmetry and so reconstructs its Fermi surface, have been of long standing theoretical and experimental interest. When projecting our correlators onto the hot spot as a function of momenta, we establish the existence of a fixed point with the scaling structure postulated in Ref. 11, describing the quantum phase transition between two Fermi liquids: from the metal with preserved SU(2) spin symmetry to the metallic antiferromagnet which spontaneously breaks spin symmetry. Our computation will be carried in the context of the ‘spinfermion’ model of antiferromagnetic fluctuations in a Fermi liquid[9] This involves a spin density wave order parameter φ at wavevector K = (π, π) coupled to fermions Ψ moving on a square lattice. We shall ignore this complications and focus our attention continuous SDW transitions at zero temperature
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