arXiv subjects

Tzu-Chen Huang

Publications and source records attributed to Tzu-Chen Huang.

13 recordsLinked to original sources

arXiv2026

Cyclic Haagerup-Izumi fusion categories at every odd order

We construct a complex spherical fusion category with cyclic Haagerup-Izumi fusion rules for every odd n >= 3, and deduce pseudo-unitary existence. The proof has four parts: explicit real coefficients and their quadratic identities; a contour calculation for a range of cubic Fourier coefficients; algebraic completion of all cubics; and categorical reconstruction. Matrix inversion supplies reflection, and an extension of the dimension-field automorphism supplies the positive-dimensional category.

math.QA↗

arXiv2025

Deformed LDPC codes with spontaneously broken non-invertible duality symmetries

Low-density parity check (LDPC) codes are a well known class of Pauli stabiliser Hamiltonians that furnish fixed-point realisations of nontrivial gapped phases such as symmetry breaking and topologically ordered (including fracton) phases. In this work, we propose symmetry-preserving deformations of these models, in the presence of a transverse field, and identify special points along the deformations with interesting features: (i) the special point is frustration-free, (ii) its ground states include a product state and the code space of the underlying code, and (iii) it remains gapped in the thermodynamic (infinite volume) limit. So the special point realises a first-order transition between (or the coexistence of) the trivial gapped phase and the nontrivial gapped phase associated with the code. In addition, if the original model has a non-invertible duality symmetry, then so does the deformed model. In this case, the duality symmetry is spontaneously broken at the special point, consistent with the associated anomaly. A key step in proving the gap is a coarse-graining/blocking procedure on the Tanner graph of the code that allows us to apply the martingale method successfully. Our model, therefore, provides the first application of the martingale method to a frustration-free model, that is not commuting projector, defined on an arbitrary Tanner graph. We also discuss several familiar examples on Euclidean spatial lattice. Of particular interest is the 2+1d transverse field Ising model: while there is no non-invertible duality symmetry in this case, our results, together with known numerical results, suggest the existence of a tricritical point in the phase diagram.

cond-mat.str-el↗

arXiv2025

Deep learning lattice gauge theories

Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of $\mathbb{Z}_N$ lattice gauge theories in $2+1$ dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For $\mathbb{Z}_2$, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the $\mathbb{Z}_3$ case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory.

hep-lat↗

arXiv2025

Duality-preserving deformation of 3+1d lattice $\mathbb Z_2$ gauge theory with exact gapped ground states

We propose and analyze a deformation of the 3+1d lattice $\mathbb Z_2$ gauge theory that preserves the non-invertible Wegner duality symmetry at the self-dual point. We identify a frustration-free point along this deformation where there are nine exactly degenerate ground states (on a periodic cubic lattice) even at finite volume. One of these ground states is a trivial product state and the rest are the topologically-ordered ground states of the 3+1d toric code. We also prove that the frustration-free point is gapped in the thermodynamic limit. Our model, therefore, realizes a gapped phase with spontaneously broken Wegner duality symmetry. Furthermore, by imposing the Gauss law constraints energetically, all the above features can be realized on a tensor product Hilbert space. Finally, we discuss a generalization of this deformation to the 3+1d lattice $\mathbb Z_N$ gauge theory and conjecture the possible phase diagram.

cond-mat.str-el↗

arXiv2024

The Geometry of the Modular Bootstrap

We explore the geometry behind the modular bootstrap and its image in the space of Taylor coefficients of the torus partition function. In the first part, we identify the geometry as an intersection of planes with the convex hull of moment curves on $R^+{\otimes}\mathbb{Z}$, with boundaries characterized by the total positivity of generalized Hankel matrices. We phrase the Hankel constraints as a semi-definite program, which has several advantages, such as constant computation time with increasing central charge. We derive bounds on the gap, twist-gap, and the space of Taylor coefficients themselves. We find that if the gap is above $Δ^*_{gap}$, where $\frac{c{-}1}{12}<Δ^*_{gap}< \frac{c}{12}$, all coefficients become bounded on both sides and kinks develop in the space. In the second part, we propose an analytic method of imposing the integrality condition for the degeneracy number in the spinless bootstrap, which leads to a non-convex geometry. We find that even at very low derivative order this condition rules out regions otherwise allowed by bootstraps at high derivative order.

hep-th↗

arXiv2021

Scattering Amplitudes For All Masses and Spins

We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an extra SU(2) little group index for massive particles, with the amplitudes for spin S particles transforming as symmetric rank 2S tensors. We systematically characterise all possible three particle amplitudes compatible with Poincare symmetry. Unitarity, in the form of consistent factorization, imposes algebraic conditions that can be used to construct all possible four-particle tree amplitudes. This also gives us a convenient basis in which to expand all possible four-particle amplitudes in terms of what can be called "spinning polynomials". Many general results of quantum field theory follow the analysis of four-particle scattering, ranging from the set of all possible consistent theories for massless particles, to spin-statistics, and the Weinberg-Witten theorem. We also find a transparent understanding for why massive particles of sufficiently high spin can not be "elementary". The Higgs and Super-Higgs mechanisms are naturally discovered as an infrared unification of many disparate helicity amplitudes into a smaller number of massive amplitudes, with a simple understanding for why this can't be extended to Higgsing for gravitons. We illustrate a number of applications of the formalism at one-loop, giving few-line computations of the electron (g-2) as well as the beta function and rational terms in QCD. "Off-shell" observables like correlation functions and form-factors can be thought of as scattering amplitudes with external "probe" particles of general mass and spin, so all these objects--amplitudes, form factors and correlators, can be studied from a common on-shell perspective.

hep-th↗

arXiv2021

Construction of two-dimensional topological field theories with non-invertible symmetries

We construct the defining data of two-dimensional topological field theories (TFTs) enriched by non-invertible symmetries/topological defect lines. Simple formulae for the three-point functions and the lasso two-point functions are derived, and crossing symmetry is proven. The key ingredients are open-to-closed maps and a boundary crossing relation, by which we show that a diagonal basis exists in the defect Hilbert spaces. We then introduce regular TFTs, provide their explicit constructions for the Fibonacci, Ising and Haagerup $\mathcal{H}_3$ fusion categories, and match our formulae with previous bootstrap results. We end by explaining how non-regular TFTs are obtained from regular TFTs via generalized gauging.

hep-th↗

arXiv2021

Numerical evidence for a Haagerup conformal field theory

We numerically study an anyon chain based on the Haagerup fusion category, and find evidence that it leads in the long-distance limit to a conformal field theory whose central charge is $\sim 2$. Fusion categories generalize the concept of finite group symmetries to non-invertible symmetry operations, and the Haagerup fusion category is the simplest one which comes neither from finite groups nor affine Lie algebras. As such, ours is the first example of conformal field theories which have truly exotic generalized symmetries.

cond-mat.stat-mech↗

arXiv2021

The $F$-Symbols for Transparent Haagerup-Izumi Categories with $G = \mathbb{Z}_{2n+1}$

A fusion category is called transparent if the associator involving any invertible object is the identity map. For the Haagerup-Izumi fusion rings with $G = \mathbb{Z}_{2n+1}$ (the $\mathbb{Z}_3$ case is the Haagerup fusion ring with six simple objects), the transparent ansatz reduces the number of independent $F$-symbols from order $\mathcal{O}(n^6)$ to $\mathcal{O}(n^2)$, rendering the pentagon identity practically solvable. Transparent Haagerup-Izumi fusion categories are thereby constructively classified up to $G = \mathbb{Z}_9$, recovering all known Haagerup-Izumi fusion categories to this order, and producing new ones. Transparent Haagerup-Izumi fusion categories additionally satisfying $S_4$ tetrahedral invariance are further classified up to $G = \mathbb{Z}_{15}$, and the explicit $F$-symbols for the unitary ones, including the Haagerup $\mathcal{H}_3$ fusion category, are compactly presented. The $F$-symbols for the Haagerup $\mathcal{H}_2$ fusion category are also presented. Going beyond, the transparent ansatz offers a viable course towards constructing novel fusion categories for new fusion rings.

math.CT↗

arXiv2021

Topological Field Theory with Haagerup Symmetry

We construct a (1+1)$d$ topological field theory (TFT) whose topological defect lines (TDLs) realize the transparent Haagerup $\mathcal{H}_3$ fusion category. This TFT has six vacua, and each of the three non-invertible simple TDLs hosts three defect operators, giving rise to a total of 15 point-like operators. The TFT data, including the three-point coefficients and lasso diagrams, are determined by solving all the sphere four-point crossing equations and torus one-point modular invariance equations. We further verify that the Cardy states furnish a non-negative integer matrix representation under TDL fusion. While many of the constraints we derive are not limited to the this particular TFT with six vacua, we leave open the construction of TFTs with two or four vacua. Finally, TFTs realizing the Haagerup $\mathcal{H}_1$ and $\mathcal{H}_2$ fusion categories can be obtained by gauging algebra objects. This note makes a modest offering in our pursuit of exotica and the quest for their eventual conformity.

hep-th↗

arXiv2021

The EFT-Hedron

We re-examine the constraints imposed by causality and unitarity on the low-energy effective field theory expansion of four-particle scattering amplitudes, exposing a hidden "totally positive" structure strikingly similar to the positive geometries associated with grassmannians and amplituhedra. This forces the infinite tower of higher-dimension operators to lie inside a new geometry we call the "EFThedron". We initiate a systematic investigation of the boundary structure of the EFThedron, giving infinitely many linear and non-linear inequalities that must be satisfied by the EFT expansion in any theory. We illustrate the EFThedron geometry and constraints in a wide variety of examples, including new consistency conditions on the scattering amplitudes of photons and gravitons in the real world.

hep-th↗

arXiv2020

condLSTM-Q: A novel deep learning model for predicting Covid-19 mortality in fine geographical Scale

Predictive models with a focus on different spatial-temporal scales benefit governments and healthcare systems to combat the COVID-19 pandemic. Here we present the conditional Long Short-Term Memory networks with Quantile output (condLSTM-Q), a well-performing model for making quantile predictions on COVID-19 death tolls at the county level with a two-week forecast window. This fine geographical scale is a rare but useful feature in publicly available predictive models, which would especially benefit state-level officials to coordinate resources within the state. The quantile predictions from condLSTM-Q inform people about the distribution of the predicted death tolls, allowing better evaluation of possible trajectories of the severity. Given the scalability and generalizability of neural network models, this model could incorporate additional data sources with ease, and could be further developed to generate other useful predictions such as new cases or hospitalizations intuitively.

cs.LG↗

arXiv2020

Duality and Axionic Weak Gravity

The axionic weak gravity conjecture predicts the existence of instantons whose actions are less than their charges in appropriate units. We show that the conjecture is satisfied for the axion-dilaton-gravity system if we assume duality constraints on the higher derivative corrections in addition to positivity bounds which follow from unitarity, analyticity, and locality of UV scattering amplitudes. On the other hand, the conjecture does not follow if we assume the positivity bounds only. This presents an example where derivation of the weak gravity conjecture requires more detailed UV information than the consistency of scattering amplitudes.

hep-th↗