Publications

Order by: publication date number of citations

• Quantum phases and transitions in spin chains with non-invertible symmetries

  Arkya Chatterjee, Ömer M. Aksoy, Xiao-Gang Wen

  SciPost Phys. 17, 115 (2024) · published 16 October 2024 | Toggle abstract · pdf

  Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are implemented by transformations that do not form a group. Such symmetries appear in large families of gapless states of quantum matter and constrain their low-energy dynamics. To provide a UV-complete description of such symmetries, it is useful to construct lattice models that respect these symmetries exactly. In this paper, we discuss two families of one-dimensional lattice Hamiltonians with finite on-site Hilbert spaces: one with (invertible) $S_3$ symmetry and the other with non-invertible $\mathsf{Rep}(S_3)$ symmetry. Our models are largely analytically tractable and demonstrate all possible spontaneous symmetry breaking patterns of these symmetries. Moreover, we use numerical techniques to study the nature of continuous phase transitions between the different symmetry-breaking gapped phases associated with both symmetries. Both models have self-dual lines, where the models are enriched by so-called intrinsically non-invertible symmetries generated by Kramers-Wannier-like duality transformations. We provide explicit lattice operators that generate these non-invertible self-duality symmetries. We show that the enhanced symmetry at the self-dual lines is described by a 2+1d symmetry-topological-order (SymTO) of type $JK_4\boxtimes \overline{JK}_4$. The condensable algebras of the SymTO determine the allowed gapped and gapless states of the self-dual $S_3$-symmetric and $\mathsf{Rep}(S_3)$-symmetric models.

  6 citations

• Fisher zeroes and the fluctuations of the spectral form factor of chaotic systems

  Guy Bunin, Laura Foini, Jorge Kurchan

  SciPost Phys. 17, 114 (2024) · published 15 October 2024 | Toggle abstract · pdf

  The spectral form factor of quantum chaotic systems has the familiar 'ramp $+$ plateau' form. Techniques to determine its form in the semiclassical or the thermodynamic limit have been devised, in both cases based on the average over an energy range or an ensemble of systems. For a single instance, fluctuations are large, do not go away in the limit, and depend on the element of the ensemble itself, thus seeming to question the whole procedure. Considered as the modulus of a partition function in complex inverse temperature $\beta_R+i\beta_I$ ($\beta_I \equiv \tau$ the time), the spectral form factor has regions of Fisher zeroes, the analogue of Yang-Lee zeroes for the complex temperature plane. The large spikes in the spectral form factor are in fact a consequence of near-misses of the line parametrized by $\beta_I$ to these zeroes. The largest spikes are indeed extensive and extremely sensitive to details, but we show that they are both exponentially rare and exponentially thin. Motivated by this, and inspired by the work of Derrida on the Random Energy Model, we study here a modified model of random energy levels in which we introduce level repulsion. We also check that the mechanism giving rise to spikes is the same in the SYK model.

  1 citation

• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement

  Takuya Okuda, Aswin Parayil Mana, Hiroki Sukeno

  SciPost Phys. 17, 113 (2024) · published 15 October 2024 | Toggle abstract · pdf

  Calderbank-Shor-Steane (CSS) codes are a class of quantum error correction codes that contains the toric code and fracton models. A procedure called foliation defines a cluster state for a given CSS code. We use the CSS chain complex and its tensor product with other chain complexes to describe the topological structure in the foliated cluster state, and argue that it has a symmetry-protected topological order protected by generalized global symmetries supported on cycles in the foliated CSS chain complex. We demonstrate the so-called anomaly inflow between CSS codes and corresponding foliated cluster states by explicitly showing the equality of the gauge transformations of the bulk and boundary partition functions defined as functionals of defect world-volumes. We show that the bulk and boundary defects are related via measurement of the bulk system. Further, we provide a procedure to obtain statistical models associated with general CSS codes via the foliated cluster state, and derive a generalization of the Kramers-Wannier-Wegner duality for such statistical models with insertion of twist defects. We also study the measurement-assisted gauging method with cluster-state entanglers for CSS/fracton models based on recent proposals in the literature, and demonstrate a non-invertible fusion of duality operators. Using the cluster-state entanglers, we construct the so-called strange correlator for general CSS/fracton models. Finally, we introduce a new family of subsystem-symmetric quantum models each of which is self-dual under the generalized Kramers-Wannier-Wegner duality transformation, which becomes a non-invertible symmetry.

• The Higgs mechanism with diagrams: A didactic approach

  Jochem Kip, Ronald Kleiss

  SciPost Phys. Lect. Notes 88 (2024) · published 14 October 2024 | Toggle abstract · pdf

  We present a paedagogical treatment of the electroweak Higgs mechanism based solely on Feynman diagrams and S-matrix elements, without recourse to (gauge) symmetry arguments. Throughout, the emphasis is on Feynman rules and the Schwinger-Dyson equations; it is pointed out that particular care is needed in the treatment of tadpole diagrams and their symmetry factors.

• On exactly solvable Yang-Baxter models and enhanced symmetries

  Khalil Idiab, Stijn Jurrien van Tongeren

  SciPost Phys. 17, 110 (2024) · published 10 October 2024 | Toggle abstract · pdf

  We study Yang-Baxter deformations of the flat space string that result in exactly solvable models, finding the Nappi-Witten model and its higher dimensional generalizations. We then consider the spectra of these models obtained by canonical quantization in light-cone gauge, and match them with an integrability-based Bethe Ansatz approach. By considering a generalized light-cone gauge we can describe the model by a nontrivially Drinfel'd twisted S matrix, explicitly verifying the twisted structure expected for such deformations. Next, the reformulation of the Nappi-Witten model as a Yang-Baxter deformation shows that Yang-Baxter models can have more symmetries than suggested by the $r$ matrix defining the deformation. We discuss these enhanced symmetries in more detail for some trivial and nontrivial examples. Finally, we observe that there are nonunimodular but Weyl-invariant Yang-Baxter models of a type not previously considered.

  1 citation

• Twisted holography on AdS$_3 \times S^3 \times$ K3 & the planar chiral algebra

  Víctor E. Fernández, Natalie M. Paquette, Brian R. Williams

  SciPost Phys. 17, 109 (2024) · published 9 October 2024 | Toggle abstract · pdf

  In this work, we revisit and elaborate on twisted holography for AdS$_3 × S^3 × X$ with $X= T^4$, K3, with a particular focus on K3. We describe the twist of supergravity, identify the corresponding (generalization of) BCOV theory, and enumerate twisted supergravity states. We use this knowledge, and the technique of Koszul duality, to obtain the $N → ∞$, or planar, limit of the chiral algebra of the dual CFT. The resulting symmetries are strong enough to fix planar 2 and 3-point functions in the twisted theory or, equivalently, in a 1/4-BPS subsector of the original duality. This technique can in principle be used to compute corrections to the chiral algebra perturbatively in $1/N$.

  1 citation

• Generating lattice non-invertible symmetries

  Weiguang Cao, Linhao Li, Masahito Yamazaki

  SciPost Phys. 17, 104 (2024) · published 4 October 2024 | Toggle abstract · pdf

  Lattice non-invertible symmetries have rich fusion structures and play important roles in understanding various exotic topological phases. In this paper, we explore methods to generate new lattice non-invertible transformations/symmetries from a given non-invertible seed transformation/symmetry. The new lattice non-invertible symmetry is constructed by composing the seed transformations on different sites or sandwiching a unitary transformation between the transformations on the same sites. In addition to known non-invertible symmetries with fusion algebras of Tambara-Yamagami $\mathbb Z_N×\mathbb Z_N$ type, we obtain a new non-invertible symmetry in models with $\mathbb Z_N$ dipole symmetries. We name the latter the dipole Kramers-Wannier symmetry because it arises from gauging the dipole symmetry. We further study the dipole Kramers-Wannier symmetry in depth, including its topological defect, its anomaly and its associated generalized Kennedy-Tasaki transformation.

  5 citations

• $G_2$-manifolds from 4d N=1 theories, part I: Domain walls

  Andreas P. Braun, Evyatar Sabag, Matteo Sacchi, Sakura Schäfer-Nameki

  SciPost Phys. 17, 102 (2024) · published 3 October 2024 | Toggle abstract · pdf

  We propose new $G_2$-holonomy manifolds, which geometrize the Gaiotto-Kim 4d $\mathcal{N}=1$ duality domain walls of 5d $\mathcal{N}=1$ theories. These domain walls interpolate between different extended Coulomb branch phases of a given 5d superconformal field theory. Our starting point is the geometric realization of such a 5d superconformal field theory and its extended Coulomb branch in terms of M-theory on a non-compact singular Calabi-Yau three-fold and its Kähler cone. We construct the 7-manifold that realizes the domain wall in M-theory by fibering the Calabi-Yau three-fold over a real line, whilst varying its Kähler parameters as prescribed by the domain wall construction. In particular this requires the Calabi-Yau fiber to pass through a canonical singularity at the locus of the domain wall. Due to the 4d $\mathcal{N}=1$ supersymmetry that is preserved on the domain wall, we expect the resulting 7-manifold to have holonomy $G_2$. Indeed, for simple domain wall theories, this construction results in 7-manifolds, which are known to admit torsion-free $G_2$-holonomy metrics. We develop several generalizations to new 7-manifolds, which realize domain walls in 5d SQCD theories and walls between 5d theories which are UV-dual.

  1 citation

• Topological data analysis of monopole current networks in $U(1)$ lattice gauge theory

  Xavier Crean, Jeffrey Giansiracusa, Biagio Lucini

  SciPost Phys. 17, 100 (2024) · published 2 October 2024 | Toggle abstract · pdf

  In $4$-dimensional pure compact $U(1)$ lattice gauge theory, we analyse topological aspects of the dynamics of monopoles across the deconfinement phase transition. We do this using tools from Topological Data Analysis (TDA). We demonstrate that observables constructed from the zeroth and first homology groups of monopole current networks may be used to quantitatively and robustly locate the critical inverse coupling $\beta_{c}$ through finite-size scaling. Our method provides a mathematically robust framework for the characterisation of topological invariants related to monopole currents, putting on firmer ground earlier investigations. Moreover, our approach can be generalised to the study of Abelian monopoles in non-Abelian gauge theories.

• The giant graviton expansion in $AdS_5 \times S^5$

  Giorgos Eleftheriou, Sameer Murthy, Martí Rosselló

  SciPost Phys. 17, 098 (2024) · published 1 October 2024 | Toggle abstract · pdf

  The superconformal index of $\frac12$-BPS states of $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory has a known infinite $q$-series expression with successive terms suppressed by $q^N$. We derive a holographic bulk interpretation of this series by evaluating the corresponding functional integral in the dual AdS$_5 × S^5$. The integral localizes to a product of small fluctuations of the vacuum and of the collective modes of an arbitrary number of giant-gravitons wrapping an $S^3$ of maximal size inside the $S^5$. The quantum mechanics of the small fluctuations of one maximal giant is described by a supersymmetric version of the Landau problem. The quadratic fluctuation determinant reduces to a sum over the supersymmetric ground states, and precisely reproduces the first non-trivial term in the infinite series. Further, we show that the terms corresponding to multiple giants are obtained precisely by the matrix versions of the above super-quantum-mechanics.

  1 citation