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1. 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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2. 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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3. Perturbation theory for evolution of cooperation on networks

   https://doi.org/10.1007/s00285-023-01941-5  

   Meng, Lingqi; Masuda, Naoki (June 2023, Journal of Mathematical Biology)

   Abstract Network structure is a mechanism for promoting cooperation in social dilemma games. In the present study, we explore graph surgery, i.e., to slightly perturb the given network, towards a network that better fosters cooperation. To this end, we develop a perturbation theory to assess the change in the propensity of cooperation when we add or remove a single edge to/from the given network. Our perturbation theory is for a previously proposed random-walk-based theory that provides the threshold benefit-to-cost ratio,$$(b/c)^*$$ ${(b/c)}^{\ast }$, which is the value of the benefit-to-cost ratio in the donation game above which the cooperator is more likely to fixate than in a control case, for any finite networks. We find that$$(b/c)^*$$ ${(b/c)}^{\ast }$decreases when we remove a single edge in a majority of cases and that our perturbation theory captures at a reasonable accuracy which edge removal makes$$(b/c)^*$$ ${(b/c)}^{\ast }$small to facilitate cooperation. In contrast,$$(b/c)^*$$ ${(b/c)}^{\ast }$tends to increase when we add an edge, and the perturbation theory is not good at predicting the edge addition that changes$$(b/c)^*$$ ${(b/c)}^{\ast }$by a large amount. Our perturbation theory significantly reduces the computational complexity for calculating the outcome of graph surgery. 

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4. Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

   https://doi.org/10.21468/SciPostPhys.17.2.034  

   Nikolaenko, Alexander; Zhang, Ya-Hui (January 2024, SciPost Physics)

   Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo couplingJ_K $J_K$at fixed doping x. At large positiveJ_K $J_K$, we confirm the expected conventional Luttinger liquid phase with2k_F=\frac{1+x}{2} $2k_F=\frac{1+x}{2}$(in units of2\pi $2\pi$), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In theJ_K ≤ 0 $J_K\le 0$side, our simulation finds the existence of a fractional Luttinger liquid (LL\star $\star$) phase with2k_F=\frac{x}{2} $2k_F=\frac{x}{2}$, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL\star $\star$) phase in higher dimensions. The LL\star $\star$phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positiveJ_K $J_K$. Then we mainly focus on the “critical regime” between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) ofJ_K $J_K$, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around0.035 J $0.035J$) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponentz=+ $z=+$. The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference. 

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5. Semileptonic form factors for $$B\rightarrow D^*\ell \nu $$ at nonzero recoil from $$2+1$$-flavor lattice QCD: Fermilab Lattice and MILC Collaborations

   https://doi.org/10.1140/epjc/s10052-022-10984-9  

   Bazavov, A.; DeTar, C. E.; Du, D.; El-Khadra, A. X.; Gámiz, E.; Gelzer, Z.; Gottlieb, S.; Heller, U. M.; Kronfeld, A. S.; Laiho, J.; et al (December 2022, The European Physical Journal C)

   Abstract We present the first unquenched lattice-QCD calculation of the form factors for the decay$$B\rightarrow D^*\ell \nu $$ $B\to D^{\ast }\ell \nu$at nonzero recoil. Our analysis includes 15 MILC ensembles with$$N_f=2+1$$ $N_f=2+1$flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from$$a\approx 0.15$$ $a\approx 0.15$fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valencebandcquarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element$$|V_{cb}|$$ $|V_{\mathrm{cb}}|$. We obtain$$\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}$$ $\left(V_{\mathrm{cb}}\right)=(38.40\pm 0.{68}_{\text{th}}\pm 0.{34}_{\text{exp}}\pm 0.{18}_{\text{EM}})\times {10}^{-3}$. The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall$$\chi ^2\text {/dof} = 126/84$$ ${\chi }^2\text{/dof}=126/84$, which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict$$R(D^*) = 0.265 \pm 0.013$$ $R\left(D^{\ast }\right)=0.265\pm 0.013$, which confirms the current tension between theory and experiment. 

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