Publications

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• Integrable Floquet systems related to logarithmic conformal field theory

  Vsevolod I. Yashin, Denis V. Kurlov, Aleksey K. Fedorov, Vladimir Gritsev

  SciPost Phys. 14, 084 (2023) · published 26 April 2023 | Toggle abstract · pdf

  We study an integrable Floquet quantum system related to lattice statistical systems in the universality class of dense polymers. These systems are described by a particular non-unitary representation of the Temperley-Lieb algebra. We find a simple Lie algebra structure for the elements of Temperley-Lieb algebra which are invariant under shift by two lattice sites, and show how the local Floquet conserved charges and the Floquet Hamiltonian are expressed in terms of this algebra. The system has a phase transition between local and non-local phases of the Floquet Hamiltonian. We provide a strong indication that in the scaling limit this non-equilibrium system is described by the logarithmic conformal field theory.

  4 citations

• The non-rational limit of D-series minimal models

  Sylvain Ribault

  SciPost Phys. Core 3, 002 (2020) · published 31 July 2020 | Toggle abstract · pdf

  We study the limit of D-series minimal models when the central charge tends to a generic irrational value $c\in (-\infty, 1)$. We find that the limit theory's diagonal three-point structure constant differs from that of Liouville theory by a distribution factor, which is given by a divergent Verlinde formula. Nevertheless, correlation functions that involve both non-diagonal and diagonal fields are smooth functions of the diagonal fields' conformal dimensions. The limit theory is a non-trivial example of a non-diagonal, non-rational, solved two-dimensional conformal field theory.

  4 citations

• Pivoting through the chiral-clock family

  Nick G. Jones, Abhishodh Prakash, Paul Fendley

  SciPost Phys. 18, 094 (2025) · published 14 March 2025 | Toggle abstract · pdf

  The Onsager algebra, invented to solve the two-dimensional Ising model, can be used to construct conserved charges for a family of integrable $N$-state chiral clock models. We show how it naturally gives rise to a "pivot" procedure for this family of chiral Hamiltonians. These Hamiltonians have an anti-unitary CPT symmetry that when combined with the usual $\mathbb{Z}_N$ clock symmetry gives a non-Abelian dihedral symmetry group $D_{2N}$. We show that this symmetry gives rise to symmetry-protected topological (SPT) order in this family for all even $N$, and representation-SPT (RSPT) physics for all odd $N$. The simplest such example is a next-nearest-neighbour chain generalising the spin-1/2 cluster model, an SPT phase of matter. We derive a matrix-product state representation of its fixed-point ground state along with the ensuing entanglement spectrum and symmetry fractionalisation. We analyse a rich phase diagram combining this model with the Onsager-integrable chiral Potts chain, and find trivial, symmetry-breaking and (R)SPT orders, as well as extended gapless regions. For odd $N$, the phase transitions are "unnecessarily" critical from the SPT point of view.

  4 citations

• A Framework for Studying a Quantum Critical Metal in the Limit $N_f\rightarrow0$

  Petter Säterskog

  SciPost Phys. 4, 015 (2018) · published 27 March 2018 | Toggle abstract · pdf

  We study a model in 1+2 dimensions composed of a spherical Fermi surface of $N_f$ flavors of fermions coupled to a massless scalar. We present a framework to non-perturbatively calculate general fermion $n$-point functions of this theory in the limit $N_f\rightarrow0$ followed by $k_F\rightarrow\infty$ where $k_F$ sets both the size and curvature of the Fermi surface. Using this framework we calculate the zero-temperature fermion density-density correlation function in real space and find an exponential decay of Friedel oscillations.

  4 citations

• Higher-genus Fay-like identities from meromorphic generating functions

  Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli

  SciPost Phys. 18, 093 (2025) · published 14 March 2025 | Toggle abstract · pdf

  A possible way of constructing polylogarithms on Riemann surfaces of higher genera facilitates integration kernels, which can be derived from generating functions incorporating the geometry of the surface. Functional relations among polylogarithms rely on identities for those integration kernels. In this article, we derive identities for Enriquez' meromorphic generating function and investigate the implications for the associated integration kernels. The resulting identities are shown to be exhaustive and therefore reproduce all identities for Enriquez' kernels conjectured in arXiv:2407.11476 recently.

  4 citations

• Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

  Mostafa Tanhayi Ahari, Sumanta Bandyopadhyay, Zohar Nussinov, Alexander Seidel, Gerardo Ortiz

  SciPost Phys. 15, 043 (2023) · published 2 August 2023 | Toggle abstract · pdf

  We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor $\nu=2/3$. The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the "DNA" of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-body $M$-clustering property within any given number of Landau levels, that is, wave functions with $M$th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for the $M=3$ case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.

  4 citations

• Soliton gas of the integrable Boussinesq equation and its generalised hydrodynamics

  Thibault Bonnemain, Benjamin Doyon

  SciPost Phys. 18, 075 (2025) · published 28 February 2025 | Toggle abstract · pdf

  Generalised hydrodynamics (GHD) is a recent and powerful framework to study many-body integrable systems, quantum or classical, out of equilibrium. It has been applied to several models, from the delta Bose gas to the XXZ spin chain, the KdV soliton gas and many more. Yet it has only been applied to (1+1)-dimensional systems and generalisation to higher dimensions of space is non-trivial. We study the Boussinesq equation which, while generally considered to be less physically relevant than the KdV equation, is interesting as a stationary reduction of the (boosted) Kadomtsev-Petviashvili (KP) equation, a prototypical and universal example of a nonlinear integrable PDE in (2+1) dimensions. We follow a heuristic approach inspired by the Thermodynamic Bethe Ansatz in order to construct the GHD of the Boussinesq soliton gas. Such approach allows for a statistical mechanics interpretation of the Boussinesq soliton gas that comes naturally with the GHD picture. This is to be seen as a first step in the construction of the KP soliton gas, yielding insight on some classes of solutions from which we may be able to build an intuition on how to devise a more general theory. This also offers another perspective on the construction of anisotropic bidirectional soliton gases previously introduced phenomenologically by Congy et al (2021).

  4 citations

• The propagator of the finite XXZ spin-$\tfrac{1}{2}$ chain

  Gyorgy Z. Fehér, Balázs Pozsgay

  SciPost Phys. 6, 063 (2019) · published 28 May 2019 | Toggle abstract · pdf

  We derive contour integral formulas for the real space propagator of the spin-$\tfrac12$ XXZ chain. The exact results are valid in any finite volume with periodic boundary conditions, and for any value of the anisotropy parameter. The integrals are on fixed contours, that are independent of the Bethe Ansatz solution of the model and the string hypothesis. The propagator is obtained by two different methods. First we compute it through the spectral sum of a deformed model, and as a by-product we also compute the propagator of the XXZ chain perturbed by a Dzyaloshinskii-Moriya interaction term. As a second way we also compute the propagator through a lattice path integral, which is evaluated exactly utilizing the so-called $F$-basis in the mirror (or quantum) channel. The final expressions are similar to the Yudson representation of the infinite volume propagator, with the volume entering as a parameter. As an application of the propagator we compute the Loschmidt amplitude for the quantum quench from a domain wall state.

  4 citations

• Thermodynamic limit of the two-spinon form factors for the zero field XXX chain

  Nikolai Kitanine, Giridhar Kulkarni

  SciPost Phys. 6, 076 (2019) · published 25 June 2019 | Toggle abstract · pdf

  In this paper we propose a method based on the algebraic Bethe ansatz leading to explicit results for the form factors of quantum spin chains in the thermodynamic limit. Starting from the determinant representations we retrieve in particular the formula for the two-spinon form factors for the isotropic XXX Heisenberg chain obtained initially in the framework of the $q$-vertex operator approach.

  4 citations

• Matrix product operator representations for the local conserved quantities of the Heisenberg chain

  Kyoichi Yamada, Kohei Fukai

  SciPost Phys. Core 6, 069 (2023) · published 19 October 2023 | Toggle abstract · pdf

  We present the explicit expressions for the matrix product operator (MPO) representation for the local conserved quantities of the Heisenberg chain. The bond dimension of the MPO grows linearly with the locality of the charges. The MPO has more simple form than the local charges themselves, and their Catalan tree patterns naturally emerge from the matrix products. The MPO representation of local conserved quantities is generalized to the integrable SU(N) invariant spin chain.

  4 citations