Publications

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• Robust extended states in Anderson model on partially disordered random regular graphs

  Daniil Kochergin, Ivan M. Khaymovich, Olga Valba, Alexander Gorsky

  SciPost Phys. 16, 106 (2024) · published 19 April 2024 | Toggle abstract · pdf

  In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction $\beta$ of the sites being disordered, while the rest remain clean. It is shown that the mobility edge in the spectrum survives in a certain range of parameters (d,$\beta$) at infinitely large uniformly distributed disorder. The critical curve separating extended and localized states is derived analytically and confirmed numerically. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood.

  4 citations

• Hamiltonian truncation crafted for UV-divergent QFTs

  Olivier Delouche, Joan Elias Miro, James Ingoldby

  SciPost Phys. 16, 105 (2024) · published 19 April 2024 | Toggle abstract · pdf

  We develop the theory of Hamiltonian Truncation (HT) to systematically study RG flows that require the renormalization of coupling constants. This is a necessary step towards making HT a fully general method for QFT calculations. We apply this theory to a number of QFTs defined as relevant deformations of d=1+1 CFTs. We investigated three examples of increasing complexity: The deformed Ising, Tricritical-Ising, and non-unitary minimal model M(3,7). The first two examples provide a crosscheck of our methodologies against well established characteristics of these theories. The M(3,7) CFT deformed by its $\mathbb{Z}_2$-even operators shows an intricate phase diagram that we clarify. At a boundary of this phase diagram we show that this theory flows, in the IR, to the M(3,5) CFT.

  6 citations

• CFT and lattice correlators near an RG domain wall between minimal models

  Cameron V. Cogburn, Andrew Liam Fitzpatrick, Hao Geng

  SciPost Phys. Core 7, 021 (2024) · published 19 April 2024 | Toggle abstract · pdf

  Conformal interfaces separating two conformal field theories (CFTs) provide maps between different CFTs, and naturally exist in nature as domain walls between different phases. One particularly interesting construction of a conformal interface is the renormalization group (RG) domain wall between CFTs. For a given Virasoro minimal model $\mathcal{M}_{k+3,k+2}$, an RG domain wall can be generated by a specific deformation which triggers an RG flow towards its adjacent Virasoro minimal model $\mathcal{M}_{k+2,k+1}$ with the deformation turned on over part of the space. An algebraic construction of this domain wall was proposed by Gaiotto in [J. High Energy Phys. 12, 103 (2012)]. In this paper, we will provide a study of this RG domain wall for the minimal case $k=2$, which can be thought of as a nonperturbative check of the construction. In this case the wall is separating the Tricritical Ising Model (TIM) CFT and the Ising Model (IM) CFT. We will check the analytical results of correlation functions from the RG brane construction with the numerical density matrix renormalization group (DMRG) calculation using a lattice model proposed in [arXiv.1206.1332, Science 344, 280 (2014)], and find a perfect agreement. We comment on possible experimental realizations of this RG domain wall.

  9 citations

• Crossed product algebras and generalized entropy for subregions

  Shadi Ali Ahmad, Ro Jefferson

  SciPost Phys. Core 7, 020 (2024) · published 10 April 2024 | Toggle abstract · pdf

  An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a von Neumann factor of type III$_{1}$, in which entropy cannot be well-defined because such algebras do not admit a trace or density states. However, associated to the algebra is a modular group of automorphisms characterizing the local dynamics of degrees of freedom in the region, and the crossed product of the algebra with its modular group yields a type II$_∞$ factor, in which traces and hence von Neumann entropy can be well-defined. In this work, we generalize recent constructions of the crossed product algebra for the TFD to, in principle, arbitrary spacetime regions in arbitrary QFTs, formally paving the way to the study of entanglement entropy without UV divergences. In contrast to previous works, we emphasize that this construction is independent of gravity. In this sense, the crossed product construction represents a refinement of Haag's assignment of nets of observable algebras to spacetime regions by providing a natural construction of a type II factor. We present several concrete examples: a QFT in Rindler space, a CFT in an open ball of Minkowski space, and arbitrary boundary subregions in AdS/CFT. In the holographic setting, we provide a novel argument for why the bulk dual must be the entanglement wedge, and discuss the distinction arising from boundary modular flow between causal and entanglement wedges for excited states and disjoint regions.

  29 citations

• Symmetries and anomalies of Kitaev spin-S models: Identifying symmetry-enforced exotic quantum matter

  Ruizhi Liu, Ho Tat Lam, Han Ma, Liujun Zou

  SciPost Phys. 16, 100 (2024) · published 9 April 2024 | Toggle abstract · pdf

  We analyze the internal symmetries and their anomalies in the Kitaev spin-$S$ models. Importantly, these models have a lattice version of a $\mathbb{Z}_2$ 1-form symmetry, denoted by $\mathbb{Z}_2^{[1]}$. There is also an ordinary 0-form $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^T$ symmetry, where $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}$ are $\pi$ spin rotations around two orthogonal axes, and $\mathbb{Z}_2^T$ is the time reversal symmetry. The anomalies associated with the full $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^T×\mathbb{Z}_2^{[1]}$ symmetry are classified by $\mathbb{Z}_2^{17}$. We find that for $S∈\mathbb{Z}$ the model is anomaly-free, while for $S∈\mathbb{Z}+\frac{1}{2}$ there is an anomaly purely associated with the 1-form symmetry, but there is no anomaly purely associated with the ordinary symmetry or mixed anomaly between the 0-form and 1-form symmetries. The consequences of these symmetries and anomalies apply to not only the Kitaev spin-$S$ models, but also any of their perturbed versions, assuming that the perturbations are local and respect the symmetries. If these local perturbations are weak, generically these consequences still apply even if the perturbations break the 1-form symmetry. A notable consequence is that there should generically be a deconfined fermionic excitation carrying no fractional quantum number under the $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^T$ symmetry if $S∈\mathbb{Z}+\frac{1}{2}$, which implies symmetry-enforced exotic quantum matter. We also discuss the consequences for $S∈\mathbb{Z}$.

  11 citations

• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

  Sahand Seifnashri

  SciPost Phys. 16, 098 (2024) · published 9 April 2024 | Toggle abstract · pdf

  We study 't Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the "anomaly cocycle" using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group $H^3(G,U(1)) × H^2(G,U(1))$. The first factor captures the anomaly in the internal symmetry group $G$, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving $G$ and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.

  34 citations

• Generalized charges, part I: Invertible symmetries and higher representations

  Lakshya Bhardwaj, Sakura Schäfer-Nameki

  SciPost Phys. 16, 093 (2024) · published 4 April 2024 | Toggle abstract · pdf

  $q$-charges describe the possible actions of a generalized symmetry on $q$-dimensional operators. In Part I of this series of papers, we describe $q$-charges for invertible symmetries; while the discussion of $q$-charges for non-invertible symmetries is the topic of Part II. We argue that $q$-charges of a standard global symmetry, also known as a 0-form symmetry, correspond to the so-called $(q+1)$-representations of the 0-form symmetry group, which are natural higher-categorical generalizations of the standard notion of representations of a group. This generalizes already our understanding of possible charges under a 0-form symmetry! Just like local operators form representations of the 0-form symmetry group, higher-dimensional extended operators form higher-representations. This statement has a straightforward generalization to other invertible symmetries: $q$-charges of higher-form and higher-group symmetries are $(q+1)$-representations of the corresponding higher-groups. There is a natural extension to higher-charges of non-genuine operators (i.e. operators that are attached to higher-dimensional operators), which will be shown to be intertwiners of higher-representations. This brings into play the higher-categorical structure of higher-representations. We also discuss higher-charges of twisted sector operators (i.e. operators that appear at the boundary of topological operators of one dimension higher), including operators that appear at the boundary of condensation defects.

  49 citations

• Radiative asymptotic symmetries of 3D Einstein-Maxwell theory

  Jorrit Bosma, Marc Geiller, Sucheta Majumdar, Blagoje Oblak

  SciPost Phys. 16, 092 (2024) · published 3 April 2024 | Toggle abstract · pdf

  We study the null asymptotic structure of Einstein-Maxwell theory in three-dimensional (3D) spacetimes. Although devoid of bulk gravitational degrees of freedom, the system admits a massless photon and can therefore accommodate electromagnetic radiation. We derive fall-off conditions for the Maxwell field that contain both Coulombic and radiative modes with non-vanishing news. The latter produces non-integrability and fluxes in the asymptotic surface charges, and gives rise to a non-trivial 3D Bondi mass loss formula. The resulting solution space is thus analogous to a dimensional reduction of 4D pure gravity, with the role of gravitational radiation played by its electromagnetic cousin. We use this simplified setup to investigate choices of charge brackets in detail, and compute in particular the recently introduced Koszul bracket. When the latter is applied to Wald-Zoupas charges, which are conserved in the absence of news, it leads to the field-dependent central extension found earlier in [Class. Quantum Gravity 32, 245001 (2015)]. We also consider (Anti-)de Sitter asymptotics to further exhibit the analogy between this model and 4D gravity with leaky boundary conditions.

  5 citations

• Conformal boundary conditions for a 4d scalar field

  Lorenzo Di Pietro, Edoardo Lauria, Pierluigi Niro

  SciPost Phys. 16, 090 (2024) · published 3 April 2024 | Toggle abstract · pdf

  We construct unitary, stable, and interacting conformal boundary conditions for a free massless scalar in four dimensions by coupling it to edge modes living on a boundary. The boundary theories we consider are bosonic and fermionic QED$_3$ with $N_f$ flavors and a Chern-Simons term at level $k$, in the large-$N_f$ limit with fixed $k/N_f$. We find that interacting boundary conditions only exist when $k≠ 0$. To obtain this result we compute the $\beta$ functions of the classically marginal couplings at the first non-vanishing order in the large-$N_f$ expansion, and to all orders in $k/N_f$ and in the couplings. To check vacuum stability we also compute the large-$N_f$ effective potential. We compare our results with the the known conformal bootstrap bounds.

  6 citations

• Higher-group symmetry in finite gauge theory and stabilizer codes

  Maissam Barkeshli, Yu-An Chen, Po-Shen Hsin, Ryohei Kobayashi

  SciPost Phys. 16, 089 (2024) · published 3 April 2024 | Toggle abstract · pdf

  A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper, we show how such gauge theories possess a higher-group global symmetry, which we study in detail. We derive the $d$-group global symmetry and its 't Hooft anomaly for topological finite group gauge theories in $(d+1)$ space-time dimensions, including non-Abelian gauge groups and Dijkgraaf-Witten twists. We focus on the 1-form symmetry generated by invertible (Abelian) magnetic defects and the higher-form symmetries generated by invertible topological defects decorated with lower dimensional gauged symmetry-protected topological (SPT) phases. We show that due to a generalization of the Witten effect and charge-flux attachment, the 1-form symmetry generated by the magnetic defects mixes with other symmetries into a higher group. We describe such higher-group symmetry in various lattice model examples. We discuss several applications, including the classification of fermionic SPT phases in (3+1)D for general fermionic symmetry groups, where we also derive a simpler formula for the $[O_5] ∈ H^5(BG, U(1))$ obstruction that has appeared in prior work. We also show how the $d$-group symmetry is related to fault-tolerant non-Pauli logical gates and a refined Clifford hierarchy in stabilizer codes. We discover new logical gates in stabilizer codes using the $d$-group symmetry, such as a controlled Z gate in the (3+1) D $\mathbb{Z}_2$ toric code.

  25 citations