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1. Fractionalization of coset non-invertible symmetry and exotic Hall conductance

   https://doi.org/10.21468/SciPostPhys.17.3.095  

   Hsin, Po-Shen; Kobayashi, Ryohei; Zhang, Carolyn (January 2024, SciPost Physics)

   We investigate fractionalization of non-invertible symmetry in (2+1)D topological orders. We focus on coset non-invertible symmetries obtained by gauging non-normal subgroups of invertible0 $0$-form symmetries. These symmetries can arise as global symmetries in quantum spin liquids, given by the quotient of the projective symmetry group by a non-normal subgroup as invariant gauge group. We point out that such coset non-invertible symmetries in topological orders can exhibit symmetry fractionalization: each anyon can carry a “fractional charge” under the coset non-invertible symmetry given by a gauge invariant superposition of fractional quantum numbers. We present various examples using field theories and quantum double lattice models, such as fractional quantum Hall systems with charge conjugation symmetry gauged and finite group gauge theory from gauging a non-normal subgroup. They include symmetry enrichedS_3 $S_3$andO(2) $O\left(2\right)$gauge theories. We show that such systems have a fractionalized continuous non-invertible coset symmetry and a well-defined electric Hall conductance. The coset symmetry enforces a gapless edge state if the boundary preserves the continuous non-invertible symmetry. We propose a general approach for constructing coset symmetry defects using a “sandwich” construction: non-invertible symmetry defects can generally be constructed from an invertible defect sandwiched by condensation defects. The anomaly free condition for finite coset symmetry is also identified. 

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2. Higher-group symmetry of (3+1)D fermionic $$\mathbb{Z}_2$$ gauge theory: Logical CCZ, CS, and T gates from higher symmetry

   https://doi.org/10.21468/SciPostPhys.16.5.122  

   Barkeshli, Maissam; Hsin, Po-Shen; Kobayashi, Ryohei (January 2024, SciPost Physics)

   It has recently been understood that the complete global symmetry of finite group topological gauge theories contains the structure of a higher-group. Here we study the higher-group structure in (3+1)D\mathbb{Z}_2 ${\mathbb{Z}}_2$gauge theory with an emergent fermion, and point out that pumping chiralp+ip $p+ip$topological states gives rise to a\mathbb{Z}_{8} ${\mathbb{Z}}_8$0-form symmetry with mixed gravitational anomaly. This ordinary symmetry mixes with the other higher symmetries to form a 3-group structure, which we examine in detail. We then show that in the context of stabilizer quantum codes, one can obtain logical CCZ and CS gates by placing the code on a discretization ofT^3 $T^3$(3-torus) andT^2 \rtimes_{C_2} S^1 $T^2{⋊}_{C_2}{S}^1$(2-torus bundle over the circle) respectively, and pumpingp+ip $p+ip$states. Our considerations also imply the possibility of a logicalT $T$gate by placing the code on\mathbb{RP}^3 ${ℝ\mathbb{P}}^3$and pumping ap+ip $p+ip$topological state. 

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3. Conformal geometry from entanglement

   https://doi.org/10.21468/SciPostPhys.18.3.102  

   Kim, Isaac H; Li, Xiang; Lin, Ting-Chun; McGreevy, John; Shi, Bowen (January 2025, SciPost Physics)

   In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap. We introduce a novel pair of information-theoretic quantities(\mathfrak{c}_{\textrm{tot}}, \eta) $({𝔠}_{\text{tot}},\eta )$that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure. We posit that, for a topological groundstate, the quantity\mathfrak{c}_{\textrm{tot}} ${𝔠}_{\text{tot}}$is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i)\mathfrak{c}_{\textrm{tot}} ${𝔠}_{\text{tot}}$is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii)\eta $\eta$is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on groundstate entanglement. We show that stationarity of\mathfrak{c}_{\textrm{tot}} ${𝔠}_{\text{tot}}$is equivalent to a vector fixed-point equation involving\eta $\eta$, making our assumption locally checkable. We also derive similar results for 1+1D systems under a suitable set of assumptions. 

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4. Quantum Symmetries of Noncommutative Tori

   https://doi.org/10.1007/s00220-025-05337-y  

   Evans, David_E; Jones, Corey (June 2025, Communications in Mathematical Physics)

   Abstract We consider the problem of building non-invertible quantum symmetries (as characterized by actions of unitary fusion categories) on noncommutative tori. We introduce a general method to construct actions of fusion categories on inductive limit C*-algberas using finite dimenionsal data, and then apply it to obtain AT-actions of arbitrary Haagerup-Izumi categories on noncommutative 2-tori, of the even part of the$$E_{8}$$ $E_8$subfactor on a noncommutative 3-torus, and of$$\text {PSU}(2)_{15}$$ $\text{PSU}{\left(2\right)}_{15}$on a noncommutative 4-torus. 

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5. QLBT: a linear Boltzmann transport model for heavy quarks in a quark-gluon plasma of quasi-particles

   https://doi.org/10.1140/epjc/s10052-022-10308-x  

   Liu, Feng-Lei; Xing, Wen-Jing; Wu, Xiang-Yu; Qin, Guang-You; Cao, Shanshan; Wang, Xin-Nian (April 2022, The European Physical Journal C)

   Abstract We develop a new heavy quark transport model, QLBT, to simulate the dynamical propagation of heavy quarks inside the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. Our QLBT model is based on the linear Boltzmann transport (LBT) model with the ideal QGP replaced by a collection of quasi-particles to account for the non-perturbative interactions among quarks and gluons of the hot QGP. The thermal masses of quasi-particles are fitted to the equation of state from lattice QCD simulations using the Bayesian statistical analysis method. Combining QLBT with our advanced hybrid fragmentation-coalescence hadronization approach, we calculate the nuclear modification factor$$R_\mathrm {AA}$$ $R_{\mathrm{AA}}$and the elliptic flow$$v_2$$ $v_2$ofDmesons at the Relativistic Heavy-Ion Collider and the Large Hadron Collider. By comparing our QLBT calculation to the experimental data on theDmeson$$R_\mathrm {AA}$$ $R_{\mathrm{AA}}$and$$v_2$$ $v_2$, we extract the heavy quark transport parameter$$\hat{q}$$ $\hat{q}$and diffusion coefficient$$D_\mathrm {s}$$ $D_s$in the temperature range of$$1-4~T_\mathrm {c}$$ $1-4T_c$, and compare them with the lattice QCD results and other phenomenological studies. 

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