arXiv subjects

Mikolaj D. Uryszek

Publications and source records attributed to Mikolaj D. Uryszek.

4 recordsLinked to original sources

arXiv2023

Stability of the Néel quantum critical point in the presence of Dirac fermions

We investigate the stability of the Néel quantum critical point of two-dimensional quantum antiferromagnets, described by a non-linear $σ$ model (NL$σ$M), in the presence of a Kondo coupling to $N_f$ flavours of two-component Dirac fermion fields. The long-wavelength order parameter fluctuations are subject to Landau damping by electronic particle-hole fluctuations. Using momentum-shell RG, we demonstrate that the Landau damping is weakly irrelevant at the Néel quantum critical point, despite the fact that the corresponding self-energy correction dominates over the quadratic gradient terms in the IR limit. In the ordered phase, the Landau damping increases under the RG, indicative of damped spin-wave excitations. Although the Kondo coupling is weakly relevant, sufficiently strong Landau damping renders the Néel quantum critical point quasi-stable for $N_f\ge 4$ and thermodynamically stable for $N_f<4$. In the latter case, we identify a new multi-critical point which describes the transition between the Néel critical and Kondo run-away regimes. The symmetry breaking at this fixed point results in the opening of a gap in the Dirac fermion spectrum. Approaching the multi-critical point from the disordered phase, the fermionic quasiparticle residue vanishes, giving rise to non-Fermi-liquid behavior.

cond-mat.str-el↗

arXiv2022

Interplay of interactions and disorder at the charge-density wave transition of two-dimensional Dirac semimetals

We consider the effects of weak quenched fermionic disorder on the quantum-phase transition between the Dirac semimetal and charge density wave (CDW) insulator in two spatial dimensions. The symmetry breaking transition is described by the Gross-Neveu-Yukawa (GNY) theory of Dirac fermions coupled to an Ising order parameter field. Treating the disorder using the replica method, we consider chemical potential, vector potential (gauge), and random mass disorders, which all arise from non-magnetic charge impurities. We self-consistently account for the Landau damping of long-wavelength order-parameter fluctuations by using the non-perturbative RPA re-summation of fermion loops, and compute the renormalization-group (RG) flow to leading order in the disorder strength and $1/N$ ($N$ the number of Dirac fermion flavors). We find two fixed points, the clean GNY critical point which is stable against weak disorder, and a dirty GNY multi-critical point, at which the chemical potential disorder is finite and the other forms of disorder are irrelevant. We investigate the scaling of physical observables at this finite-disorder multi-critical point which breaks Lorentz invariance and gives rise to distinct non-Fermi liquid behavior.

cond-mat.str-el↗

arXiv2020

Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: exact $1/N_f$ exponents

We consider the fermionic quantum criticality of anisotropic nodal point semimetals in $d = d_L + d_Q$ spatial dimensions that disperse linearly in $d_L$ dimensions, and quadratically in the remaining $d_Q$ dimensions. When subject to strong interactions, these systems are susceptible to semimetal-insulator transitions concurrent with spontaneous symmetry breaking. Such quantum critical points are described by effective field theories of anisotropic nodal fermions coupled to dynamical order parameter fields. We analyze the universal scaling in the physically relevant spatial dimensions, generalizing to a large number $N_f$ of fermion flavors for analytic control. Landau damping by gapless fermionic excitations gives rise to non-analytic self-energy corrections to the bosonic order-parameter propagator that dominate the long-wavelength behavior. We show that perturbative momentum shell RG leads to non-universal, cutoff dependent results, as it does not correctly account for this non-analytic structure. In turn, using a completely general soft cutoff formulation, we demonstrate that the correct IR scaling of the dressed bosonic propagator can be deduced by enforcing that results are independent of the cutoff scheme. Using this soft cutoff approach, we compute the exact critical exponents for anisotropic semi-Dirac fermions $(d_L=1$, $d_Q=1)$ to leading order in $1/N_f$, and to all loop orders. Applying the same method to relativistic Dirac fermions, we reproduce the critical exponents obtained by other methods, such as conformal bootstrap...

cond-mat.str-el↗

arXiv2019

Quantum Criticality of Semi-Dirac Fermions in 2+1 Dimensions

Two-dimensional semi-Dirac fermions are quasiparticles that disperse linearly in one direction and quadratically in the other. We investigate instabilities of semi-Dirac fermions towards charge, spin-density wave and superconducting orders, driven by short-range interactions. We analyze the critical behavior of the Yukawa theories for the different order parameters using Wilson momentum shell RG. We generalize to a large number $N_f$ of fermion flavors to achieve analytic control in 2+1 dimensions and calculate critical exponents at one-loop order, systematically including $1/N_f$ corrections. The latter depend on the specific form of the bosonic infrared propagator in 2+1 dimensions, which needs to be included to regularize divergencies. The $1/N_f$ corrections are surprisingly small, suggesting that the expansion is well controlled in the physical dimension. The order-parameter correlations inherit the electronic anisotropy of the semi-Dirac fermions, leading to correlation lengths that diverge along the spatial directions with distinct exponents, even at the mean-field level. We conjecture that the proximity to the critical point may stabilize novel modulated order phases.

cond-mat.str-el↗