arXiv subjects

Junchen Rong

Publications and source records attributed to Junchen Rong.

At least 37 records · Page 2Linked to original sources

arXiv2023

Many versus one: the disorder operator and entanglement entropy in fermionic quantum matter

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 provides new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.

cond-mat.str-el↗

arXiv2023

Spontaneous breaking of finite group symmetries at all temperatures

We study conformal field theories with finite group symmetries with spontaneous symmetry breaking (SSB) phases that persist at all temperatures. We work with two $λϕ^4$ theories coupled through their mass terms. The two $λϕ^4$ theories are chosen to preserve either the cubic symmetry group or the tetrahedral symmetry group. A one-loop calculation in the $4-ε$ 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.

hep-th↗

arXiv2023

Fully packed quantum loop model on the square lattice: phase diagram and application for Rydberg atoms

The quantum dimer and loop models attract great attentions, partially because the fundamental importance in the phases and phase transitions emerging in these prototypical constrained systems, and partially due to their intimate relevance toward the on-going experiments on Rydberg atom arrays in which the blockade mechanism naturally enforces the local constraint. Here we show, by means of the sweeping cluster quantum Monte Carlo method, the complete ground state phase diagram of the fully packed quantum loop model on the square lattice. We find between the lattice nematic (LN) phase with strong dimer attraction and the staggered phase (SP) with strong dimer repulsion, there emerges a resonating plaquette (RP) phase with off-diagonal translational symmetry breaking. Such a quantum phase is separated from the LN via a first order transition and from the SP by the famous Rokhsar-Kivelson point. Our renormalization group analysis reveals the different flow directions, fully consistent with the order parameter histogram in Monte Carlo simulations. The realization and implication of our phase diagram in Rydberg experiments are proposed.

cond-mat.str-el↗

arXiv2022

Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid

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.

cond-mat.str-el↗

arXiv2022

Precision Bootstrap for the $\mathcal{N}=1$ Super-Ising Model

In this note we report an improved determination of the scaling dimensions and OPE coefficients of the minimal supersymmetric extension of the 3d Ising model using the conformal bootstrap. We also show how this data can be used as input to the Lorentzian inversion formula, finding good agreement between analytic calculations and numerical extremal spectra once mixing effects are resolved.

hep-th↗

arXiv2021

The old conformal bootstrap revisited

The "old" conformal bootstrap was originally formulated by Migdal and Polyakov (MP) as a method for calculating conformal dimensions self-consistently. In this work we revisit the MP bootstrap and apply efficient multi-loop Feynman integral techniques in order to solve the corresponding equations. We obtain solutions at first order in the skeleton expansion for finite coupling and for integer values of the spacetime dimension. We focus in particular on the $ϕ^3$ theory in seven dimensions and the $O(N)$ vector models in three dimensions.

hep-th↗

arXiv2021

A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions

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 $d=2+ε$ dimensions.

hep-th↗

arXiv2021

Seeking SUSY fixed points in the $4-ε$ expansion

We use the $4-ε$ expansion to search for fixed points corresponding to $2+1$ dimensional $\mathcal{N}$=1 Wess-Zumino models of $N_Φ$ scalar superfields interacting through a cubic superpotential. In the $N_Φ=3$ case, we classify all SUSY fixed points that are perturbatively unitary. In the $N_Φ=4$ and $N_Φ=5$ cases, we focus on fixed points where the scalar superfields form a single irreducible representation of the symmetry group (irreducible fixed points). For $N_Φ=4$ we show that the S5 invariant super Potts model is the only irreducible fixed point where the four scalar superfields are fully interacting. For $N_Φ=5$, we go through all Lie subgroups of O(5) and then use the GAP system for computational discrete algebra to study finite subgroups of O(5) up to order 800. This analysis gives us three fully interacting irreducible fixed points. Of particular interest is a subgroup of O(5) that exhibits O(3)/Z2 symmetry. It turns out this fixed point can be generalized to a new family of models, with $N_Φ=\frac{\rm N(N-1)}{2}-1$ and O(N)/Z2 symmetry, that exists for arbitrary integer N$\geq3$.

hep-th↗

arXiv2021

Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs

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 $2 N_c(d)$ 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 $(Δ_ϕ, Δ_T)=(d-1, 2d)$ 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 $N=\infty$.

hep-th↗

arXiv2020

On $ϕ^3$ Theory Above Six Dimensions

We study the scalar $ϕ^3$ theory above six dimensions. The beta function $β(g)=-εg-\frac{3}{4}g^3$ in $d=6-2ε$ dimensions has a UV fixed point when $ε<0$. Like the $O(N)$ vector models above four dimensions, such a fixed point observed perturbatively in fact corresponds to a pair of complex CFTs separated by a branch cut. Using both the numerical bootstrap method and Gliozzi's fusion rule truncation method, we argue that the fixed points of the $ϕ^3$ theory above six dimensions exist.

hep-th↗

arXiv2020

Stability of Topological character of Weyl Semi-metal, and Topological Dipole in Holography

We discuss the stability of the topological invariant of the strongly interacting Weyl semi-metal at finite temperature. We find that if the interactions and temperature of the system are controlled by the holography, the topology is stable even in the case the Fermi surface become fuzzy. We give an argument to show that although the self energy changes the spectral function significantly to make the Fermi surface fuzzy, it cannot change the singularity structure of the Berry phase, which leads to the stability of the topology. We also find that depending on the mass term structure of the fermion Lagrangian, topological dipoles can be created.

hep-th↗

arXiv2019

Evidence for the Holographic dual of ${\cal N}=3$ Solution in Massive Type IIA

We calculate the Kaluza-Klein spectrum of spin-2 fluctuations around the ${\cal N}=3$ warped ${\rm AdS}_4\times M_6$ solution in massive IIA supergravity. This solution was conjectured to be dual to the $D=3$ ${\cal N}=3$ superconformal ${\rm SU}(N)$ Chern-Simons matter theory with level $k$ and 2 adjoint chiral multiplets. The ${\rm SO}(3)_R\times{\rm SO}(3)_D$ isometry of the ${\cal N}=3$ solution is identified with the ${\rm SU}(2)_F\times {\rm SU}(2)_{\cal R}$ global symmetry of the dual ${\cal N}=3$ SCFT. We show that the ${\rm SO}(3)_R\times{\rm SO}(3)_D$ quantum numbers and the ${\rm AdS}$ energies carried by the BPS spin-2 modes match precisely with those of the spin-2 gauge invariant operators in the short multiplets of operators in the ${\cal N}=3$ SCFT. We also compute the Euclidean action of the ${\cal N}=3$ solution and the free energy of the ${\cal N}=3$ SCFT on $S^3$, in the limit $N\gg k$. Remarkably, the results show a complete agreement.

hep-th↗

arXiv2019

Bootstrapping the $\mathcal{N}=1$ Wess-Zumino models in three dimensions

Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional N = 1 Wess-Zumino models with cubic superpotetential $W\sim d_{ijk}Φ_iΦ_jΦ_k$. The tensor $d_{ijk}$ is taken to be the invariant tensor of either permutation group $S_N$, special unitary group $SU(N)$, or a series of groups called F4 family of Lie groups. Due to the equation of motion, at the Wess-Zumino fixed point, the operator $d_{ijk}Φ_iΦ_jΦ_k$ is a (super)descendant of $Φ_i$ . We observe such super-multiplet recombination in numerical bootstrap, which allows us to determine the scaling dimension of the super-field $Φ_i$.

hep-th↗

arXiv2018

Bootstrapping minimal $\mathcal{N}=1$ superconformal field theory in three dimensions

Using numerical bootstrap method, we determine the critical exponents of the minimal three-dimensional $\mathcal{N}=1$ superconformal field theory (SCFT) to be $η_σ=0.168888(60)$ and $ω=0.882(9)$. The model was argued in arXiv:1301.7449 to describe a quantum critical point (QCP) at the boundary a $3+1$D topological superconductor. More interestingly, the QCP can be reached by tuning a single parameter, where supersymmetry (SUSY) is realised as an emergent symmetry. By imposing emergent SUSY in numerical bootstrap, we find that the conformal scaling dimension of the real scalar operator $σ$ is highly restricted. If we further assume the SCFT to have only two time-reversal parity odd relevant operators, $σ$ and $σ'$, we find that allowed region for $Δ_σ$ and $Δ_{σ'}$ becomes an isolated island. The result is obtained by considering not only the four point correlator $\langle σσσσ\rangle$, but also $\langle σεσε\rangle$ and $\langle εεεε\rangle$, with $ε\sim σ^2$ being the superconformal descendant of $σ$.

hep-th↗

arXiv2018

Spectrum universality properties of holographic Chern-Simons theories

We give a master formula for the spin-2 spectrum of a class of three-dimensional Chern-Simons theories at large $N$, with flavour group containing SU(3), that arise as infrared fixed points of the D2-brane worldvolume field theory and have AdS$_4$ duals in massive type IIA supergravity. We use this formula to compute the spin-2 spectrum of the individual theories, discuss its supermultiplet structure and, for an ${\cal N}=2$ theory in this class, the spectrum of protected operators with spin 2. We also show that the trace of the Kaluza-Klein graviton mass matrix on the dual AdS$_4$ solutions enjoys certain universality properties. These are shown to relate the class of AdS$_4$ massive IIA solutions under consideration to a similar class of AdS$_4$ solutions of $D=11$ supergravity with the same symmetries. Finally, for the ${\cal N}=2$ AdS$_4$ solution in this class, we study the entire spectrum at lowest Kaluza-Klein level and relate it to an analogue solution in $D=11$ supergravity.

hep-th↗

arXiv2017

Scalar CFTs and Their Large N Limits

We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a series of kinks whose locations approach $(Δ^{\text{Ising}}_σ,Δ^{\text{Ising}}_ε)$ at $N\rightarrow \infty$. Setting $N=4$, we study the cubic anisotropic fixed point with three spin components. As byproducts of our numerical bootstrap work, we discover another series of kinks whose identification with previous known CFTs remains a mystery. We also show that "minimal models" of $\mathcal{W}_3$ algebra saturate the numerical bootstrap bounds of CFTs with $S_3$ symmetry.

hep-th↗

arXiv2016

$ϕ^3$ theory with $F_4$ flavor symmetry in $6-2ε$ dimensions: 3-loop renormalization and conformal bootstrap

We consider $ϕ^3$ theory in $6-2ε$ with $F_4$ global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in $ϕ$ are also computed. We then employ conformal bootstrap technique to study the fixed point predicted from the perturbative approach. For each putative scaling dimension of $ϕ$ ($Δ_ϕ)$, we obtain the corresponding upper bound on the scaling dimension of the second lowest scalar primary in the ${\mathbf 26}$ representation $(Δ^{\rm 2nd}_{\mathbf 26})$ which appears in the OPE of $ϕ\timesϕ$. In $D=5.95$, we observe a sharp peak on the upper bound curve located at $Δ_ϕ$ equal to the value predicted by the 3-loop computation. In $D=5$, we observe a weak kink on the upper bound curve at $(Δ_ϕ,Δ^{\rm 2nd}_{\mathbf 26})$=$(1.6,4)$.

hep-th↗

arXiv2015

Holographic RG Flow in a New $SO(3)\times SO(3)$ Sector of $ω$-Deformed $SO(8)$ Gauged ${\cal N}=8$ Supergravity

We consider a certain ${\cal N}=1$ supersymmetric, $SO(3)\times SO(3)$ invariant, subsector of the $ω$-deformed family of $SO(8)$-gauged ${\cal N}=8$ four-dimensional supergravities. The theory contains two scalar fields and two pseudoscalar fields. We look for stationary points of the scalar potential, corresponding to AdS vacua in the theory. One of these, which breaks all supersymmetries but is nonetheless stable, is new. It exists only when $ω\ne 0$. We construct supersymmetric domain wall solutions in the truncated theory, and we give a detailed analysis of their holographic dual interpretations using the AdS/CFT correspondence. Domain walls where the pseudoscalars vanish were studied previously, but those with non-vanishing pseudoscalars, which we analyse numerically, are new. The pseudoscalars are associated with supersymmetric mass deformations in the CFT duals. When $ω$ is zero, the solutions can be lifted to M-theory, where they approach the Coulomb-branch flows of dielectric M5-branes wrapped on $S^3$ in the deep IR.

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