Publications

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• Fusion of irreducible modules in the periodic Temperley–Lieb algebra

  Yacine Ikhlef, Alexi Morin-Duchesne

  SciPost Phys. 17, 132 (2024) · published 12 November 2024 | Toggle abstract · pdf

  We propose a new family $\mathsf{Y}_{k,\ell,x,y,[z,w]}$ of modules over the enlarged periodic Temperley–Lieb algebra $\mathsf{\mathcal EPTL}_N(\beta)$. These modules are built from link states with two marked points, similarly to the modules $\mathsf{X}_{k,\ell,x,y,z}$ that we constructed in a previous paper. They however differ in the way that defects connect pairwise. We analyse the decomposition of $\mathsf{Y}_{k,\ell,x,y,[z,w]}$ over the irreducible standard modules $\mathsf{W}_{k,x}$ for generic values of the parameters $z$ and $w$, and use it to deduce the fusion rules for the fusion $\mathsf{W} × \mathsf{W}$ of standard modules. These turn out to be more symmetric than those obtained previously using the modules $\mathsf{X}_{k,\ell,x,y,z}$. From the work of Graham and Lehrer, it is known that, for $\beta = -q-q^{-1}$ where $q$ is not a root of unity, there exists a set of non-generic values of the twist $y$ for which the standard module $\mathsf{W}_{\ell,y}$ is indecomposable yet reducible with two composition factors: a radical submodule $\mathsf{R}_{\ell,y}$ and a quotient module $\mathsf{Q}_{\ell,y}$. Here, we construct the fusion products $\mathsf{W}×\mathsf{R}$, $\mathsf{W}×\mathsf{Q}$ and $\mathsf{Q} × \mathsf{Q}$, and analyse their decomposition over indecomposable modules. For the fusions involving the quotient modules $\mathsf{Q}$, we find very simple results reminiscent of $\mathfrak{sl}(2)$ fusion rules. This construction with modules $\mathsf{Y}_{k,\ell,x,y,[z,w]}$ is a good lattice regularization of the operator product expansion in the underlying logarithmic bulk conformal field theory. Indeed, it fits with the correspondence between standard modules and connectivity operators, and is useful for the calculation of their correlation functions. Remarkably, we show that the fusion rules $\mathsf{W}×\mathsf{Q}$ and $\mathsf{Q}×\mathsf{Q}$ are consistent with the known fusion rules of degenerate primary fields.

• Extremality as a consistency condition on subregion duality

  Ronak M. Soni

  SciPost Phys. 17, 133 (2024) · published 13 November 2024 | Toggle abstract · pdf

  In JT gravity coupled to a CFT, I argue without using the path integral that the entanglement wedge of a boundary region is bounded by a quantum extremal surface (QES). For any candidate not bounded by a QES, a unitary in the complement can make reconstruction within the candidate inconsistent with boundary causality. The case without islands is a direct consequence of subregion duality, and the case with islands can also be dealt with with a stronger assumption.

• Boundary chaos: Spectral form factor

  Felix Fritzsch, Tomaž Prosen

  SciPost Phys. 17, 142 (2024) · published 22 November 2024 | Toggle abstract · pdf

  Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed boundary chaos, in terms of the spectral form factor and its fluctuations. We exactly calculate the latter in the limit of large local Hilbert space dimension $q$ for different classes of random boundary interactions and find it to coincide with random matrix theory, possibly after a non-zero Thouless time. The latter effect is due to a drastic enhancement of the spectral form factor, when integer time and system size fulfill a resonance condition. We compare our semiclassical (large $q$) results with numerics at small local Hilbert space dimension ($q=2,3$) and observe qualitatively similar features as in the semiclassical regime.

• Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry

  Nikolai A. Stepanov, Mikhail A. Skvortsov

  SciPost Phys. 13, 021 (2022) · published 16 August 2022 | Toggle abstract · pdf

  We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction (Whitney's problem). Considered on the entire time axis, the problem admits a unique solution that always remains in the upper half plane. We formulate the problem of statistical description of this never-falling trajectory and solve it by a field-theoretical technique assuming a white-noise driving. In our approach based on the supersymmetric formalism of Parisi and Sourlas, statistic properties of the never-falling trajectory are expressed in terms of the zero mode of the corresponding transfer-matrix Hamiltonian. The emerging mathematical structure is similar to that of the Fokker-Planck equation, which however is written for the "square root" of the probability distribution function. Our results for the statistics of the non-falling trajectory are in perfect agreement with direct numerical simulations of the stochastic pendulum equation. In the limit of strong driving (no gravitation), we obtain an exact analytical solution for the instantaneous joint probability distribution function of the pendulum's angle and its velocity.

• Non-chiral vertex operator algebra associated to Lorentzian lattices and Narain CFTs

  Ranveer Kumar Singh, Madhav Sinha

  SciPost Phys. 17, 047 (2024) · published 12 August 2024 | Toggle abstract · pdf

  Frenkel, Lepowsky, and Meurman constructed a vertex operator algebra (VOA) associated to any even, integral, Euclidean lattice. In the language of physics, these are examples of chiral conformal field theories (CFT). In this paper, we define non-chiral vertex operator algebra and some associated notions. We then give a construction of a non-chiral VOA associated to an even, integral, Lorentzian lattice and construct their irreducible modules. We obtain the moduli space of such modular invariant non-chiral CFTs based on even, self-dual Lorentzian lattices of signature $(m,n)$ assuming the validity of a technical result about automorphisms of the lattice. We finally show that Narain conformal field theories in physics are examples of non-chiral VOA. Our formalism helps us to identify the chiral algebra of Narain CFTs in terms of a particular sublattice and give us the decomposition of its partition function into sum of characters.

• Out-of-equilibrium full counting statistics in Gaussian theories of quantum magnets

  Riccardo Senese, Jacob H. Robertson, Fabian H. L. Essler

  SciPost Phys. 17, 139 (2024) · published 20 November 2024 | Toggle abstract · pdf

  We consider the probability distributions of the subsystem (staggered) magnetization in ordered and disordered models of quantum magnets in D dimensions. We focus on Heisenberg antiferromagnets and long-range transverse-field Ising models as particular examples. By employing a range of self-consistent time-dependent mean-field approximations in conjunction with Holstein-Primakoff, Dyson-Maleev, Schwinger boson and modified spin-wave theory representations we obtain results in thermal equilibrium as well as during non-equilibrium evolution after quantum quenches. To extract probability distributions we derive a simple formula for the characteristic function of generic quadratic observables in any Gaussian theory of bosons.

• The superconducting clock-circuit: Improving the coherence of Josephson radiation beyond the thermodynamic uncertainty relation

  David Scheer, Jonas Völler, Fabian Hassler

  SciPost Phys. 17, 140 (2024) · published 21 November 2024 | Toggle abstract · pdf

  In the field of superconducting electronics, the on-chip generation of AC radiation is essential for further advancements. Although a Josephson junction can emit AC radiation from a purely DC voltage bias, the coherence of this radiation is significantly limited by Johnson-Nyquist noise. We relate this limitation to the thermodynamic uncertainty relation (TUR) in the field of stochastic thermodynamics. Recent findings indicate that the thermodynamic uncertainty relation can be broken by a classical pendulum clock. We demonstrate how the violation of the TUR can be used as a design principle for radiation sources by showing that a superconducting clock circuit emits coherent AC radiation from a DC bias.

• General features and contact modeling of $N$-body isolated resonances near threshold

  Ludovic Pricoupenko

  SciPost Phys. 17, 108 (2024) · published 8 October 2024 | Toggle abstract · pdf

  $N$-body non efimovian bound or quasi-bound states for particles with short range interactions are considered in arbitrary dimensions. The different resonance regimes near the threshold are depicted by using a generalization of the effective range approximation. This two-parameter description can be used in various contexts from ultracold to hadronic physics. The universal character of these states makes it possible a formulation in terms of a contact model. The singularity at the contact imposes the introduction of a modified scalar product to solve the normalization catastrophe and to restore the self-adjoint character of the model. An equivalence with the standard scalar product used for realistic finite range models is derived.

• Hole doping and electronic correlations in Cr substituted BaFe$_{2}$As$_{2}$

  Marli dos Reis Cantarino, Kevin R. Pakuszewski, Bjoern Salzmann, Pedro H. A. Moya, Wagner R. da Silva Neto, Gabriel S. Freitas, Pascoal G. Pagliuso, Cris Adriano, Walber H. Brito, Fernando A. Garcia

  SciPost Phys. 17, 141 (2024) · published 22 November 2024 | Toggle abstract · pdf

  For a significant composition range, the suppression of the spin density wave transition temperature ($T_{\text{SDW}}$) in Cr- and Mn-substituted BaFe$_{2}$As$_{2}$ (CrBFA and MnBFA, respectively) coincides as a function of Cr/Mn content, despite the distinct electronic effects of these substitutions. Additionally, for any Cr/Mn content superconductivity (SC) is absent and this topic is particularly less explored in the case of CrBFA. In this work, we employ angle-resolved photoemission spectroscopy (ARPES) and combined density functional theory plus dynamical mean field theory (DFT+DMFT) to address the evolution of the Fermi surface (FS) and electronic correlations in CrBFA. Our findings reveal that incorporating Cr leads to an effective hole doping of the states near the FS, which is well described within the virtual crystal approximation (VCA). Moreover, analysis of the ARPES spectra of the bands with main $d_{yz}$-orbital character reveals a fractional scaling of the imaginary part of self-energy as a function of the binding energy, a signature property of Hund's correlations. Our DFT+DMFT calculations support these experimental findings. We conclude that CrBFA is a correlated electron system for which the changes in the FS as a function of Cr are unrelated to the suppression of $T_{\text{SDW}}$. In addition, we suggest that the absence of SC is primarily due to the competition between Cr local moments and the Fe-derived itinerant spin fluctuations.

• Renormalization approach to the superconducting Kondo model

  Steffen Sykora, Tobias Meng

  SciPost Phys. 13, 016 (2022) · published 12 August 2022 | Toggle abstract · pdf

  An approach to bound states based on unitary transformations of Hamiltonians is presented. The method is applied to study the interaction between electrons in a BCS $s$-wave superconductor and a quantum spin. It is shown that known results from the t-matrix method and numerical studies are reproduced by this new method. As a main advantage, the method can straightforwardly be extended to study the topological properties of combined bound states in chains of many magnetic impurities. It also provides a uniform picture of the interplay between the Yu-Shiba-Rusinov (YSR) bound states and the Kondo singlet state.