Publications

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• Critical spin chains and loop models with $PSU(n)$ symmetry

  Paul Roux, Jesper Lykke Jacobsen, Sylvain Ribault, Hubert Saleur

  SciPost Phys. 18, 033 (2025) · published 27 January 2025 | Toggle abstract · pdf

  Starting with the Ising model, statistical models with global symmetries provide fruitful approaches to interesting physical systems, for example percolation or polymers. These include the $O(n)$ model (symmetry group $O(n)$) and the Potts model (symmetry group $S_Q$). Both models make sense for $n,Q∈ \mathbb{C}$ and not just $n,Q∈ \mathbb{N}$, and both give rise to a conformal field theory in the critical limit. Here, we study similar models based on the group $PSU(n)$. We focus on the two-dimensional case, where the models can be described either as gases of non-intersecting orientable loops, or as alternating spin chains. This allows us to determine their spectra either by computing a twisted torus partition function, or by studying representations of the walled Brauer algebra. In the critical limit, our models give rise to a CFT that exists for any $n∈\mathbb{C}$ and has a global $PSU(n)$ symmetry. Its spectrum is similar to those of the $O(n)$ and Potts CFTs, but a bit simpler. We conjecture that the $O(n)$ CFT is a $\mathbb{Z}_2$ orbifold of the $PSU(n)$ CFT, where $\mathbb{Z}_2$ acts as complex conjugation.

  4 citations

• Site-wise dynamic defects in a non-conserving exclusion process

  Nikhil Bhatia, Arvind Kumar Gupta

  SciPost Phys. Core 8, 009 (2025) · published 27 January 2025 | Toggle abstract · pdf

  Motivated by the significant influence of the defects in the dynamics of the natural or man-made transportation systems, we propose an open, dynamically disordered, totally asymmetric simple exclusion process featuring bulk particle attachment and detachment. The site-wise dynamic defects might randomly emerge or vanish at any lattice location, and their presence slows down the motion of the particles. Using a mean-field approach, we obtain an analytical expression for both particle and defect density and validate them using Monte Carlo simulation. The study investigates the steady-state characteristics of the system, including phase transitions, analysis of boundary layers, and phase diagrams. Our approach streamlines the defect dynamics by integrating two parameters into one called the obstruction factor, which helps in determining an effective binding constant. The impact of the obstruction factor on the phase diagram is explored across various combinations of binding constants and detachment rates. A critical value of the obstruction factor is obtained, about which an infinitesimal change results in a substantial qualitative change in the structure of the phase diagrams. Further, the effect of the detachment rate is studied, and critical values along which the system observes a quantitative transition of the stationary phases are obtained as a function of the obstruction factor. Overall, the system shows stationary phases ranging from three to seven depending upon the value of the obstruction factor, the binding constant, and the detachment rate. Moreover, we scrutinized the impact of the obstruction factor on the shock dynamics and found no finite-size effect.

• (SPT-)LSM theorems from projective non-invertible symmetries

  Salvatore D. Pace, Ho Tat Lam, and Ömer M. Aksoy

  SciPost Phys. 18, 028 (2025) · published 22 January 2025 | Toggle abstract · pdf

  Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram and entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible symmetries and lattice translations in a generalized $1+1$D quantum XY model based on group-valued qudits. This model is specified by a finite group $G$ and enjoys a projective $\mathsf{Rep}(G)× Z(G)$ and translation symmetry, where symmetry operators obey a projective algebra in the presence of symmetry defects. For invertible symmetries, such projective algebras imply Lieb-Schultz-Mattis (LSM) anomalies. However, this is not generally true for non-invertible symmetries, and we derive a condition on $G$ for the existence of an LSM anomaly. When this condition is not met, we prove an SPT-LSM theorem: any unique and gapped ground state is necessarily a non-invertible weak symmetry protected topological (SPT) state with non-trivial entanglement, for which we construct an example fixed-point Hamiltonian. The projectivity also affects the dual symmetries after gauging $\mathsf{Rep}(G)× Z(G)$ sub-symmetries, giving rise to non-Abelian and non-invertible dipole symmetries, as well as non-invertible translations. We complement our analysis with the SymTFT, where the projectivity causes it to be a topological order non-trivially enriched by translations. Throughout the paper, we develop techniques for gauging $\mathsf{Rep}(G)$ symmetry and inserting its symmetry defects on the lattice, which are applicable to other non-invertible symmetries.

  9 citations

• Integrability of open boundary driven quantum circuits

  Chiara Paletta, Tomaž Prosen

  SciPost Phys. 18, 027 (2025) · published 22 January 2025 | Toggle abstract · pdf

  In this paper, we address the problem of Yang-Baxter integrability of doubled quantum circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are only coupled at the left or right boundary. We investigate the cases where the bulk is given by elementary six vertex unitary gates of either the free fermionic XX type or interacting XXZ type. By using the Sklyanin's construction of reflection algebra, we obtain the most general solutions of the boundary Yang-Baxter equation for such a setup. We use this solution to build, from the transfer matrix formalism, integrable circuits with two step discrete time Floquet (aka brickwork) dynamics. We prove that, only if the bulk is a free-model, the boundary matrices are in general non-factorizable, and for particular choice of free parameters yield non-trivial unitary dynamics with boundary interaction between the two chains. Then, we consider the limit of continuous time evolution and we give the interpretation of a restricted set of the boundary terms in the Lindbladian setting. Specifically, for a particular choice of free parameters, the solutions correspond to an open quantum system dynamics with the source terms representing injecting or removing particles from the boundary of the spin chain.

  7 citations

• Boundary overlap in the open XXZ spin chain

  Charbel Abetian, Nikolai Kitanine, Veronique Terras

  SciPost Phys. 18, 026 (2025) · published 21 January 2025 | Toggle abstract · pdf

  In this paper we compute the overlaps of the ground states for the open spin chains after a change of one of the boundary magnetic fields. It can be considered as the first step toward the study of the boundary quench problem: behaviour of an open spin chain after an abrupt change of one boundary magnetic field.

  1 citation

• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections

  Salvatore D. Pace, Guilherme Delfino, Ho Tat Lam, Ömer M. Aksoy

  SciPost Phys. 18, 021 (2025) · published 17 January 2025 | Toggle abstract · pdf

  Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated symmetries in ${1+1}$ dimensions. Working with local Hamiltonians of spin chains, we explore the dual symmetries after gauging and their potential new spatial modulations. We establish sufficient conditions for the existence of an isomorphism between the modulated symmetries and their dual, naturally implemented by lattice reflections. For instance, in systems of prime qudits, translation invariance guarantees this isomorphism. For non-prime qudits, we show using techniques from ring theory that this isomorphism can also exist, although it is not guaranteed by lattice translation symmetry alone. From this isomorphism, we identify new Kramers-Wannier dualities and construct related non-invertible reflection symmetry operators using sequential quantum circuits. Notably, this non-invertible reflection symmetry exists even when the system lacks ordinary reflection symmetry. Throughout the paper, we illustrate these results using various simple toy models.

  22 citations

• R-matrices and Miura operators in 5d Chern-Simons theory

  Nafiz Ishtiaque, Saebyeok Jeong, Yehao Zhou

  SciPost Phys. Core 8, 003 (2025) · published 13 January 2025 | Toggle abstract · pdf

  We derive Miura operators for $W$- and $Y$-algebras from first principles as the expectation value of the intersection between a topological line defect and a holomorphic surface defect in 5-dimensional non-commutative $\mathfrak{gl}(1)$ Chern-Simons theory. The expectation value, viewed as the transition amplitude for states in the defect theories forming representations of the affine Yangian of $\mathfrak{gl}(1)$, satisfies the Yang-Baxter equation and is thus interpreted as an R-matrix. To achieve this, we identify the representations associated with the line and surface defects by calculating the operator product expansions (OPEs) of local operators on the defects, as conditions that anomalous Feynman diagrams cancel each other. We then evaluate the expectation value of the defect intersection using Feynman diagrams. When the line and surface defects are specified, we demonstrate that the expectation value precisely matches the Miura operators and their products.

  2 citations

• Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach

  Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov

  SciPost Phys. 18, 010 (2025) · published 10 January 2025 | Toggle abstract · pdf

  By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $\rho(E)$ for the Lévy and the Lévy -Rosenzweig-Porter random matrices which off-diagonal elements are strongly non-Gaussian with power-law tails. This makes the standard Hubbard-Stratonovich transformation inapplicable to such problems. We used, instead, the functional Hubbard-Stratonovich transformation which allowed to solve the problem analytically for large sizes of matrices. We show that $\rho(E)$ depends crucially on the control parameter that drives the system through the transition between the ergodic and the fractal phases and it can be used as an order parameter.

  2 citations

• Dynamics of systems with varying number of particles: From Liouville equations to general master equations for open systems

  Mauricio J. del Razo, Luigi Delle Site

  SciPost Phys. 18, 001 (2025) · published 6 January 2025 | Toggle abstract · pdf

  A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number through internal dynamics such as reactions. The physico-mathematical modeling of these systems is extremely challenging, with the major difficulty being the time dependence of the number of degrees of freedom and the additional constraint that the increment or reduction of the number and species of particles must not violate basic physical laws. Theoretical models, in such a case, represent the key tool for the design of computational strategies for numerical studies that deliver trustful results. In this manuscript, we review complementary physico-mathematical approaches of varying number of particles inspired by rather different specific numerical goals. As a result of the analysis on the underlying common structure of these models, we propose a unifying master equation for general dynamical systems with varying number of particles. This equation embeds all the previous models and can potentially model a much larger range of complex systems, ranging from molecular to social agent-based dynamics.

  1 citation

• B-type D-branes in hybrid models

  Johanna Knapp, Robert Pryor

  SciPost Phys. 17, 165 (2024) · published 12 December 2024 | Toggle abstract · pdf

  A hybrid model is a fibration of a Landau-Ginzburg orbifold over a geometric base. We study B-type D-branes in hybrid models. Imposing B-type supersymmetry on the boundary action, we show that D-branes are specified by matrix factorisations in the fibre direction, together with some geometric data associated to the base. We also deduce conditions for the compatibility of these branes with the bulk orbifold actions and R-symmetry. We construct examples of hybrid B-branes which are generalisations of well-studied branes in geometric and Landau-Ginzburg models. Hybrid models can arise at limiting points of the stringy Kähler moduli space of Calabi-Yaus, and can be realised as phases of the corresponding gauged linear sigma models (GLSMs). Using GLSM techniques, we establish connections between geometric branes and hybrid branes. As explicit examples, we consider one- and two-parameter Calabi-Yau hybrids with a $\mathbb{P}^1$-base.

  1 citation