Critical Wess-Zumino models with four supercharges in the functional renormalization group approach

Feldmann, Polina; Wipf, Andreas; Zambelli, Luca

doi:10.1103/physrevd.98.096005

Cited by 13 publications

(15 citation statements)

References 132 publications

(181 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Concomitant with the topological phase transition from second-order to topological insulator, time-reversal symmetry and inversion symmetry emerge. The previous works has shown the possibility of emergent Lorentz symmetry [63][64][65][66][67][68][69][70], emergent chiral symmetry [71][72][73], and even emergent supersymmetry [74][75][76][77][78][79][80][81][82][83][84][85]. Here, by providing the concrete example, we show that emergent symmetries could happen for the discrete time-reversal and inversion symmetries, which enrich the family of emergent symmetries [86].…”

supporting

confidence: 50%

Coulomb Instabilities of a Three-Dimensional Higher-Order Topological Insulator

Zhao

Qiang

et al. 2021

Phys. Rev. Lett.

View full text Add to dashboard Cite

supporting

confidence: 50%

Coulomb Instabilities of a Three-Dimensional Higher-Order Topological Insulator

Zhao

Qiang

et al. 2021

Phys. Rev. Lett.

View full text Add to dashboard Cite

“…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.…”

Section: A Methodsmentioning

confidence: 99%

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

et al. 2018

View full text Add to dashboard Cite

The quantum phase transition to a Z3-ordered Kekulé valence bond solid in two-dimensional Dirac semimetals is governed by a fermion-induced quantum critical point, which renders the putatively discontinuous transition continuous. We study the resulting universal critical behavior in terms of a functional RG approach, which gives access to the scaling behavior on the symmetry-broken side of the phase transition, for general dimension and number of Dirac fermions. In particular, we investigate the emergence of the fermion-induced quantum critical point for space-time dimensions 2 < d < 4. We determine the integrated RG flow from the Dirac semi-metal to the symmetrybroken regime and analyze the underlying fixed point structure. We show that the fermion-induced criticality leads to a scaling form with two divergent length scales, due to the breaking of the discrete Z3 symmetry. This provides another source of scaling corrections, besides the one stemming from being in the proximity to the first order transition. arXiv:1802.00364v1 [cond-mat.str-el]

show abstract

“…(2) The conformal bootstrap has emerged as a numerical tool to determine critical exponents for fermionic models [43][44][45][46]. (3) Nonperturbative field-theoretical methods like the functional renormalization group (FRG) have managed to explore sophisticated truncation schemes [47][48][49][50][51][52]. (4) The perturbative renormalization group (pRG) has seen substantial advances in computational technology and the development of suitable algorithms which facilitate the calculation of higherloop orders.…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of Dirac fermions from perturbative renormalization

2018

View full text Add to dashboard Cite

Gapless Dirac fermions appear as quasiparticle excitations in various condensed-matter systems. They feature quantum critical points with critical behavior in the 2+1 dimensional Gross-Neveu universality class. The precise determination of their critical exponents defines a prime benchmark for complementary theoretical approaches, such as lattice simulations, the renormalization group and the conformal bootstrap. Despite promising recent developments in each of these methods, however, no satisfactory consensus on the fermionic critical exponents has been achieved, so far. Here, we perform a comprehensive analysis of the Ising Gross-Neveu universality classes based on the recently achieved four-loop perturbative calculations. We combine the perturbative series in 4 − spacetime dimensions with the one for the purely fermionic Gross-Neveu model in 2+ dimensions by employing polynomial interpolation as well as two-sided Padé approximants. Further, we provide predictions for the critical exponents exploring various resummation techniques following the strategies developed for the three-dimensional scalar O(n) universality classes. We give an exhaustive appraisal of the current situation of Gross-Neveu universality by comparison to other methods. For large enough number of spinor components N ≥ 8 as well as for the case of emergent supersymmetry N = 1, we find our renormalization group estimates to be in excellent agreement with the conformal bootstrap, building a strong case for the validity of these values. For intermediate N as well as in comparison with recent Monte Carlo results, deviations are found and critically discussed. arXiv:1806.04977v1 [cond-mat.str-el]

show abstract

Critical Wess-Zumino models with four supercharges in the functional renormalization group approach

Cited by 13 publications

References 132 publications

Coulomb Instabilities of a Three-Dimensional Higher-Order Topological Insulator

Coulomb Instabilities of a Three-Dimensional Higher-Order Topological Insulator

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

Critical behavior of Dirac fermions from perturbative renormalization

Contact Info

Product

Resources

About