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Physical Review Letters

Conformal Dimensions in the Large Charge Sectors at the [Formula : see text] Wilson-Fisher Fixed Point

Debasish Banerjee, Shailesh Chandrasekharan A, Domenico Orlando, Reffert Susanne

Published Jan 1, 2019• 0 citations
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Wilson–Fisher expansion near upper critical dimension has proven to be an invaluable conceptual and computational tool in our understanding of the universal critical behavior in the [Formula: see text] field theories that describe low-energy physics of the canonical models, such as Ising, XY, and Heisenberg. Here, I review its application to a class of the Gross–Neveu–Yukawa (GNY) field theories, which emerge as possible universal description of a number of quantum phase transitions in electronic two-dimensional systems such as graphene and d-wave superconductors. GNY field theories may be viewed as minimal modifications of the [Formula: see text] field theories in which the order parameter is coupled to relativistic Dirac fermions through Yukawa term and which still exhibit critical fixed points in the suitably formulated Wilson–Fisher [Formula: see text]-expansion. I discuss the unified GNY field theory for a set of different symmetry-breaking patterns, with focus on the semimetal-Néel-ordered-Mott insulator quantum phase transition in the half-filled Hubbard model on the honeycomb lattice, for which a comparison between the state-of-the-art [Formula: see text]-expansion, quantum Monte Carlo, large N, and functional renormalization-group calculations can be made.

arXiv:2304.07654•Modern Physics Letters B•Oct 8, 2024•16 citations
We study the O(4) Wilson-Fisher fixed point in 2+1 dimensions in fixed large-charge sectors identified by products of two spin-j representations (j_{L},j_{R}). Using effective field theory we derive a formula for the conformal dimensions D(j_{L},j_{R}) of the leading operator in terms of two constants, c_{3/2} and c_{1/2}, when the sum j_{L}+j_{R} is much larger than the difference |j_{L}-j_{R}|. We compute D(j_{L},j_{R}) when j_{L}=j_{R} with Monte Carlo calculations in a discrete formulation of the O(4) lattice field theory, and show excellent agreement with the predicted formula and estimate c_{3/2}=1.068(4) and c_{1/2}=0.083(3).
We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-Q fields at the Wilson-Fisher fixed point in the O(2) universality class. Using it, we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global U(1) charge can be obtained via a series expansion in the inverse charge 1/Q. We find that the conformal dimensions of the lowest operator with a fixed charge Q are almost entirely determined by the first few terms in the series.
Wilson–Fisher expansion near upper critical dimension has proven to be an invaluable conceptual and computational tool in our understanding of the universal critical behavior in the [Formula: see text] field theories that describe low-energy physics of the canonical models, such as Ising, XY, and Heisenberg. Here, I review its application to a class of the Gross–Neveu–Yukawa (GNY) field theories, which emerge as possible universal description of a number of quantum phase transitions in electronic two-dimensional systems such as graphene and d-wave superconductors. GNY field theories may be viewed as minimal modifications of the [Formula: see text] field theories in which the order parameter is coupled to relativistic Dirac fermions through Yukawa term and which still exhibit critical fixed points in the suitably formulated Wilson–Fisher [Formula: see text]-expansion. I discuss the unified GNY field theory for a set of different symmetry-breaking patterns, with focus on the semimetal-Néel-ordered-Mott insulator quantum phase transition in the half-filled Hubbard model on the honeycomb lattice, for which a comparison between the state-of-the-art [Formula: see text]-expansion, quantum Monte Carlo, large N, and functional renormalization-group calculations can be made.