With the coupled Dyson-Schwinger equations in the framework of the unified QED3 theory,we study the phase transition between the antiferromagnet(AF) and the d-wave superconductor (dSC) of planar cuprates at T=0.By solving the coupled Dyson-Schwinger equations both analytically and numerically in rainbow approximation in Landau gauge and comparing the obtained results with that given in the 1/N expansion,we find that there exists a chiral symmetry breaking from dSC phase to AF phase when the quasi- fermion flavors N■4 in half-filling and the AF phase can possibly coexist with the dSC phase in the underdoped region.By comparing the pressure between the coexistent AF-dSC phase and dSC phase,we find that AF-dSC coexisting phase is the stable phase,the AF phase can then coexist with the dSC phase.
With the coupled Dyson-Schwinger equations in the framework of the unified QED3 theory,we study the phase transition between the antiferromagnet(AF) and the d-wave superconductor (dSC) of planar cuprates at T=0.By solving the coupled Dyson-Schwinger equations both analytically and numerically in rainbow approximation in Landau gauge and comparing the obtained results with that given in the 1/N expansion,we find that there exists a chiral symmetry breaking from dSC phase to AF phase when the quasi- fermion flavors N■4 in half-filling and the AF phase can possibly coexist with the dSC phase in the underdoped region.By comparing the pressure between the coexistent AF-dSC phase and dSC phase,we find that AF-dSC coexisting phase is the stable phase,the AF phase can then coexist with the dSC phase.
We study the effect of gapless quasiparticles in a d-wave superconductor on the T=0 end point of the Kosterlitz-Thouless transition line in underdoped high-temperature superconductors. Starting from a lattice model that has gapless fermions coupled to three-dimensional XY phase fluctuations of the superconducting order parameter, we propose a continuum field theory to describe the quantum phase transition between the d-wave superconductor and the spin-density-wave insulator. Without fermions, the theory reduces to the standard Higgs scalar electrodynamics (HSE), which is known to have the critical point in the inverted XY universality class. Extending the renormalization group calculation for the HSE to include the coupling to fermions, we find that the qualitative effect of fermions is to increase the portion of the space of coupling constants where the transition is discontinuous. The critical exponents at the stable fixed point vary continuously with the number of fermion fields N, and we estimate the correlation length exponent $(\ensuremath{\nu}=0.65)$ and the vortex field anomalous dimension $({\ensuremath{\eta}}_{\ensuremath{\Phi}}=\ensuremath{-}0.48)$ at the quantum critical point for the physical case N=2. The stable critical point in the theory disappears for the number of Dirac fermions N>Nc, with ${N}_{c}\ensuremath{\approx}3.4$ in our approximation. We discuss the relationship between the superconducting and the chiral (SDW) transitions, and point to some interesting parallels between our theory and the Thirring model.
Within the framework of a relativistic non-Abelian gauge theory approach to the physics of spin–charge separation in doped quantum antiferromagnetic planar systems, proposed recently by the authors, we are examining here the effects of constant external magnetic fields on excitations about the superconducting state in the model. The electrically-charged Dirac fermions (holons), describing excitations about specific points on the fermi surface, e.g. those corresponding to the nodes of a d-wave superconducting gap in high-T c cuprates, condense, resulting in the opening of a Kosterlitz–Thouless–like gap (KT) at such nodes. This leads, in general, to a second superconducting phase transition, which occurs at low temperatures[Formula: see text], in addition to the high-T c superconductivity [Formula: see text] due to the bulk of the fermi surface for holons in a (d-wave) spin–charge separated superconductor. In the presence of strong external magnetic fields at the surface regions of the planar superconductor, in the direction perpendicular to the superconducting planes, these KT gaps appear to be enhanced. Our preliminary analysis, based on analytic Schwinger–Dyson treatments, seems to indicate that for an even number of Dirac fermion species, required in our model as a result of gauging a particle–hole SU(2) symmetry, Parity or Time Reversal violation does not necessarily occurs. Based on these considerations, we argue that recent experimental findings, concerning thermal conductivity plateaux of quasiparticles in planar high-T c cuprates in strong external magnetic fields, may indicate the presence of such KT gaps, caused by charged Dirac-fermion excitations in these materials, as suggested in the above model.
A version of non‐compact QED in 2+1 dimensions (QED3), with anisotropies introduced by differing Fermi and gap velocities in the spatial directions has been proposed as an effective theory of the SDW‐pseudogap phase transition in underdoped cuprates at T=0. Preliminary simulations using lattice gauge theory techniques suggest that matters are a little more complicated than previously thought; in particular, measurements of the fermion propagator in Landau gauge indicate that one should be cautious in inferring properties of this form of QED3 from those of isotropic QED3.
Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here, we report unbiased quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same on site symmetries as the standard Hubbard model on a 2D square lattice. Using QMC simulations, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.
Unconventional superconductors such as cuprates often host competing nodal superconductivity and antiferromagnetism. These systems are typically modeled as a repulsive Hubbard model whose unbiased simulation suffers from the fermion sign-problem at any non-zero doping. Here we will exploit the fact that neither of these phases, the nodal d-wave superconductor or the antiferromagnet, require any doping for their existence, and construct a sign-problem-free repulsive Hubbard model with an additional bosonic field which hosts both of these phases. Using Quantum Monte Carlo (QMC) simulations, supplemented with mean-field theory and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the chiral Gross-Neveu-Heisenberg theory.
We investigate a zero-temperature itinerant antiferromagnetic transition where the fermions possess a d-wave gap. This problem pertains to both the nodal liquid insulating phase and the d-wave superconducting phase of the underdoped cuprates. We find that a non-trivial quantum phase transition exists, and that the quantum critical point is dominated by a long-ranged interaction (∣x−y∣−2d) of the Néel order parameter, which is induced by the Dirac-like fermions near gap nodes. We formulate a Ginzburg-Landau functional and estimate the critical exponents via the large-N expansion method.