We consider interacting (2+1)-dimensional Dirac fermions with competing symmetry-breaking electronic instabilities, as described by relativistic quantum field theories of the Gross-Neveu-Yukawa flavor with anti-commuting mass terms. We demonstrate, using a combination of nonperturbative field-theoretical analysis and an adapted quantum Monte Carlo approach, that such systems exhibit a strong-coupling quantum multicritical fixed point with an emerging enhanced symmetry. Moreover, an extended phase coexistence regime expands out from this high-symmetry point. Our results disagree with recent results on the presence of a deconfined quantum criticality in (2+1)-dimensional Dirac fermions for the particular case of O(3) Neel and Z(2) Kekule symmetry-breaking instabilities on the graphene lattice. The robustness of these phenomena with respect to the microscopic symmetries furthermore demonstrates their relevance for a wide range of Dirac materials of current interest, from both theory and ongoing experiments.
We consider interacting (2+1)-dimensional Dirac fermions with competing symmetry-breaking electronic instabilities, as described by relativistic quantum field theories of the Gross-Neveu-Yukawa flavor with anti-commuting mass terms. We demonstrate, using a combination of nonperturbative field-theoretical analysis and an adapted quantum Monte Carlo approach, that such systems exhibit a strong-coupling quantum multicritical fixed point with an emerging enhanced symmetry. Moreover, an extended phase coexistence regime expands out from this high-symmetry point. Our results disagree with recent results on the presence of a deconfined quantum criticality in (2+1)-dimensional Dirac fermions for the particular case of O(3) Neel and Z(2) Kekule symmetry-breaking instabilities on the graphene lattice. The robustness of these phenomena with respect to the microscopic symmetries furthermore demonstrates their relevance for a wide range of Dirac materials of current interest, from both theory and ongoing experiments.
We consider a model of Dirac fermions in 2+1 dimensions with dynamically generated, anticommuting SO(3) Néel and Z_{2} Kekulé mass terms that permits sign-free quantum Monte Carlo simulations. The phase diagram is obtained from finite-size scaling and includes a direct and continuous transition between the Néel and Kekulé phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. While the bare symmetries of our model do not allow for spinon-carrying Z_{3} vortices in the Kekulé mass, the emergent SO(4) invariance permits an interpretation of the transition in terms of deconfined quantum criticality. The phase diagram also features a tricritical point at which the Néel, Kekulé, and semimetallic phases meet. The present sign-free approach can be generalized to a variety of other mass terms and thereby provides a new framework to study exotic critical phenomena.
We analyze emergent quantum multicriticality for strongly interacting, massless Dirac fermions in two spatial dimensions (d=2) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break O(S1) and O(S2) symmetries in the ordered phase. Performing a renormalization-group analysis by using the $\ensuremath{\epsilon}=(3\ensuremath{-}d)$ expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an enlarged O(S1+S2) chiral symmetry. Such a fixed point acts as an exotic quantum multicritical point (MCP), governing the continuous semimetal-insulator as well as insulator-insulator (for example, antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either O(S1) or O(S2) chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power-law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher-dimensional Dirac fermions is also outlined.
We analyze the possibility of emergent quantum multicritical points (MCPs) with enlarged chiral symmetry, when strongly interacting gapless Dirac fermions acquire a comparable propensity toward the nucleation of Kekul\'e valence-bond solid (KVBS) and charge-density-wave (Nb=1) or s-wave pairing (Nb=2) or antiferromagnet (Nb=3) in a honeycomb lattice, where Nb counts the number of bosonic order-parameter components. Besides the cubic terms present in the order-parameter description of KVBS due to the breaking of a discrete Z3 symmetry, quantum fluctuations generate new cubic vertices near the high-symmetry MCPs. All cubic terms are strongly relevant at the bare level near three spatial dimensions, about which we perform a leading-order renormalization group analysis of coupled Gross-Neveu-Yukawa field theory. We show that due to nontrivial Yukawa interactions among gapless bosonic and fermionic degrees of freedom, all cubic terms ultimately become irrelevant at an O(2+Nb) symmetric MCP, at leas near two spatial dimensions, where Nb=1,2,3. Therefore, MCPs with an enlarged O(2+Nb) symmetry near KVBS ordering are stable.
We study quantum multicritical behavior in a $(2+1)\text{\ensuremath{-}}\mathrm{dimensional}$ Gross-Neveu-Yukawa field theory with eight-component Dirac fermions coupled to two triplets of order parameters that act as Dirac masses and transform as (1,0)+(0,1) representation under the $\mathrm{S}\mathrm{O}(4)\ensuremath{\simeq} \mathrm{S}\mathrm{O}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(3)$ symmetry group. This field theory is relevant to spin-1/2 fermions on honeycomb or $\ensuremath{\pi}$-flux lattices, for example, near the transition points between an s-wave superconductor and a charge-density wave, on one side, and N\'eel order, on the other. Two triplets of such order parameters always allow for a common pair of two other order parameters that would complete them to the maximal set of compatible (anticommuting) orders of five. We first derive a unitary transformation in the Nambu (particle-hole) space which maps any two such triplets, possibly containing some superconducting orders, onto purely insulating order parameters. This allows one to consider a universal SO(4) Gross-Neveu-Yukawa description of the multicriticality without any Nambu doubling. We then proceed to derive the renormalization-group flow of the coupling constants at one-loop order in $4\ensuremath{-}\ensuremath{\epsilon}$ space-time dimensions, allowing also a more general set of order parameters transforming under $\mathrm{S}\mathrm{O}({n}_{a})\ifmmode\times\else\texttimes\fi{}\mathrm{S}\mathrm{O}({n}_{b})$. While for na=nb>2 in the bosonic sector and with fermions decoupled there is a stable fixed point of the flow, the Yukawa coupling to fermions quickly leads to its elimination by a generic fixed-point collision in the relevant range of fermion flavor numbers Nf. This suggests the replacement of the critical behavior by a runaway flow in the physical case na=nb=3. The structure of the renormalization group flow at ${n}_{a}\ensuremath{\ne}{n}_{b}$ is also discussed, and some nonperturbative arguments in favor of the stability of the decoupled critical point when na=3 and nb=1 in D=2+1 are provided.
In this paper we discuss the Neˊel and Kekuleˊ valence bond solids quantum criticality in graphene Dirac semimetal. Considering the quartic four-fermion interaction g(ψˉiΓijψj)2 that contains spin,valley, and sublattice degrees of freedom in the continuum field theory, we find the microscopic symmetry is spontaneously broken when the coupling g is greater than a critical value gc. The symmetry breaking gaps out the fermion and leads to semimetal-insulator transition. All possible quartic fermion-bilinear interactions give rise to the uniform critical coupling, which exhibits the multicritical point for various orders and the Landau-forbidden quantum critical point. We also investigate the typical critical point between Neˊel and Kekuleˊ valence bond solid transition when the symmetry is broken. The quantum criticality is captured by the Wess-Zumino-Witten term and there exist a mutual-duality for Neˊel-Kekuleˊ VBS order. We show the emergent spinon in the Neˊel-Kekuleˊ VBS transition , from which we conclude the phase transition is a deconfined quantum critical point. Additionally, the connection between the index theorem and zero energy mode bounded by the topological defect in the Kekuleˊ VBS phase is studied to reveal the Neˊel-Kekuleˊ VBS duality.