arXiv subjects

Marius de Leeuw

Publications and source records attributed to Marius de Leeuw.

At least 19 recordsLinked to original sources

arXiv2026

On deforming and breaking integrability

In this paper we study nearest-neighbour deformations of integrable models. After expanding in the deformation parameter, we identify four possible types of deformations. First there are deformations that simply break or preserve integrability. Then we find two different subtle cases. The first case is where the deformation is only integrable if all orders of the deformation parameter are taken into account. An example of these are the long-range deformations that appear in holographic models. The second case is when the deformation is perturbatively integrable to some order in the deformation parameter but can not be extended to an integrable model. In this paper we work this out for the XXZ spin chain and discuss the level statistics of each of these cases. We find numerical evidence that the onset of chaos occurs differently in each of these models. For the perturbatively integrable models, we find that the deformation strength at which chaos appears demonstrates a volume-scaling intermediate between strong and weak integrability breaking models.

cond-mat.stat-mech↗

arXiv2026

A perturbative approach to the non-relativistic string spectrum

In this letter we use a perturbative approach to find the spectrum of non-relativistic strings in the String Newton-Cartan (SNC) AdS$_5\times$S$^5$ spacetime. We perturb the bosonic sector of the action around a BMN-like folded string solution in light-cone gauge. We find strong evidence that the theory is described by a combination of massive and massless free fields in an anti-de Sitter background by showing that interaction terms up to six scalars vanish after field redefinitions.

hep-th↗

arXiv2026

Constrained integrability and anyonic chains

We review the notion of Yang-Baxter integrability for spin chains that have Hilbert spaces with constraints, such as a Rydberg blockade. We focus on anyonic chains, whose constraints arise from the fusion rules of the fusion categories on which they are based. We discuss the emergence of Temperley-Lieb algebras and present a new result on which types of anyonic chains exhibit them. We then give an overview of known results for integrable anyonic chains and extend them to several fusion categories up to rank $7$. Using a modification of the boost operator formalism, we find several new integrable anyonic chains and discuss some of their properties. These include spin-$\frac32$ models for $\mathfrak{su}(2)_k$ fusion categories, anyonic chains based on the Tambara-Yamagami fusion categories TY$(\mathbb{Z}_n)$, and product fusion categories Fib$\times$Fib and Fib$\times$Ising. We review recent results for spin chains based on the Haagerup-Izumi fusion category HI$(\mathbb{Z}_3)$, and present preliminary numerics for a HI$(\mathbb{Z}_5)$ model.

hep-th↗

arXiv2026

All 4 x 4 solutions of the quantum Yang-Baxter equation

In this paper, we complete the classification of 4 x 4 solutions of the Yang-Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions, then consider regular and non-regular Lax operators and study their relation to the quantum Yang-Baxter equation. We show that for regular solutions there is a correspondence, which is lost in the non-regular case. In particular, we find non-regular Lax operators whose R-matrix from the fundamental commutation relations is regular but does not satisfy the Yang-Baxter equation. These R-matrices satisfy a modified Yang-Baxter equation instead.

math-ph↗

arXiv2026

An integrable deformed Landau-Lifshitz model with particle production?

We discuss the continuum limit of a non-Hermitian deformation of the Heisenberg XXX spin chain. This model appeared in the classification of $4\times4$ solutions of the Yang--Baxter equation and it has the particular feature that the transfer matrix is non-diagonalisable. We show that the model is given by a Drinfeld twist of the XXX spin chain and its continuum limit is a non-unitary deformation of the Landau-Lifshitz model. We compute the tower of conserved charges for this deformed Landau-Lifshitz model and show that they are generated by a boost operator. We furthermore show that it gives a non-vanishing $1\to 2$ S-matrix, where one of the outgoing particles has vanishing energy and momentum, and thus it does not fulfil the usual "no particle production" condition of integrability. We argue that this result is natural when looked from the point of view of the non-diagonalisability of the spin chain.

hep-th↗

arXiv2026

The quantum group structure of long-range integrable deformations

Quantum integrable spin chains are known to possess a large family of long-range deformations generated by the local, boost and bilocal operators. Although these deformations are well-understood on the level of the pairwise commuting charges, the underlying quantum group structures had not yet been recognised. In this paper, we provide a quantum group-theoretical description for the family of long-range deformations of arbitrary homogeneous Yang-Baxter integrable spin chains up to first order in the deformation parameter. In particular, we show that the deformations are obtained via a twist of the algebraic structure of the underlying quantum group. This twisting results in a generally non-associative algebra that has a non-trivial Drinfeld associator. The Drinfeld associator is then shown to encode the information about the long-range interaction terms for the integrable spin chain. Moreover, the deformed quantum group is shown to contain a large perturbatively associative substructure, thus ensuring the perturbative integrability of the long-range model. The deformed quantum group provides explicit expressions for the Lax operators and R-matrices of the long-range deformed models, which manifestly satisfy the RLL relation and the Yang-Baxter equation up to first order in the deformation parameter. In order to derive the results, we introduce algebra elements that we call the algebraic charge densities. As a side result, we provide a conjecture for the explicit expressions of the undeformed charge densities in terms of these algebra elements.

math-ph↗

arXiv2026

Temperley-Lieb integrable models and fusion categories

We show that every fusion category containing a non-invertible, self-dual object $a$ gives rise to an integrable anyonic chain whose Hamiltonian density satisfies the Temperley-Lieb algebra. This spin chain arises by considering the projection onto the identity channel in the fusion process $a\otimes a$. We relate these models to Pasquier's construction of ADE lattice models. We then exploit the underlying Temperley-Lieb structure to discuss the spectrum of these models and argue that these models are gapped when the quantum dimension of $a$ is greater than 2. We show that for fusion categories where the dimension is close to 2, such as the Fib$\times$Fib and Haagerup fusion categories, the finite size effects are large and they can obscure the numerical analysis of the gap.

cond-mat.str-el↗

arXiv2025

Integrable models on Rydberg atom chains

We initiate a systematic study of integrable models for spin chains with constrained Hilbert spaces; we focus on spin-1/2 chains with the Rydberg constraint. We extend earlier results for medium-range spin chains to the constrained Hilbert space, and formulate an integrability condition. This enables us to construct new integrable models with fixed interaction ranges. We classify all time- and space-reflection symmetric integrable Rydberg-constrained Hamiltonians of range 3 and 4. At range 3, we find a single family of integrable Hamiltonians: the so-called RSOS quantum chains, which are related to the well-known RSOS models of Andrews, Baxter, and Forrester. At range 4 we find two families of models, the first of which is the constrained XXZ model. We also find a new family of models depending on a single coupling $z$. We provide evidence of two critical points related to the golden ratio $ϕ$, at $z=ϕ^{-1/2}$ and $z=ϕ^{3/2}$. We also perform a partial classification of integrable Hamiltonians for range 5.

cond-mat.str-el↗

arXiv2025

Integrable Conformal Defects in N=4 SYM

In this paper we classify integrable conformal defects in N=4 SYM theory for which the scalar fields pick up a non-trivial vacuum expectation value. Defects of this form correspond to Dirichlet boundary conditions that have a pole at the defect. These set-ups typically appear on the field theory side of probe brane set-ups in the AdS/CFT correspondence. We show that such defects, for any codimension, are related to fuzzy spheres. We discuss the properties of the different possible fuzzy spheres that can appear and present the corresponding Matrix Product States. We furthermore set-up the quantum field theoretic framework by computing the mass matrix and finding the propagators.

hep-th↗

arXiv2024

Integrable and critical Haagerup spin chains

We construct the first integrable models based on the Haagerup fusion category $H_3$. We introduce a Haagerup version of the anyonic spin chain and use the boost operator formalism to identify two integrable Hamiltonians of PXP type on this chain. The first of these is an analogue of the golden chain; it has a topological symmetry based on $H_3$ and satisfies the Temperley-Lieb algebra with parameter $δ=(3+\sqrt{13})/2$. We prove its integrability using a Lax formalism, and construct the corresponding solution to the Yang--Baxter equation. We present numerical evidence that this model is gapless with a dynamical critical exponent $z\neq 1$. The second integrable model we find breaks the topological symmetry. We present numerical evidence that this model reduces to a CFT in the large volume limit with central charge $c\sim3/2$.

cond-mat.stat-mech↗

arXiv2024

All regular $4 \times 4$ solutions of the Yang-Baxter equation

We complete the classification of $4\times 4$ regular solutions of the Yang-Baxter equation. Apart from previously known models, we find four new models of non-difference form. All the new models give rise to Hamiltonians and transfer matrices that have a non-trivial Jordan block structure. One model corresponds to a non-diagonalisable integrable deformation of the XXX spin chain.

hep-th↗

arXiv2023

Lifting integrable models and long-range interactions

In this paper we discuss a constructive approach to check whether a constant Hamiltonian is Yang-Baxter integrable. We then apply our method to long-range interactions and find the Lax operator and $R$-matrix of the two-loop SU(2) sector in N=4 SYM. We show that all known integrable long-range deformations of the 6-vertex models of this type can be obtained from a Lax operator and an $R$-matrix. Finally we discuss what happens at higher loops and highlight some general structures that these models seem to exhibit.

hep-th↗

arXiv2023

B-type anomaly coefficients for the D3-D5 domain wall

We compute type-B Weyl anomaly coefficients for the domain wall version of N = 4 SYM that is holographically dual to the D3-D5 probe-brane system with flux. Our starting point is the explicit expression for the improved energy momentum tensor of N = 4 SYM. We determine the two-point function of this operator in the presence of the domain wall and extract the anomaly coefficients from the result. In the same process we determine the two-point function of the displacement operator.

hep-th↗

arXiv2023

Flag Integrable Models and Generalized Graded Algebras

We introduce new classes of integrable models that exhibit a structure similar to that of flag vector spaces. We present their Hamiltonians, R-matrices and Bethe-ansatz solutions. These models have a new type of generalized graded algebra symmetry.

hep-th↗

arXiv2023

Hidden quasi-local charges and Gibbs ensemble in a Lindblad system

We consider spin-1/2 chains with external driving that breaks the continuous symmetries of the Hamiltonian. We introduce a family of models described by the Lindblad equation with local jump operators. The models have hidden strong symmetries in the form of quasi-local charges, leading to multiple non-equilibrium steady states. We compute them exactly in the form of Matrix Product Operators, and argue that they are the analogues of quantum many body scars in the Lindbladian setting. We observe that the dynamics leads to the emergence of a Gibbs ensemble constructed from the hidden charges.

cond-mat.stat-mech↗

arXiv2023

A range three elliptic deformation of the Hubbard model

In this paper we present a new integrable deformation of the Hubbard model. Our deformation gives rise to a range 3 interaction term in the Hamiltonian which does not preserve spin or particle number. This is the first non-trivial medium range deformation of the Hubbard model that is integrable. Our model can be mapped to a new integrable nearest-neighbour model via a duality transformation. The resulting nearest-neighbour model also breaks spin conservation. We compute the $R$-matrices for our models, and find that there is a very unusual dependence on the spectral parameters in terms of the elliptic amplitude.

cond-mat.stat-mech↗

arXiv2022

The Bethe ansatz for a new integrable open quantum system

In this paper we apply the nested algebraic Bethe ansatz to compute the eigenvalues and the Bethe equations of the transfer matrix of the new integrable Lindbladian found in [1]. We show that it can be written as an integrable spin chain consisting of two interacting XXZ spin chains. We numerically compute the Liouville gap and its dependence on the parameters in the system such as scaling with the system length and interaction strength.

cond-mat.stat-mech↗

arXiv2022

Spin Chain Overlaps and the Twisted Yangian

Using considerations based on the thermodynamical Bethe ansatz as well representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the $SO(6)$ spin chain and matrix product states built from matrices whose commutators generate an irreducible representation of $\mathfrak{so}(5)$. The latter play the role of boundary states in a domain wall version of ${\cal N}=4$ SYM theory which has non-vanishing, $SO(5)$ symmetric vacuum expectation values on one side of a co-dimension one wall. This theory, which constitutes a defect CFT, is known to be dual to a D3-D7 probe brane system. We likewise show that the same methodology makes it possible to prove an overlap formula, earlier presented without proof, which is of relevance for the similar D3-D5 probe brane system.

hep-th↗