Chiral Tricritical Point: A New Universality Class in Dirac Systems

Abstract

Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed-matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this Letter, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed.

Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point

“…To explain this observation, we develop a modified mean-field theory to study the effective coupling in the free energy and reveal that this anomalous phenomenon is induced by the interplay between critical fluctuations and the finite-size effects, in a quantitative manner. Moreover, we pinpoint the tricritical point separating the first-order and the continuous phase transitions, and numerically verify that this CTP acquires the critical exponents of chiral Gross-Neveu universality, confirming the renormalization group predictions 63 .…”

“…Although enormous investigations have been devoted to this issue 35,[42][43][44][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] , the numerical verification for type-II FIQCP is still lacking. Remarkably, recent studies based on the fieldtheoretical effective model propose that type-II FIQCP can also feature new tricritical behaviors, controlled by the chiral tricritical point (CTP) 63 . This CTP separates the conventional Landau-Devonshire first-order transition from the type-II FIQCP 33 , and the universal scaling behavior near this CTP is quite different from its pure bosonic counterpart.…”

Fermion-induced quantum criticality with two length scales in Dirac systems

“…The key features of the FRG approach in the present context are the following: The FRG is well-suited for calculations directly in 2+1 dimensions. It has been tested against other methods which has shown that it provides very good results in the context of Gross-NeveuYukawa models [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] . Importantly, the FRG approach already includes resummation effects through the non-perturbative threshold functions 61,62 , which is in contrast to perturbative approaches.…”

Electronic properties of the Dirac and Weyl systems with first- and higher-order dispersion in non-Fermi-liquid picture

“…The destoryed Fermi-liquid behavior can be observed by the singular Bosonic susceptibility at the nesting wavevector, and it can't be found even at low-energy limit (far away from the quantum critical point) when the ultraviolet cutoff applied is infinite during the calculation, as could be found in the many-electron system, for example, when the Fermions coupled to the 1D Ising variable [40] or the fluctuation transverse gauge field [41] or the longitudinal Bosonic excitation [2]. The non-Fermi-liquid phenomenons are widely observed in the heavy-Fermi system and the cuprate materials [42,43], including the logarithmic divergent specific heat which related to the free energy by…”