arXiv subjects

Junchen Rong

Publications and source records attributed to Junchen Rong.

At least 19 recordsLinked to original sources

arXiv2026

Crossover duality for the quantum long-range Ising chain: perturbation theory around the short-range endpoint and a DMRG test

We propose a weakly coupled description of the long-range transverse-field Ising chain near its short-range crossover at $s_*=7/4$, where the couplings decay as $r^{-1-s}$. The Ising conformal field theory is coupled to an instantaneous Gaussian field through $σχ$, extending the classical long-range Ising duality to quantum chains. The equal-time interaction generates a stress-tensor deformation that causes the velocity to run and renormalizes the dynamical critical exponent $z$. Conformal perturbation theory gives $z=1-0.720\,δ+O(δ^2)$, $1/ν=(1+z)/2+O(δ^2)$, and $ω=δ+O(δ^2)$, with $δ=s_*-s$. DMRG calculations on periodic chains of up to $128$ sites provide a consistency test using theoretical inputs for $1/ν$ and $ω$. After accounting for slow finite-size corrections, static and dynamical estimates of $z$ agree, supporting the crossover expansion at $s=1.5$ and a two-sided Padé interpolation at $s=1$, $1.25$, and $1.5$.

cond-mat.stat-mech↗

arXiv2026

A lattice construction of the Kormos-Runkel-Watts defect flows in minimal models

Kormos, Runkel, and Watts (KRW) showed that a topological defect of a diagonal minimal model $M(p,p+1)$, perturbed by a weakly relevant defect field, flows to a new conformal interface. We study the flow of the $(2,1)$ Verlinde defect $D_{(2,1)}$ driven by the spinful defect field $ϕ_{(1,3)}\otimes\barϕ_{(3,3)}$ on the lattice. The flow preserves the $(r,1)$ Verlinde lines. This preserved symmetry makes a dilute RSOS realisation possible. We study this flow numerically using both exact diagonalization and density matrix renormalization group (DMRG). At $p=4$, the flow ends on the invertible line $η=D_{(3,1)}$. At $p=5$ it ends on a non-trivial conformal interface $C_5$ with $g=1.503(2)$ and transmission coefficient $T=0.665(10)$. We report its spectrum, leading irrelevant dimension, and lattice $β$-function. Gauging $η$ maps $C_5$ to an interface of the three-state Potts model, which breaks $\mathbb{Z}_3$ but is a stable interface once the Fibonacci line $τ_{\mathrm{Fib}}$ and charge conjugation are imposed. A loop-model formulation allows us to follow the family $C_p$ at continuous $4\le p\le5$: it moves smoothly from $C_5$ to $η$ as we lower $p$.

hep-th↗

arXiv2026

Direct tests of conformal symmetry with Rydberg atoms: assessment and proposals

We propose a direct test of conformal symmetry using Rydberg-atom arrays. By arranging the atoms on a circle and measuring equal-time two-point correlation functions, the characteristic functional form predicted by conformal field theory can be tested directly. We estimate the number of experimental snapshots required to resolve this behavior with sufficient statistical precision. We further optimize the time-dependent ramp profile of the Rabi frequency~$Ω$ and detuning~$Δ$ used to prepare the target critical state adiabatically. The optimized profile achieves higher fidelity over much shorter evolution times than those employed in previous experiments. Taken together, these results suggest that a direct experimental test of conformal symmetry is feasible with current Rydberg-atom technology.

quant-ph↗

arXiv2026

On the Ising/tricritical-Ising interface: From ${W}_3$ symmetry to Rydberg atoms

We consider interfaces between critical spin-chains in different universality classes, described in the continuum limit by defect/interface conformal field theory (DCFT/ICFT). We focus on a conformal interface between the Tricritical Ising (TIM) and the Ising CFT exploring the possibility of its experimental realizations in the context of Rydberg atom arrays. Our analysis emphasizes non-invertible symmetries and consistency under modular transformations, and uses defect couplings and the defect spectrum -- including in the case of mixed boundary conditions -- to make sharp experimental predictions. The structure of the observables hinges on a newly discovered pattern of emergent ${W}_3$ chiral symmetry for the Tricritical-Ising/Ising interface.

hep-th↗

arXiv2026

Numerical evidence of a critical point in the (2+1)D SO(5) nonlinear sigma model with Wess-Zumino-Witten term

We develop an optimized continuous-field quantum Monte Carlo (QMC) algorithm to investigate the projected SO(5) nonlinear sigma model with a Wess-Zumino-Witten term, which describes half-filled Dirac fermions in 2+1 space-time dimensions akin to graphene and Yukawa coupled to a quintuplet of compatible mass terms. Our algorithm reduces the computational complexity to $O(βN_{\mathbf{q}} N_ϕ^2)$, yielding a speedup of a factor of $N_ϕ$ (the number of magnetic fluxes, i.e., system size) relative to prior works [1-4]. This advance enables us to simulate system sizes up to $N_ϕ=140$ on the torus and $N_ϕ=59$ on the sphere, far exceeding the maximum sizes previously accessed, and to map out the universal phase diagram of the model on both geometries. Most notably, we identify and characterize a critical point that separates an SO(5)-broken ordered phase at small coupling from an SO(5)-symmetric disordered phase at large coupling. The critical point becomes multicritical upon the inclusion of terms that break the SO(5) symmetry down to $\mathrm{U}(1) \times \mathrm{SU}(2)$, relevant for the deconfined phase transition between Néel antiferromagnetic and valence-bond-solid orders in quantum magnets. Our finding of a multicritical point in the phase diagram of the SO(5) nonlinear sigma model with Wess-Zumino-Witten term resolves the long-standing open question of its global structure, and our QMC algorithm opens a new avenue for systematic studies of projected Hamiltonians, ranging from correlated flat bands to fractional quantum (anomalous) Hall systems.

cond-mat.str-el↗

arXiv2026

Precise computation of universal corner entanglement entropy at 2+1 dimension: From Ising to Gaussian quantum critical points

Computing the subleading logarithmic term in the entanglement entropy (EE) of (2+1)d quantum many-body systems remains a significant challenge, despite its central role in revealing universal information about quantum states and quantum critical points (QCPs). Building on recent algorithmic advances that enable the stable calculation of EE as an exponential observable~\cite{zhouIncremental2024,zhangIntegral2024,liaoExtracting2024}, we develop a {\it bubble basis} projector quantum Monte Carlo (QMC) algorithm to precisely and efficiently compute the universal corner of EE at QCPs in a (2+1)d square-lattice transverse-field Ising model augmented with a four-body interaction. Turning on this interaction allows us to trace an Ising critical line, reaching the tricritical point, and then a line of first-order phase transition. In (2+1)d, the tricritical point is described by the Gaussian theory, where a theoretical calculation of the corner logarithmic term in the 2nd Rényi entropy term is available~\cite{UniversalCasini2007}. Our QMC results are in quantitative agreement with this theoretical value, providing a highly nontrivial benchmark of the algorithm. Furthermore, we also study the Rényi EE at the Ising critical line and on the first-order transition line, obtaining results consistent with theoretical expectations. These findings establish the long-sought connection between the universal values of an exactly solvable limit and those of a strongly correlated regime at (2+1)d.

cond-mat.str-el↗

arXiv2026

Irrational CFTs from coupled anyon chains with non-invertible symmetries?

Irrational CFTs in 1+1d with a discrete spectrum and no conserved currents other than the stress-tensor are expected to be generic, unsolvable by standard methods, and hard to construct explicitly. We introduce a lattice model that realizes a candidate for such a CFT as a conformal phase of matter without fine-tuning. The model is constructed by coupling $N\geq3$ golden anyon chains together, preserving $N$ copies of the Fibonacci non-invertible symmetry. We use the MPS/DMRG approach to study this model numerically, which allows us to calculate the corresponding conformal data, obtaining hints of its irrationality. Along the way, we characterize the phase diagram for $N=2$ coupled chains where we identify a weakly first-order phase transition as well as critical points that we are able to identify with known rational CFTs, except for one case. We also provide an extensive list of rational CFTs with $1<c<2.1$.

hep-th↗

arXiv2025

Phase transitions and remnants of fractionalization at finite temperature in the triangular lattice quantum loop model

The quantum loop and dimer models are archetypal correlated systems with local constraints. With natural foundations in statistical mechanics, they are of direct relevance to various important physical concepts and systems, such as topological order, lattice gauge theories, geometric frustrations, or more recently Rydberg arrays quantum simulators. However, how the thermal fluctuations interact with constraints has not been explored in the important class of non-bipartite geometries. Here we study, via unbiased quantum Monte Carlo simulations and field theoretical analysis, the finite-temperature phase diagram of the quantum loop model on the triangular lattice. We discover that the recently identified, "hidden" vison plaquette (VP) quantum crystal [1] experiences a finite-temperature continuous transition, which smoothly connects to the (2+1)d Cubic* quantum critical point separating the VP and $\mathbb{Z}_{2}$ quantum spin liquid phases. This finite-temperature phase transition acquires a unique property of ``remnants of fractionalization" at finite temperature, in that, both the cubic order parameter -- the plaquette loop resonance -- and its constituent -- the vison field -- exhibit independent criticality signatures. This phase transition is connected to a 3-state Potts transition between the lattice nematic phase and the high-temperature disordered phase. We discuss the relevance of our results for current experiments on quantum simulation platforms.

cond-mat.str-el↗

arXiv2025

Scalar Conformal Field Theories from Lattice Systems

We discuss scalar conformal field theories (CFTs) that can be realized in structural phase transitions. The Landau condition and Lifshitz condition are reviewed, which are necessary conditions for a structural phase transition to be second order. We also review the perturbative analysis in $4-ε$ expansion of the corresponding Landau actions, which were already analyzed thoroughly in the 80s. By identifying the global symmetries of these fixed points, it turns out that in perturbation theory only 6 different CFTs can be realized by commensurate structural phase transitions. ${\rm \textbf{Updated in version 2:}}$ We discuss how to classify all the phases of a Landau theory using the computer algebra system GAP. We also discuss the fully packed quantum loop model on the triangular lattice, where the Cubic CFT is realized. This is a lecture note based on a series of talks given by the author. The goal of the lecture note is to bridge the gap between condensed matter physicists and conformal field theorists. The note will be further updated in the future.

hep-th↗

arXiv2025

UV complete local field theory of persistent symmetry breaking in 2+1 dimensions

Spontaneous symmetry breaking can persist at all temperatures in certain biconical $\mathrm{O}(N)\times \mathbb{Z}_2$ vector models when the underlying field theories are ultraviolet complete. So far, the existence of such theories has been established in fractional dimensions for local but nonunitary models or in 2+1 dimensions but for nonlocal models. Here, we study local models at zero and finite temperature directly in 2+1 dimensions employing functional methods. At zero temperature, we establish that our approach describes the quantum critical behaviour with high accuracy for all $N\geq 2$. We then exhibit the mechanism of discrete symmetry breaking from $\mathrm{O}(N)\times \mathbb{Z}_2\to \mathrm{O}(N)$ for increasing temperature near the biconical critical point when $N$ is finite but large. We calculate the corresponding finite-temperature phase diagram and further show that the Hohenberg-Mermin-Wagner theorem is fully respected within this approach, i.e., symmetry breaking only occurs in the $\mathbb{Z}_2$ sector. Finally, we determine the critical $N$ above which this phenomenon can be observed to be $N_c \approx 15$.

hep-th↗

arXiv2024

Local/Short-range conformal field theories from long-range perturbation theory

We show that by imposing the conformal Wald identity, one can extract conformal data of the corresponding short-range/local CFT from the long-range perturbation theory. We first apply this to the O(N) vector model. We demonstrate that by properly re-sum the perturbative series, one gets reasonable estimations of the critical exponents of the local/short-range CFTs. We then apply this method to study fermionic models with four-fermion interactions. In 2+1 dimensions, the model has the Gross-Neveu coupling and the Thirring coupling. We also consider a 4+1 dimensional theory with a generalized Thirring coupling.

hep-th↗

arXiv2024

Surface phase transitions in a (1+1)-dimensional $SU(2)_1$ conformal field theory boundary coupled to a (2+1)-dimensional $Z_2$ bulk

We design a (2+1))-dimensional [(2+1)D] quantum spin model in which spin-1/2 ladders are coupled through antiferromagnetic Ising interactions. The model hosts a quantum phase transition in the (2+1)D $Z_2$ universality class from the Haldane phase to the antiferromagnetic Ising ordered phase. We focus on studying the surface properties of three different surface configurations when the Ising couplings are tuned. Different behaviors are found on different surfaces. We find ordinary and two different extraordinary surface critical behaviors (SCBs) at the bulk critical point. The ordinary SCBs belong to the surface universality class of the classical 3D Ising bulk transition. One extraordinary SCBs is induced by the topological properties of the Haldane phase. Another extraordinary SCBs at the bulk critical point is induced by an unconventional surface phase transition where the surface develops an Ising order before the bulk. This surface transition is realized by coupling a (1+1)-dimensional [(1+1)D] $SU(2)_1$ CFT boundary to a (2+1)D bulk with $Z_2$ symmetry. We find that the transition is neither a (1+1)D $Z_2$ transition, expected based on symmetry consideration, nor a Kosterlitz-Thouless-like transition, violating the previous theoretical prediction. This new surface phase transition and related extraordinary SCBs deserve further analytical and numerical exploration.

cond-mat.str-el↗

arXiv2024

Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice

Quantum loop and dimer models are prototypical correlated systems with local constraints, which are not only intimately connected to lattice gauge theories and topological orders but are also widely applicable to the broad research areas of quantum materials and quantum simulation. Employing our sweeping cluster quantum Monte Carlo algorithm, we reveal the complete phase diagram of the triangular-lattice fully packed quantum loop model. Apart from the known lattice nematic (LN) solid and the even $\mathbb{Z}_2$ quantum spin liquid (QSL) phases, we discover a hidden vison plaquette (VP) phase, which had been overlooked and misinterpreted as a QSL for more than a decade. Moreover, the VP-to-QSL continuous transition belongs to the $(2+1)$D cubic* universality class, which offers a lattice realization of the (fractionalized) cubic fixed point that had long been considered as irrelevant towards the O($3$) symmetry until corrected recently by conformal bootstrap calculations. Our results are therefore of relevance to recent developments in both experiments and theory, and facilitate further investigations of hidden phases and transitions.

cond-mat.str-el↗

arXiv2024

Cubic* criticality emerging from a quantum loop model on triangular lattice

Quantum loop and dimer models are archetypal examples of correlated systems with local constraints. Obtaining generic solutions for these models is difficult due to the lack of controlled methods to solve them in the thermodynamic limit. Nevertheless, these solutions are of immediate relevance to both statistical and quantum field theories, as well as the rapidly growing experiments in Rydberg atom arrays and quantum moiré materials, where the interplay between correlation and local constraints gives rise to a plethora of novel phenomena. In a recent work [X. Ran, Z. Yan, Y.-C. Wang, et al, arXiv:2205.04472 (2022)], it was found through sweeping cluster quantum Monte Carlo (QMC) simulations and field theory analysis that the triangular lattice quantum loop model (QLM) hosts a rich ground state phase diagram with lattice nematic, vison plaquette (VP) crystals, and the $\mathbb{Z}_2$ quantum spin liquid (QSL) close to the Rokhsar-Kivelson point. Here, we focus on the continuous quantum critical point separating the VP and QSL phases and demonstrate via both static and dynamic probes in QMC simulations that this transition is of the (2+1)D cubic* universality. In this transition, the fractionalized visons in QSL condense to give rise to the crystalline VP phase, while leaving their trace in the anomalously large anomalous dimension exponent and pronounced continua in the dimer and vison spectra compared with those at the conventional cubic or O(3) quantum critical points.

cond-mat.str-el↗

arXiv2024

Quantum criticality and entanglement for two dimensional long-range Heisenberg bilayer

The study of quantum criticality and entanglement in systems with long-range (LR) interactions is still in its early stages, with many open questions remaining. In this work, we investigate critical exponents and scaling of entanglement entropies (EE) in the LR bilayer Heisenberg model using large-scale quantum Monte Carlo (QMC) simulations and the recently developed nonequilibrium increment algorithm for measuring EE. By applying modified (standard) finite-size scaling (FSS) above (below) the upper critical dimension and field theory analysis, we obtain precise critical exponents in three regimes: the LR Gaussian regime with a Gaussian fixed point, the short-range (SR) regime with Wilson-Fisher (WF) exponents, and a LR non-Gaussian regime where the critical exponents vary continuously from LR Gaussian to SR values. We compute the Rényi EE both along the critical line and in the Néel phase and observe that as the LR interaction is enhanced, the area-law contribution in EE gradually vanishes both at quantum critical points (QCPs) and in the Néel phase. The log-correction in EE arising from sharp corners at the QCPs also decays to zero as LR interaction grows, whereas the log-correction for Néel states, caused by the interplay of Goldstone modes and restoration of the symmetry in a finite system, is enhanced as LR interaction becomes stronger. We also discuss relevant experimental settings to detect these nontrivial properties in critical behavior and entanglement information for quantum many-body systems with LR interactions.

cond-mat.str-el↗

arXiv2023

From O(3) to Cubic CFT: Conformal Perturbation and the Large Charge Sector

The Cubic CFT can be understood as the O(3) invariant CFT perturbed by a slightly relevant operator. In this paper, we use conformal perturbation theory together with the conformal data of the O(3) vector model to compute the anomalous dimension of scalar bilinear operators of the Cubic CFT. When the $Z_2$ symmetry that flips the signs of $ϕ_i$ is gauged, the Cubic model describes a certain phase transition of a quantum dimer model. The scalar bilinear operators are the order parameters of this phase transition. Based on the conformal data of the O(3) CFT, we determine the correction to the critical exponent as $η_{*}^{Cubic}-η_{*}^{O(3)}\approx -0.0215(49)$. The O(3) data is obtained using the numerical conformal bootstrap method to study all four-point correlators involving the four operators: $v=ϕ_i$, $s=\sum_i ϕ_iϕ_i$ and the leading scalar operators with O(3) isospin $j=2$ and 4. According to large charge effective theory, the leading operator with charge $Q$ has scaling dimension $Δ_{Q}=c_{3/2} Q^{3/2}+c_{1/2}Q^{1/2}$. We find a good match with this prediction up to isospin $j=6$ for spin 0 and 2 and measured the coefficients $c_{3/2}$ and $c_{1/2}$.

hep-th↗

arXiv2023

Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model

The Mermin-Wagner theorem states that spontaneous continuous symmetry breaking is prohibited in systems with short-range interactions at spatial dimension $D\le 2$. For long-range interactions with a power-law form ($1/r^α$), the theorem further forbids ferromagnetic or antiferromagnetic order at finite temperature when $α\ge 2D$. However, the situation for $α\in (2,4)$ at $D=2$ is not covered by the theorem. To address this, we conduct large-scale quantum Monte Carlo simulations and field theoretical analysis. Our findings show spontaneous breaking of $SU(2)$ symmetry in the ferromagnetic Heisenberg model with $1/r^α$-form long-range interactions at $D=2$. We determine critical exponents through finite-size analysis for $α<3$ (above the upper critical dimension with Gaussian fixed point) and $3\leα<4$ (below the upper critical dimension with non-Gaussian fixed point). These results reveal new critical behaviors in 2D long-range Heisenberg models, encouraging further experimental studies of quantum materials with long-range interactions beyond the Mermin-Wagner theorem's scope.

cond-mat.str-el↗

arXiv2023

Non-Abelian currents bootstrap

We initiate the study of correlation functions of non-Abelian spin-1 conserved current in three dimensional conformal field theories using numerical conformal bootstrap. We discuss the general framework and apply it to the particular cases of $SU(N)$ and $O(N)$ global symmetry. In both cases we obtain general bounds on operator dimensions. In the large-$N$ limit our bounds show features in correspondence of the expected position of fermionic QED$_3$ in three dimensions, as well as other interesting theories. By imposing gaps inspired by the spectrum of QED$_3$ at large-$N$, we manage to restrict the plane of certain operator dimensions to a small island, where QED$_3$ must live.

hep-th↗