Weilun Jiang, Bin-Bin Chen, Zi Hong Liu, Junchen Rong, Fakher F. Assaad, Meng Cheng, Kai Sun, Zi Yang Meng
SciPost Phys. 15, 082 (2023) ·
published 7 September 2023
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Motivated by recent development of the concept of the disorder operator and its relation with entanglement entropy in bosonic systems, here we show the disorder operator successfully probes many aspects of quantum entanglement in fermionic many-body systems. From both analytical and numerical computations in free and interacting fermion systems in 1D and 2D, we find the disorder operator and the entanglement entropy exhibit similar universal scaling behavior, as a function of the boundary length of the subsystem, but with subtle yet important differences. In 1D they both follow the $\log{L}$ scaling behavior with the coefficient determined by the Luttinger parameter for disorder operator, and the conformal central charge for entanglement entropy. In 2D they both show the universal $L\log L$ scaling behavior in free and interacting Fermi liquid states, with the coefficients depending on the geometry of the Fermi surfaces. However at a 2D quantum critical point with non-Fermi-liquid state, extra symmetry information is needed in the design of the disorder operator, so as to reveal the critical fluctuations as does the entanglement entropy. Our results demonstrate the fermion disorder operator can be used to probe quantum many-body entanglement related to global symmetry, and provide new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.
SciPost Phys. 14, 168 (2023) ·
published 22 June 2023
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We study conformal field theories with finite group symmetries with spontaneous symmetry breaking (SSB) phases which persist at all temperatures. We work with two $\lambda \phi^4$ theories coupled through their mass terms. The two $\lambda \phi^4$ theories are chosen to preserve either the cubic symmetry group, or the tetrahedral symmetry group. A one-loop calculation in the $4-\epsilon$ expansion shows that there exist infinitely many fixed points that can host an all temperature SSB phase. An analysis of the renormalization group (RG) stability matrix of these fixed points, reveals that their spectrum contains at least three relevant operators. In other words, these fixed points are tetracritical points.
SciPost Phys. 13, 014 (2022) ·
published 8 August 2022
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We apply the conformal bootstrap technique to study the $U(1)$ Dirac spin
liquid (i.e. $N_f=4$ QED$_3$) and the newly proposed $N=7$ Stiefel liquid (i.e.
a conjectured 3d non-Lagrangian CFT without supersymmetry). For the $N_f=4$
QED$_3$, we focus on the monopole operator and ($SU(4)$ adjoint) fermion
bilinear operator. We bootstrap their single correlators as well as the mixed
correlators between them. We first discuss the bootstrap kinks from single
correlators. Some exponents of these bootstrap kinks are close to the expected
values of QED$_3$, but we provide clear evidence that they should not be
identified as the QED$_3$. By requiring the critical phase to be stable on the
triangular and the kagome lattice, we obtain rigorous numerical bounds for the
$U(1)$ Dirac spin liquid and the Stiefel liquid. For the triangular and kagome
Dirac spin liquid, the rigorous lower bounds of the monopole operator's scaling
dimension are $1.046$ and $1.105$, respectively. These bounds are consistent
with the latest Monte Carlo results.
SciPost Phys. 11, 111 (2021) ·
published 22 December 2021
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We propose a roadmap for bootstrapping conformal field theories (CFTs)
described by gauge theories in dimensions $d>2$. In particular, we provide a
simple and workable answer to the question of how to detect the gauge group in
the bootstrap calculation. Our recipe is based on the notion of
\emph{decoupling operator}, which has a simple (gauge) group theoretical
origin, and is reminiscent of the null operator of $2d$ Wess-Zumino-Witten CFTs
in higher dimensions. Using the decoupling operator we can efficiently detect
the rank (i.e. color number) of gauge groups, e.g., by imposing gap conditions
in the CFT spectrum. We also discuss the physics of the equation of motion,
which has interesting consequences in the CFT spectrum as well. As an
application of our recipes, we study a prototypical critical gauge theory,
namely the scalar QED which has a $U(1)$ gauge field interacting with critical
bosons. We show that the scalar QED can be solved by conformal bootstrap,
namely we have obtained its kinks and islands in both $d=3$ and $d=2+\epsilon$
dimensions.
SciPost Phys. 10, 115 (2021) ·
published 26 May 2021
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It is well established that the $O(N)$ Wilson-Fisher (WF) CFT sits at a kink
of the numerical bounds from bootstrapping four point function of $O(N)$
vector. Moving away from the WF kinks, there indeed exists another family of
kinks (dubbed non-WF kinks) on the curve of $O(N)$ numerical bounds. Different
from the $O(N)$ WF kinks that exist for arbitary $N$ in $2<d<4$ dimensions, the
non-WF kinks exist in arbitrary dimensions but only for a large enough
$N>N_c(d)$ in a given dimension $d$. In this paper we have achieved a thorough
understanding for few special cases of these non-WF kinks. The first case is
the $O(4)$ bootstrap in 2d, where the non-WF kink turns out to be the $SU(2)_1$
Wess-Zumino-Witten (WZW) model, and all the $SU(2)_{k>2}$ WZW models saturate
the numerical bound on the left side of the kink. We further carry out
dimensional continuation of the 2d $SU(2)_1$ kink towards the 3d $SO(5)$
deconfined phase transition. We find the kink disappears at around $d=2.7$
dimensions indicating the $SO(5)$ deconfined phase transition is weakly first
order. The second interesting observation is, the $O(2)$ bootstrap bound does
not show any kink in 2d ($N_c=2$), but is surprisingly saturated by the 2d free
boson CFT (also called Luttinger liquid) all the way on the numerical curve.
The last case is the $N=\infty$ limit, where the non-WF kink sits at
$(\Delta_\phi, \Delta_T)=(d-1, 2d)$ in $d$ dimensions. We manage to write down
its analytical four point function in arbitrary dimensions, which equals to the
subtraction of correlation functions of a free fermion theory and generalized
free theory. An important feature of this solution is the existence of a full
tower of conserved higher spin current. We speculate that a new family of CFTs
will emerge at non-WF kinks for finite $N$, in a similar fashion as $O(N)$ WF
CFTs originating from free boson at $N=\infty$.
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