Talks – iTHEMS-NCTS Workshop 2025

Quantum geometric aspects, i.e., Berry phase and quantum metric, play crucial roles in electronic properties of solids. It comes from the band structure as the manifolds in Hilbert space of wavefunctions. I will review some of the representative phenomena/effects driven by the quantum geometry including quantum transport, nonlinear optics, and superconductivity.

Diffusion-based generative models have proven highly effective for image generation tasks, and their mathematical formulation can be reformulated from a quantum mechanical perspective. In this presentation, I will briefly explain this approach and then demonstrate how differences in performance between models with and without noise in the generation process can be analyzed through log-likelihood calculations by introducing a quantum mechanical counterpart to the Planck constant. This talk is based on arXiv:2403.11262.

Understanding the possible observational features of black holes in quantum theory is a promising avenue to bridge the theoretical formulation of quantum gravity and astrophysical observations. In this talk, I will discuss the observational features of a model of horizonless compact objects. The interior spacetime of the model satisfies the 4D semiclassical Einstein equation nonperturbatively for the Planck constant, and its entropy agrees with the Bekenstein-Hawking formula. In particular, the theoretical setup of the model gives rise to strong interior redshifts, which, as I will demonstrate, render this model perfect as a black hole mimicker from observational points of view, including shadow images and gravitational wave ringdowns.

The correlation functions of primordial cosmological perturbations encode valuable information about the early universe. In particular, higher-order correlations—known as non-Gaussianities—can reveal additional insights, including the mass and spin of heavy particles, through characteristic oscillatory signatures. Remarkably, such particles can have masses as large as the Hubble scale during inflation, far beyond the reach of terrestrial experiments. This approach to uncovering new particles through primordial non-Gaussianity is known as the cosmological collider program, and it has emerged as a promising avenue for probing physics beyond the Standard Model. In this talk, I will present an overview of the cosmological collider framework, highlight recent developments, and discuss my own contributions to this growing field.

We consider physical system that displays Lifshitz anisotropy. We propose new construction for Lifshitz invariant field theory (LFT) with arbitrary Lifshitz exponent. We show that such theory admits a rich family of degenerate vacuum. We determine their entropic properties both field theoretically and using AdS/LFT. We also explain how the inclusion of a new boundary action term for the massive gauge field that plays crucial role in the AdS/LFT allow us to make a new AdS/BLFT proposal for the new holographic dual for boundary Lifshitz field theory (BLFT). Finally we discuss generic effects of Lifshitz anisotropy at the quantum mechanical level. We consider a novel anisotropic Josephson Junction and show that its working may be enhanced by the anisotropy of the insulating junction layer.

Electrodynamics in four-dimensional asymptotically flat spacetime possesses an infinite-dimensional asymptotic symmetry. The symmetry is related to low-energy phenomena such as soft theorems and the memory effect, and is tightly linked to the problem of infrared divergences in QED. We explain that it is essential to work with appropriate dressed states that respect the asymptotic symmetry to obtain infrared-safe S-matrix elements.

6d supergravities with non-abelian gauge group are subject to many consistency conditions. While the absence of local gauge and gravitational anomalies allows for infinitely many models, we show that those conditions stemming from the absence of both local and global anomalies together are strong enough to leave only finitely many consistent models. To do this we distill the consequences of anomaly cancellation into a high-dimensional linear program whose dual can be efficiently studied using standard techniques. We obtain a universal bound on the number of tensor multiplets $T\leq 11\cdot 273 = 3003$ and show that this leads to a finite landscape of consistent non-abelian models. Interestingly, the model which saturates this bound has gauge algebra $[\mathfrak{e}_8\oplus\mathfrak{f}_4\oplus(\mathfrak{g}_2\oplus\mathfrak{su}_2)^{\oplus 2}]^{\oplus 273}$, which bears a striking resemblance to the model which saturates the bound $T\leq 193$ for F-theory constructions.

Recent advances in the S-matrix bootstrap—imposing unitarity, crossing, and analyticity—have clarified how perturbative UV completion can arise in effective field theories with tree-level couplings to new states. We show that, assuming supersymmetry (or equivalently gravitational couplings), higher-spin states necessarily align into linear trajectories, revealing the emergence of a string-like spectrum from first principles. We close with a discussion of possible new principles hinted at by these trajectories.

In a phase where a symmetry is (partically) spontanesouly broken, the algebra acting on the excitations, and hence its representation theory, depends both on the symmetry and the phase. The corresponding algebra is a (higher) groupoid algebra, when the symmetry is a (higher) group. When the symmetry is a non-invertible symmetry, we need a generalization, dubbed “strip algebra”. We apply the formalism to 1+1d and 3+1d gapped systems, and observe the representation theory correctly replicates the classification of excitations in each phase. Based on the papers arXiv 2408.11045 (with Clay Cordova and Nicholas Holfester) and arXiv:2501.09069 (with Finn Gagliano and Andrea Grigoletto).

Abstract not available

This talk will discuss a method to efficiently compute energy spectra in lattice quantum field theories by Hamiltonian-formulated digital quantum simulation. A quantum algorithm called coherent imaging spectroscopy quenches the ground state with a time-oscillating perturbation for various frequencies. It reads off excited energy levels from values of frequencies showing the loss of the vacuum-to-vacuum probability following the quench. I will demonstrate this algorithm for the Schwinger model which is the (1+1)-dimensional quantum electrodynamics with a topological term. During the simulation, the ground state of the Schwinger model on lattice is prepared by adiabatic state preparation and various types of quenches to the approximate ground state are applied via Suzuki-Trotter time evolution. The computational complexity estimation for physically reasonable results likely implies the efficiency of the method in the early fault-tolerant quantum computer era.

We review how UV physics affects Hawking radiation and certain trans-Planckian properties may turn off Hawking radiation around the scrambling time and thus resolve the information paradox.

Recently, from the identification of matrix integral and the gravitational path integral, we had a significant progress in our understanding of non-perturbative correspondence between bulk geometry and the boundary quantum state. In this talk, we will explain aspects of such mapping between black hole interior geometry and the boundary quantum state, constructing “length operator" in the boundary theory. Using such operator, we confirm the Susskind's conjecture that the late time two sided BH is equal superposition of black holes and white holes. Furthermore, this program can be extended to the ETH matrix model for double-scaled SYK model, whose gravity dual has discrete structure, where we can see a connection to the Krylov complexity and its generalizations.

The matrix models are non-perturbative formulations of string theory, from which many believe that spacetime arises. The matrix fluctuations around the spacetime thus created should represent both matter and gravitational fields. In my talk, I will discuss how the gravitational field emerges from the IIB matrix model. In particular, I will focus on how invariance under general coordinate transformations arises and how unitarity is guaranteed in this theory.

Higher-spin gravity is a working model of quantum gravity in 4-dimensional de Sitter space. We discuss it at the level of cubic interactions, in a lightcone formalism originally developed for Minkowski and AdS. We use the interactions' chiral structure to unlock a broader class of lightcone frames. This makes the formalism applicable to de Sitter, and brings out a causal property of the transformation between frames. We use this property to describe an evolution problem in a causal diamond, and especially in the largest causal diamond in de Sitter space - the static patch.

In this talk, we propose genuine multi-entropy, a measure aimed at capturing irreducible multipartite entanglement beyond bipartite entropy. After defining the quantity, we summarize its basic features. We then discuss implications for black holes and holography, where the measure provides a handle on multipartite correlations of holographic states and black holes. We conclude with prospective applications to condensed-matter systems and outline open problems.

Chirality (handedness) refers to the asymmetry characterized by non-superimposable mirror images of a material. In chiral crystals, there is no mirror symmetry (M) nor spatial inversion symmetry (P). The broken P-symmetry enables chiral crystals to exhibit the even-order nonlinear responses to the electromagnetic fields, e.g., nonlinear Hall effect (NLHE), second harmonic generation (SHG) and photogalvanic effect (PGE). In addition, chirality enables chiral crystal to exhibit novel properties, e.g., optical activity (natural circular dichroism) and quantized circular PGE (CPGE). Spin chirality in noncollinear magnetic structures can cause unexpected phenomena in solids by either generating Berry curvature in momentum and real spaces or breaking Kramer spin degeneracy in the electronic band structure. In this talk, I will present (1) spin-chirality induced quantum topological Hall effect [1] and topological magneto-optical Kerr and Faraday rotations [2] in noncoplanar antiferromagnets, (2) crystal chirality-induced magneto-optical effects in collinear antiferromagnets (altermagnets) [3], and magnetic moments of chiral phonons in chiral crystals [4], as revealed by our first-principles quantum mechanical calculations. The speaker thanks many collaborators, especially Jian Zhou, Qi-Feng Liang, Wanxiang Feng, Yugui Yao, and P. V. Sreenivasa. [1] J. Zhou, Q.-F. Liang, H. Weng, Y. B. Chen, S.-H. Yao, Y.-F. Chen, J. Dong and G.-Y. Guo, Predicted quantum topological Hall effect and noncoplanar antiferromagnetism in K1/2RhO2, Phys. Rev. Lett. 116, 256601 (2016). [2] W. Feng, J.-P. Hanke, X. Zhou, G.-Y. Guo, S. Blügel, Y. Mokrousov and Y. Yao, Topological magneto-optical effects and their quantization in noncoplanar antiferromagnets, Nature Commun. 11, 118 (2020). [3] X. Zhou, W. Feng, X. Yang, G.-Y. Guo and Y. Yao, Crystal chirality magneto-optical effects in collinear antiferromagnets, Phys. Rev. B 104, 024401 (2021). [4] P. V. Sreenivasa Reddy and G.-Y. Guo, Coexistent topological and chiral phonons in chiral RhGe: An ab initio study, arXiv: 2410.16000 (2024)

In this study, we introduce effective Hamiltonians that describe the random dynamics in monitored quantum systems, through the Lyapunov spectral analysis. As a result, we find that the spectral transition of the effective Hamiltonians occurs, leading to the ground-state entanglement transition [1]. Based on the coincidence between the spectral and ground-state transitions, we also extend the topological invariant and bulk-edge correspondence, concepts established in isolated quantum systems, to monitored quantum systems [2]. Our results suggest that spectrum and topology are useful for understanding measurement-induced transitions, although the dynamics is random and thus there is no static generator like a Hamiltonian.

Entanglement measures are essential tools for characterizing quantum many-body phases of matter. In (1+1)-dimensional conformal field theories (CFTs), entanglement entropy typically exhibits logarithmic scaling, with the coefficient yielding the central charge. However, for non-unitary CFTs, this central charge can be negative, leading to seemingly problematic negative entanglement entropy. We address this by introducing a generalized entanglement entropy that successfully extracts these negative central charges, demonstrated with several examples. Furthermore, in (2+1)-dimensional systems described by topological quantum field theories (TQFTs), the subleading term of entanglement entropy, known as the topological entanglement entropy (TEE), encodes crucial information about quasiparticle statistics. This talk will also present a topological derivation of the strong subadditivity of TEE.

Conformal invariance typically emerges in critical systems where the correlation length diverges, which is generally the case for Hermitian quantum systems without a spectral gap (in the thermodynamic limit). However, the situation becomes more subtle when Hermiticity is broken. In this talk, I will discuss when a non-Hermitian gapless quantum system can exhibit conformal invariance, focusing on free fermions in 1+1 dimensions. Certain universal characteristics of such systems—including a negative central charge and logarithmic couplings associated with indecomposable Jordan cell structures in the spectrum—are identified and computed in both continuum field theory and lattice formulations.

The Berry phase and its associated geometric structures have played a central role in our understanding of quantum phases of matter, from topological insulators to symmetry-protected topological phases. While the conventional Berry phase is given in terms of 1-form connection (Berry connection), recent developments point toward a natural generalization – higher Berry phases -- involving connections of higher degree forms and their associated curvatures. In this talk, I will discuss the recent developments of higher Berry phases using tensor networks and quantum field theories. I will explain how these structures can be captured by generalizing the quantum mechanical inner product to multi-wavefunction overlaps.

I shall, on behalf of our collaborators (See Refs.[1-3]), report on our recent theoretical investigations of finite momentum excitons in atomically thin transition-metal dichalcogenides (TMDs), including single and few TMD monolayers, by using the in-house code of Bethe-Salpeter equation (BSE) solver, WannierBSE.[1] Combined with open-access first-principles and Wannier90 packages, the WannierBSE package enables one to solve the DFT-based BSE in the Wannier tight binding (WTB) scheme for exciton complexes, exciton and trion, in 2D materials in an efficient and numerically economic manner. By employing WannierBSE, we investigate the full-zone band structures and momentum dependent valley polarizations of exciton in a WSe2 monolayer, showing intriguing pseudo-spin texture landscape of valley polarization over the extended reciprocal space. The symmetry analysis identifies the intrinsic depolarization nature of intra-valley bright exciton, and reveals the symmetry-sustained robustness of high degree of valley polarization of inter-valley excitons, [2] as observed in experiments. Increasing the number of monolayers, the intervalley momentum-forbidden dark excitons emerges as the true exciton ground states of multilayer TMDs. Despite the darkness, pairs of time-reversed inter-valley excitons in multi-layer TMDs could be annihilated by each other and up-converted to high energy bright excitons. Such an exciton-exciton annihilation (EEA) of intervalley dark exciton has been for the first time observed and evidenced by our recent experiment-theory-joint studies of the observed up-converted photoluminescence from multi-layer TMDs. [3] References: [1] Guan-Hao Peng, Ping-Yuan Lo, Wei-Hua Li, Yan-Chen Huang, Yan-Hong Chen, Chi-Hsuan Lee, Chih-Kai Yang, Shun-Jen Cheng. Distinctive Signatures of the Spin- and Momentum-Forbidden Dark Exciton States in the Photoluminescence of Strained WSe2 Monolayers under Thermalization. Nano Letters, 19, 2299 (2019); https://quantum.web.nycu.edu.tw/wannierbse/ [2] Ping-Yuan Lo, Guan-Hao Peng, Wei-Hua Li, Yi Yang, Shun-Jen Cheng* (2021, Nov), Full-zone valley polarization landscape of finite-momentum exciton in transition metal dichalcogenide monolayers, Phys. Rev. Research 3, 043198 (2021). [3] Yi-Hsun Chen, Ping-Yuan Lo, Kyle W Boschen, Chih-En Hsu, Yung-Ning Hsu, Luke N Holtzman, Guan-Hao Peng, Chun-Jui Huang, Madisen Holbrook, Wei-Hua Wang, Katayun Barmak, James Hone, Pawel Hawrylak, Hung-Chung Hsueh, Jeffrey A Davis, Shun-Jen Cheng, Michael S Fuhrer, Shao-Yu Chen, Efficient light upconversion via resonant exciton-exciton annihilation of dark excitons in few-layer transition metal dichalcogenides. Nature Communications 16 (1), 2935. (2025)

Protein condensates—such as nucleoli and nuclear speckles—coexist within cells and are central to numerous cellular processes. Although condensation is known to be primarily driven through liquid-liquid phase separation by interactions among intrinsically disordered regions, the precise amino acid sequence rules that allow distinct condensates to coexist remain unclear. Here, I will introduce a theoretical framework we have developed to predict heteropolymer interactions among disordered protein sequences [1]. Using this framework, we successfully determined key condensate properties, such as critical temperatures, and elucidated the conditions required for the coexistence of multiple types of condensates. [1] K. Adachi and K. Kawaguchi, Phys. Rev. X 14, 031011 (2024)

The exploration of ground-state topology in quantum materials has led to the discovery of a variety of exotic topological phases with unconventional Hall responses. In two-dimensional systems, Chern insulators exhibit the quantum anomalous Hall effect, while spin Chern insulators underlie the quantum spin Hall effect. Extending beyond charge and spin, recent advances in orbitronics have revealed a transverse response of orbital angular momentum—known as the orbital Hall effect. In this talk, I will introduce a comprehensive framework for understanding orbital Chern insulators (OCIs)—topological phases characterized by a nontrivial orbital degree of freedom. We not only establish the theoretical foundations of OCIs but also identify two-dimensional phosphorene as a promising material platform for their realization [1]. Our findings open new avenues for orbital topology in materials science and could pave the way for novel topological phases and orbitronics-based applications. [1] Yueh-Ting Yao et al., arXiv:2503.08138 (2025)

The mysterious metallic phase showing universal linear-in-temperature scattering rate: 1/τ = αP kB T / ħ with a universal constant prefactor αP ~ 1 and logarithmic-in-temperature singular specific heat coefficient, so-called “Planckian metal phase”, was observed in various high-Tc cuprate superconductors over a finite range in doping near optimal doping [1]. Revealing the mystery of the Planckian metal state is believed to be the key to understanding the mechanism for high-Tc superconductivity. Here, we propose a generic microscopic mechanism for this state based on quantum-critical local bosonic charge Kondo fluctuations coupled to both spinon and a heavy conduction-electron Fermi surfaces within the heavy-fermion formulated slave-boson t-J model [2]. A closely related idea proposed by C.H. Chung and collaborators based on critical Kondo fluctuations near Kondo breakdown quantum critical point has been used to successfully account for quantum critical strange metal states observed in various heavy-fermion compounds [3]. Our approach is motivated by the striking similarity in strange metal phenomenology between cuprates and heavy-fermion Kondo lattice systems. By a controlled perturbative renormalization group analysis of our effective heavy-fermion model, we examine the competition between the pseudogap phase, characterized by Anderson’s Resonating-Valence-Bond spin-liquid made of fermionic spin-singlet spinons, and the Fermi-liquid state, modeled by coherent electron hopping (effective charge Kondo hybridization). We find an extended quantum-critical metallic phase with a universal Planckian ħω/kBT scaling in scattering rate near a localized-delocalized (pseudogap-to-Fermi liquid) charge-Kondo breakdown transition. The d-wave superconducting ground state emerges near the transition. Unprecedented qualitative and quantitative agreements are reached between our theoretical predictions and various experiments, including optical conductivity [4], universal doping-independent field-to-temperature scaling in magnetoresistance [5], singular specific heat coefficient [6], marginal Fermi-liquid spectral function observed in ARPES [7], and Fermi surface reconstruction observed in Hall coefficients in various overdoped cuprates [5,8]. Our mechanism offers a microscopic understanding of the quantum-critical Planckian metal phase observed in cuprates and its link to the pseudogap, d-wave superconducting, and Fermi liquid phases. It offers a promising route for understanding how d-wave superconductivity emerges from such a strange metal phase in cuprates–one of the long-standing open problems in condensed matter physics since 1990s. It also shows a broader implication for the Planckian strange metal states observed in other correlated unconventional superconductors. *This work was supported by the National Science and Technology Council (NSTC) Grants 110-2112-M-A49-018-MY3, the National Center for Theoretical Sciences of Taiwan. [1] A. Legros et al., Nat. Phys. 15, 142 (2019). [2] Yung-Yeh Chang et al. , Rep. Prog. Phys. 2025 https://doi.org/10.1088/1361-6633/adc330. [3] J. Wang et al., PNAS 119, e2116980119 (2022); Yung-Yeh Chang et al., Phys. Rev. B 97, 035156 (2018); Yung-Yeh Chang et al., Phys. Rev. B 99, 094513 (2019); Yung-Yeh Chang et al., Nature Communications, 14, 581 (2023). [4] B. Michon et al., Nature Communications 14, 3033 (2023). [5] J. Ayres et al., Nature 595, 661 (2021). [6] B. Michon et al., Nature 567, 218 (2019). [7] S.D. Chen et al., Science, 366, 1099 (2019). [8] C. Proust et al., Annual Review of Condensed Matter Physics 10, 409 (2019).

Khovanov homology was introduced in 2000 by Mikhail Khovanov as a categorification of the Jones polynomial. In general, categorification refers to the process of lifting a numerical invariant to a richer algebraic category, revealing deeper structures that are often hidden at the numerical level. Indeed, Khovanov homology is strictly stronger than the Jones polynomial, and has the strength of detecting the unknot. In this talk, I will give an alternative diagrammatic view of the theory given by Bar-Natan, which enables more visual and structural understanding of Khovanov homology and related invariants.

In manifolds with special holonomy, it is interesting to study calibrated submanifolds, which are volume minimizers in their homology classes. In this talk, I will first explain a geometric rigidity result. For the important local models of manifolds with special holonomy, the geometric rigidity result holds true globally. Secondly, I will explain a result concerning their stability under the mean curvature flow. This is based on joint works with Mu-Tao Wang and Ping-Hung Lee.