arXiv subjects

Ce Shen

Publications and source records attributed to Ce Shen.

12 recordsLinked to original sources

arXiv2026

The Chen-Yang volume conjecture for long integral fillings of fundamental shadow links

We prove the Chen--Yang volume conjecture for all sufficiently long integral Dehn fillings of any fixed marked fundamental shadow-link exterior. For each fixed filling, the exponential growth of its $SO(3)$ Turaev--Viro invariants recovers its hyperbolic volume along the full sequence of odd levels. The filling coefficients may have mixed signs and unrelated magnitudes. We also establish a complete asymptotic expansion of the signed $SO(3)$ Witten--Reshetikhin--Turaev invariant and identify the absolute leading coefficient explicitly in terms of adjoint Reidemeister torsion. Fixed even colors on the filling cores recover characters of the geometric holonomy. The key difficulty is cancellation in the signed surgery sum. Our main analytic tool transfers an exact reflection symmetry from a continuous model to the finite quantum sums. We control the error below the exponential scale of the surviving contribution. We also apply the method to a one-edge state sum restricted to central colors. The dominant contributions cancel, and for each sufficiently large fixed number of blocks we determine the smaller surviving exponential rate and its nonzero leading coefficient.

math.GT↗

arXiv2026

Maximal Total Quantum Dimension at Bounded Rank in WZW Modular Tensor Categories

We determine the maximal torus topological entanglement entropy (TEE) at bounded torus ground-state degeneracy within simply connected untwisted Wess--Zumino--Witten theories. For a fixed modular tensor category $\mathcal C$, maximization over normalized torus ground states gives $\max_\psi\Gamma_{T^2}(\psi)=2\log{\mathcal D(\mathcal C)}$, attained in particular by the vacuum-flux state. The remaining problem is therefore to maximize total $\mathcal D$ at bounded categorical rank. For a simple WZW category $\mathcal C(\mathfrak g,k)$, write $r(\mathfrak g,k)$ and $\mathcal D(\mathfrak g,k)$ for its categorical rank and total quantum dimension, and define $F_{\WZW}(R)=\sup_{r(\mathfrak g,k)\leq R}2\log\mathcal D(\mathfrak g,k)$. We prove the sharp asymptotic law $\lim_{R\to\infty}\frac{F_{\WZW}(R)}{(\log_2R)^2} =\frac{7\zeta(3)}{4\pi^2}.$ The balanced symplectic sequence $Sp(2n)_n$ attains the coefficient. The constant arises from the odd Fourier modes of the type-$C$ root product at equal rank and level. A sharp entropy--spectral inequality, rank-level duality, and fixed-rank estimates give the global upper bound. A separate corollary extends the same leading law to semisimple WZW categories,equivalently finite Deligne products of simple factors. The unrestricted TQFT envelope remains open; the theorem is sharp within the stated WZW class and supplies a constructive lower bound for the general problem.

hep-th↗

arXiv2025

A 2D-CFT Factory: Critical Lattice Models from Competing Anyon Condensation Processes in SymTO/SymTFT

In this paper, we introduce a ``CFT factory'' : a novel algorithm of methodically generating 2D lattice models that would flow to 2D conformal fixed points in the infrared. These 2D models are realised by giving critical boundary conditions to 3D topological orders (symTOs/symTFTs) described by string-net models, often called the strange correlators. We engineer these critical boundary conditions by introducing a commensurate amount of non-commuting anyon condensates. The non-invertible symmetries preserved at the critical point can be controlled by studying a novel ``refined condensation tree''. Our structured method generates an infinite family of critical lattice models, including the A-series minimal models, and uncovers previously unknown critical points. Notably, we find at least three novel critical points (c$\approx 1.3$, $1.8$, and $2.5$ respectively) preserving the Haagerup symmetries, in addition to recovering previously reported ones. The condensation tree, together with a generalised Kramers-Wannier duality, predicts precisely large swathes of phase boundaries, fixes almost completely the global phase diagram, and sieves out second order phase transitions. This is not only illustrated in well-known examples (such as the 8-vertex model related to the $A_5$ category) but also further verified with precision numerics, using our improved (non-invertible) symmetry-preserving tensor-network RG, in novel examples involving the Haagerup symmetries. We show that critical couplings can be precisely encoded in the categorical data (Frobenius algebras and quantum dimensions in unitary fusion categories), thus establishing a powerful, systematic route to discovering and potentially classifying new conformal field theories.

cond-mat.str-el↗

arXiv2025

Exploring the phase diagram of $SU(2)_4$ strange correlator

We investigate the phase diagram of a quantum many-body system constructed via the strange correlator approach, based on the non-Abelian $SU(2)_4$ fusion category, to probe topological phase transitions. Using tensor network methods, we numerically compute the half-infinite chain entanglement entropy derived from the dominant eigenvector of the transfer matrix and map the entropy across a spherical two-dimensional parameter space. Our results reveal a phase diagram significantly more complex than previously reported, including a gapless phase consistent with a conformal field theory (CFT) of central charge $c=1$. Critical lines separating distinct phases are identified, with one such line bounding the CFT phase exhibiting a higher central charge $c=2$, indicative of an unconventional critical regime.

hep-th↗

arXiv2022

Virasoro Generators in the Fibonacci Model Tensor Network -- Tackling Finite Size Effects

In this paper, we extend the method implementing Virasoro operators in a tensor network we proposed in arXiv:2205.04500 and test it on the Fibonacci model, which is known to suffer from far more finite size effects. To pick up the "seed" state that would flow to the stress tensor in the thermodynamic limit, we make use of the topological idempotent that projects the transfer matrix to the trivial sector. Combined with an optimization method, the seed state can be identified. We demonstrate that the descendant states in the Fibonacci model can be correctly generated with this approximate stress tensor, giving further evidence that the method applies more generally.

cond-mat.str-el↗

arXiv2022

CFT$_D$ from TQFT$_{D+1}$ via Holographic Tensor Network, and Precision Discretisation of CFT$_2$

We show that the path-integral of conformal field theories in $D$ dimensions (CFT$_D$) can be constructed by solving for eigenstates of an RG operator following from the Turaev-Viro formulation of a topological field theory in $D+1$ dimensions (TQFT$_{D+1}$), explicitly realising the holographic sandwich relation between a symmetric theory and a TQFT. Generically, exact eigenstates corresponding to symmetric-TQFT$_D$ follow from Frobenius algebra in the TQFT$_{D+1}$. For $D=2$, we constructed eigenstates that produce 2D rational CFT path-integral exactly, which, curiously connects a continuous field theoretic path-integral with the Turaev-Viro state sum. We also devise and illustrate numerical methods for $D=2,3$ to search for CFT$_D$ as phase transition points between symmetric TQFT$_D$. Finally since the RG operator is in fact an exact analytic holographic tensor network, we compute ``bulk-boundary'' correlator and compare with the AdS/CFT dictionary at $D=2$. Promisingly, they are numerically compatible given our accuracy, although further works will be needed to explore the precise connection to the AdS/CFT correspondence.

hep-th↗

arXiv2022

Virasoro and Kac-Moody algebra in generic tensor network representations of 2d critical lattice partition functions

In this paper, we propose a general implementation of the Virasoro generators and Kac-Moody currents in generic tensor network representations of 2-dimensional critical lattice models. Our proposal works even when a quantum Hamiltonian of the lattice model is not available, which is the case in many numerical computations involving numerical blockings. We tested our proposal on the 2d Ising model, and also the dimer model, which works to high accuracy even with a fairly small system size. Our method makes use of eigenstates of a small cylinder to generate descendant states in a larger cylinder, suggesting some intricate algebraic relations between lattice of different sizes.

cond-mat.str-el↗

arXiv2020

A (Dummy's) Guide to Working with Gapped Boundaries via (Fermion) Condensation

We study gapped boundaries characterized by "fermionic condensates" in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We also connect these results with topological defects in super modular invariant CFTs. To render our discussion self-contained, we provide a pedagogical review of relevant mathematical results, so that physicists without prior experience in tensor category should be able to pick them up and apply them readily

hep-th↗

arXiv2019

Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy II -- Cutting through the boundary

We compute the entanglement entropy in a 2+1 dimensional topological order in the presence of gapped boundaries. Specifically, we consider entanglement cuts that cut through the boundaries. We argue that based on general considerations of the bulk-boundary correspondence, the "twisted characters" feature in the Renyi entropy, and the topological entanglement entropy is controlled by a "half-linking number" in direct analogy to the role played by the S-modular matrix in the absence of boundaries. We also construct a class of boundary states based on the half-linking numbers that provides a "closed-string" picture complementing an "open-string" computation of the entanglement entropy. These boundary states do not correspond to diagonal RCFT's in general. These are illustrated in specific Abelian Chern-Simons theories with appropriate boundary conditions.

hep-th↗

arXiv2019

Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy

In this paper, we study gapped edges/interfaces in a 2+1 dimensional bosonic topological order and investigate how the topological entanglement entropy is sensitive to them. We present a detailed analysis of the Ishibashi states describing these edges/interfaces making use of the physics of anyon condensation in the context of Abelian Chern-Simons theory, which is then generalized to more non-Abelian theories whose edge RCFTs are known. Then we apply these results to computing the entanglement entropy of different topological orders. We consider cases where the system resides on a cylinder with gapped boundaries and that the entanglement cut is parallel to the boundary. We also consider cases where the entanglement cut coincides with the interface on a cylinder. In either cases, we find that the topological entanglement entropy is determined by the anyon condensation pattern that characterizes the interface/boundary. We note that conditions are imposed on some non-universal parameters in the edge theory to ensure existence of the conformal interface, analogous to requiring rational ratios of radii of compact bosons.

hep-th↗

arXiv2019

A Defect Verlinde Formula

We revisit the problem of boundary excitations at a topological boundary or junction defects between topological boundaries in non-chiral bosonic topological orders in 2+1 dimensions. Based on physical considerations, we derive a formula that relates the fusion rules of the boundary excitations, and the "half-linking" number between condensed anyons and confined boundary excitations. This formula is a direct analogue of the Verlinde formula. We also demonstrate how these half-linking numbers can be computed in explicit Abelian and non-Abelian examples. As a fundamental property of topological orders and their allowed boundaries, this should also find applications in finding suitable platforms realizing quantum computing devices.

hep-th↗

arXiv2015

Anti-Parity-Time Symmetric Optics via Flying Atoms

The recently-developed notion of 'parity-time (PT) symmetry' in optical systems with a controlled gain-loss interplay has spawned an intriguing way of achieving optical behaviors that are presently unattainable with standard arrangements. In most experimental studies so far, however, the implementations rely highly on the advances of nanotechnologies and sophisticated fabrication techniques to synthesize solid-state materials. Here, we report the first experimental demonstration of optical anti-PT symmetry, a counterpart of conventional PT symmetry, in a warm atomic-vapor cell. By exploiting rapid coherence transport via flying atoms, our scheme illustrates essential features of anti-PT symmetry with an unprecedented precision on phase-transition threshold, and substantially reduces experimental complexity and cost. This result represents a significant advance in non-Hermitian optics by bridging a firm connection with the field of atomic, molecular and optical physics, where novel phenomena and applications in quantum and nonlinear optics aided by (anti-)PT symmetry could be anticipated.

physics.optics↗