Publications

Order by: publication date number of citations

• Can one hear the full nonlinearity of a PDE from its small excitations?

  Maxim Olshanii, Danshyl Boodhoo

  SciPost Phys. Core 8, 055 (2025) · published 25 August 2025 | Toggle abstract · pdf

  In this article, we show how one can restore an unknown nonlinear partial differential equation of a sine-Gordon type from its linearization around an unknown stationary kink. The key idea is to regard the ground state of the linear problem as the translation-related Goldstone mode of the nonlinear PDE sought after.

• Lattice random walks and quantum A-period conjecture

  Li Gan

  SciPost Phys. 19, 053 (2025) · published 21 August 2025 | Toggle abstract · pdf

  We derive explicit closed-form expressions for the generating function $C_N(A)$, which enumerates classical closed random walks on square and triangular lattices with $N$ steps and a signed area $A$, characterized by the number of moves in each hopping direction. This enumeration problem is mapped to the trace of powers of anisotropic Hofstadter-like Hamiltonian and is connected to the cluster coefficients of exclusion particles: Exclusion strength parameter $g = 2$ for square lattice walks, and a mixture of $g = 1$ and $g = 2$ for triangular lattice walks. By leveraging the intrinsic link between the Hofstadter model and high energy physics, we propose a conjecture connecting the above signed area enumeration $C_N(A)$ in statistical mechanics to the quantum A-period of associated toric Calabi–Yau threefold in topological string theory: Square lattice walks correspond to local $\mathbb{F}_0$ geometry, while triangular lattice walks are associated with local $\mathcal{B}_3$.

  1 citation

• Twisted S-duality

  Surya Raghavendran, Philsang Yoo

  SciPost Phys. 19, 049 (2025) · published 20 August 2025 | Toggle abstract · pdf

  We study an $\mathrm{SL}(2, \mathbb{Z})$ symmetry of a variant of BCOV theory in three complex dimensions. Using conjectural descriptions of twists of superstrings in terms of topological strings, we argue that this action can be thought of as a version of S-duality that preserves an $\mathrm{SU}(3)$-invariant twist of type IIB supergravity. We analyze how $\mathrm{SL}(2, \mathbb{Z})$ acts on various deformations of the holomorphic-topological twist of 4-dimensional $\mathcal{N}=4$ supersymmetric gauge theory, which come from residual supertranslations and superconformal symmetries, and are of relevance to geometric Langlands theory and gauge-theoretic constructions of the Yangian.

• A brief note on the G$_2$ Affleck-Kennedy-Lieb-Tasaki chain

  Hosho Katsura, Dirk Schuricht

  SciPost Phys. Core 8, 052 (2025) · published 15 August 2025 | Toggle abstract · pdf

  We consider the valence bond solid (VBS) state built of singlet pairs of fundamental representations and projected onto adjoint representations of the exceptional Lie group G$_2$. The two-point correlation function in the VBS state is non-vanishing only for nearest neighbours, but possesses finite string order. We construct a parent Hamiltonian for the VBS state, which constitutes the G$_2$ analog of the famous AKLT chain.

• Efficiency of dynamical decoupling for (almost) any spin–boson model

  Alexander Hahn, Daniel Burgarth, Davide Lonigro

  SciPost Phys. 19, 035 (2025) · published 13 August 2025 | Toggle abstract · pdf

  Dynamical decoupling is a technique aimed at suppressing the interaction between a quantum system and its environment by applying frequent unitary operations on the system alone. In the present paper, we analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment initially prepared in a thermal state. We find sufficient conditions under which dynamical decoupling works for such systems, and—most importantly—we find bounds for the convergence speed of the procedure. Our analysis is based on a new Trotter theorem for multiple Hamiltonians and involves a rigorous treatment of the evolution of mixed quantum states via unbounded Hamiltonians. A comparison with numerical experiments shows that our bounds reproduce the correct scaling in various relevant system parameters. Furthermore, our analytical treatment allows for quantifying the decoupling efficiency for boson baths with infinitely many modes, in which case a numerical treatment is unavailable.

  1 citation

• A field theory representation of sum of powers of principal minors and physical applications

  Morteza Nattagh Najafi, Abolfazl Ramezanpour, Mohammad Ali Rajabpour

  SciPost Phys. Core 8, 051 (2025) · published 12 August 2025 | Toggle abstract · pdf

  We introduce a novel field theory representation for the Sum of Powers of Principal Minors (SPPM), a mathematical construct with profound implications in quantum mechanics and statistical physics. We begin by establishing a Berezin integral formulation of the SPPM problem, showcasing its versatility through various symmetries including $SU(n)$, its subgroups, and particle-hole symmetry. This representation not only facilitates new analytical approaches but also offers deeper insights into the symmetries of complex quantum systems. For instance, it enables the representation of the Hubbard model's partition function in terms of the SPPM problem. We further develop three mean field techniques to approximate SPPM, each providing unique perspectives and utilities: the first method focuses on the evolution of symmetries post-mean field approximation, the second, based on the bosonic representation, enhances our understanding of the stability of mean field results, and the third employs a variational approach to establish a lower bound for SPPM. These methods converge to identical consistency relations and values for SPPM, illustrating their robustness. The practical applications of our theoretical advancements are demonstrated through two compelling case studies. First, we exactly solve the SPPM problem for the Laplacian matrix of a chain, a symmetric tridiagonal matrix, allowing for precise benchmarking of mean-field theory results. Second, we present the first analytical calculation of the Shannon-Rényi entropy for the transverse field Ising chain, revealing critical insights into phase transitions and symmetry breaking in the ferromagnetic phase. This work not only bridges theoretical gaps in understanding principal minors within quantum systems but also sets the stage for future explorations in more complex quantum and statistical physics models.

• U(1) gauging, continuous TQFTs, and higher symmetry structures

  Adrien Arbalestrier, Riccardo Argurio, Luigi Tizzano

  SciPost Phys. 19, 032 (2025) · published 12 August 2025 | Toggle abstract · pdf

  Quantum field theories can exhibit various generalized symmetry structures, among which higher-group symmetries and non-invertible symmetry defects are particularly prominent. In this work, we explore a new general scenario in which these two structures are intertwined. This phenomenon arises in four dimensions when gauging one of multiple $U(1)$ 0-form symmetries in the presence of mixed 't Hooft anomalies. We illustrate this with two distinct models that flow to an IR gapless phase and a gapped phase, respectively, and examine how this symmetry structure manifests in each case. Additionally, we investigate a five-dimensional model where a similar structure exists intrinsically. Our main tool is a symmetry TQFT in one higher dimension, formulated using non-compact gauge fields and having infinitely many topological operators. We carefully determine its boundary conditions and provide a detailed discussion on various dressing choices for its bulk topological operators.

  2 citations

• Anomalous continuous translations

  Nathan Seiberg

  SciPost Phys. 19, 031 (2025) · published 11 August 2025 | Toggle abstract · pdf

  We discuss a large class of non-relativistic continuum field theories where the Euclidean spatial symmetry of the classical theory is violated in the quantum theory by an Adler-Bell-Jackiw-like anomaly. In particular, the continuous translation symmetry of the classical theory is broken in the quantum theory to a discrete symmetry. Furthermore, that discrete symmetry is extended by an internal symmetry, making it non-Abelian. This presentation streamlines and extends the discussion in [SciPost Phys. 18, 063 (2025)]. In an Appendix, we present an elementary introduction to 't Hooft and Adler-Bell-Jackiw anomalies using a well-known system.

  3 citations

• Integrable fishnet circuits and Brownian solitons

  Žiga Krajnik, Enej Ilievski, Tomaž Prosen, Benjamin J. A. Héry, Vincent Pasquier

  SciPost Phys. 19, 027 (2025) · published 21 July 2025 | Toggle abstract · pdf

  We introduce classical many-body dynamics on a one-dimensional lattice comprising local two-body maps arranged on discrete space-time mesh that serve as discretizations of Hamiltonian dynamics with arbitrarily time-varying coupling constants. Time evolution is generated by passing an auxiliary degree of freedom along the lattice, resulting in a 'fishnet' circuit structure. We construct integrable circuits consisting of Yang-Baxter maps and demonstrate their general properties, using the Toda and anisotropic Landau-Lifschitz models as examples. Upon stochastically rescaling time, the dynamics is dominated by fluctuations and we observe solitons undergoing Brownian motion.

• Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models

  A. Liashyk, S. Pakuliak, E. Ragoucy

  SciPost Phys. 19, 023 (2025) · published 18 July 2025 | Toggle abstract · pdf

  We compute scalar products of off-shell Bethe vectors in models with $o_{2n+1}$ symmetry. The scalar products are expressed as a sum over partitions of the Bethe parameter sets, the building blocks being the so-called highest coefficients. We prove some recurrence relations and a residue theorem for these highest coefficients, and prove that they are consistent with the reduction to $gl_n$ invariant models. We also express the norm of on-shell Bethe vectors as a Gaudin determinant.

  2 citations