arXiv subjects

Eric Vernier

Publications and source records attributed to Eric Vernier.

At least 19 recordsLinked to original sources

arXiv2026

Correlation and entanglement dynamics of free fermions in disguise

We study the nonequilibrium dynamics following a quantum quench in spin chains that can be solved via a mapping to free fermions in disguise. These models feature an exponential degeneracy of all energy eigenvalues, raising the question of the validity of the established framework describing the properties of integrable systems out of equilibrium. We present two main results. First, we develop an analytic method to compute the quasi-momentum distribution function characterizing the generalized Gibbs ensemble, and derive an analytic formula to compute the corresponding expectation values for special observables. Second, we adapt the standard formula for the entanglement growth based on the quasi-particle picture, discussing how our constructions do not explicitly make use of the zero-energy auxiliary free fermions responsible of the exponential degeneracies. We test our theoretical predictions against numerical tensor-network computations for different initial states and Hamiltonian parameters. For the local observables, we find excellent agreement. For the entanglement dynamics, we find small deviations suggesting that the standard quasi-particle picture is only approximately correct for the initial state considered. Our results represent a first step towards the extension of the established framework of integrable systems out of equilibrium to models hosting free fermions in disguise.

cond-mat.stat-mech↗

arXiv2026

Lattice non-invertible symmetry from non-commuting transfer matrices

Conventional quantum integrability is encoded in a commuting algebra of transfer matrices. By contrast, several models possess additional non-commuting conserved charges with important physical consequences, yet the nature of the corresponding symmetry has remained elusive. Focusing on the XXZ spin chain at roots of unity, we show that the non-Abelian analogue of the commuting transfer-matrix algebra is governed by quadratic relations following from a new class of unbalanced Yang--Baxter/RLL relations. This quadratic algebra is shown to encode precisely the Onsager algebra, for which we construct explicit matrix-product representations of both its generators and its duality defect line. The latter obeys $\mathbb{Z}_N$ Tambara--Yamagami fusion rules, thereby providing a lattice realization of the topological defect lines of the compactified boson conformal field theory. Our results identify non-Abelian transfer-matrix algebras as a microscopic origin for Onsager symmetry and dualities in lattice models.

cond-mat.stat-mech↗

arXiv2025

Strong zero modes in integrable spin-S chains

We derive exact strong zero mode (ESZM) operators for integrable spin-S chains with open boundary conditions and a boundary field. Their locality properties are generally weaker than in the previously known cases, but they still imply infinite coherence times in the vicinity of the edges. We explain how such integrable chains possess multiple ground states describing a first-order quantum phase transition, and that the odd number of such states for integer S makes the weaker locality properties necessary. We make contact with more traditional approaches by showing how the ESZM for S=1/2 acts on energy eigenstates given by solutions of the Bethe equations.

cond-mat.stat-mech↗

arXiv2025

XYZ integrability the easy way

Sutherland showed that the XYZ quantum spin-chain Hamiltonian commutes with the eight-vertex model transfer matrix, so that Baxter's subsequent tour de force proves the integrability of both. The proof requires parametrising the Boltzmann weights using elliptic theta functions and showing they satisfy the Yang-Baxter equation. We here give a simpler derivation of the integrability of the XYZ chain by explicitly constructing an extensive sequence of conserved charges from a matrix-product operator. We show that they commute with the XYZ Hamiltonian with periodic boundary conditions or an arbitrary boundary magnetic field. A straightforward generalisation yields impurity interactions that preserve the integrability. Placing such an impurity at the edge gives an integrable generalisation of the Kondo problem with a gapped bulk. We make contact with the traditional approach by relating our matrix-product operator to products of the eight-vertex model transfer matrix.

cond-mat.stat-mech↗

arXiv2025

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

Construction and simulability of quantum circuits with free fermions in disguise

We provide a systematic construction for local quantum circuits hosting free fermions in disguise, both with staircase and brickwork architectures. Similar to the original Hamiltonian model introduced by Fendley, these circuits are defined by the fact that the Floquet operator corresponding to a single time step can not be diagonalized by means of any Jordan-Wigner transformation, but still displays a free-fermionic spectrum. Our construction makes use of suitable non-local transfer matrices commuting with the Floquet operator, allowing us to establish the free fermionic spectrum. We also study the dynamics of these circuits after they are initialized in arbitrary product states, proving that the evolution of certain local observables can be simulated efficiently on classical computers. Our work proves recent conjectures in the literature and raises new questions on the classical simulability of free fermions in disguise.

quant-ph↗

arXiv2025

The Hilbert-space structure of free fermions in disguise

Free fermions in disguise (FFD) Hamiltonians describe spin chains which can be mapped to free fermions, but not via a Jordan-Wigner transformation. Although the mapping gives access to the full Hamiltonian spectrum, the computation of spin correlation functions is generally hard. Indeed, the dictionary between states in the spin and free-fermion Hilbert spaces is highly non-trivial, due to the non-linear and non-local nature of the mapping, as well as the exponential degeneracy of the Hamiltonian eigenspaces. In this work, we provide a series of results characterizing the Hilbert space associated to FFD Hamiltonians. We focus on the original model introduced by Paul Fendley and show that the corresponding Hilbert space admits the exact factorization $\mathcal{H}=\mathcal{H}_F\otimes \mathcal{H}_D$, where $\mathcal{H}_F$ hosts the fermionic operators, while $\mathcal{H}_D$ accounts for the exponential degeneracy of the energy eigenspaces. By constructing a family of spin operators generating the operator algebra supported on $\mathcal{H}_D$, we further show that $\mathcal{H}_D=\mathcal{H}_{F'}\otimes \mathcal{H}_{\widetilde{D}}$, where $\mathcal{H}_{F'}$ hosts ancillary free fermions in disguise, while $\mathcal{H}_{\widetilde{D}}$ is generated by the common eigenstates of an extensive set of commuting Pauli strings. Our construction allows us to fully resolve the exponential degeneracy of all Hamiltonian eigenspaces and is expected to have implications for the computation of spin correlation functions, both in and out of equilibrium.

cond-mat.stat-mech↗

arXiv2024

Dynamical symmetry restoration in the Heisenberg spin chain

The entanglement asymmetry is an observable independent tool to investigate the relaxation of quantum many body systems through the restoration of an initially broken symmetry of the dynamics. In this paper we use this to investigate the effects of interactions on quantum relaxation in a paradigmatic integrable model. Specifically, we study the dynamical restoration of the $U(1)$ symmetry corresponding to rotations about the $z$-axis in the XXZ model quenched from a tilted ferromagnetic state. We find two distinct patterns of behaviour depending upon the interaction regime of the model. In the gapless regime, at roots of unity, we find that the symmetry restoration is predominantly carried out by bound states of spinons of maximal length. The velocity of these bound states is suppressed as the anisotropy is decreased towards the isotropic point leading to slower symmetry restoration. By varying the initial tilt angle, one sees that symmetry restoration is slower for an initally smaller tilt angle, signifying the presence of the quantum Mpemba effect. In the gapped regime however, spin transport for non maximally tilted states, is dominated by smaller bound states with longer bound states becoming frozen. This leads to a much longer time scales for restoration compared to the gapless regime. In addition, the quantum Mpemba effect is absent in the gapped regime.

cond-mat.stat-mech↗

arXiv2024

Generalized hydrodynamics of integrable quantum circuits

Quantum circuits make it possible to simulate the continuous-time dynamics of a many-body Hamiltonian by implementing discrete Trotter steps of duration $\tau$. However, when $\tau$ is sufficiently large, the discrete dynamics exhibit qualitative differences compared to the original evolution, potentially displaying novel features and many-body effects. We study an interesting example of this phenomenon, by considering the integrable Trotterization of a prototypical integrable model, the XXZ Heisenberg spin chain. We focus on the well-known bipartition protocol, where two halves of a large system are prepared in different macrostates and suddenly joined together, yielding non-trivial nonequilibrium dynamics. Building upon recent results and adapting the generalized hydrodynamics (GHD) of integrable models, we develop an exact large-scale description of an explicit one-dimensional quantum-circuit setting, where the input left and right qubits are initialized in two distinct product states. We explore the phenomenology predicted by the GHD equations, which depend on the Trotter step and the gate parameters. In some phases of the parameter space, we show that the quantum-circuit large-scale dynamics is qualitatively different compared to the continuous-time evolution. In particular, we find that a single microscopic defect at the junction, such as the addition of a single qubit, may change the nonequilibrium macrostate appearing at late time.

cond-mat.stat-mech↗

arXiv2024

Integrability of Goldilocks quantum cellular automata

Goldilocks quantum cellular automata (QCA) have been simulated on quantum hardware and produce emergent small-world correlation networks. In Goldilocks QCA, a single-qubit unitary is applied to each qubit in a one-dimensional chain subject to a balance constraint: a qubit is updated if its neighbors are in different computational-basis states. We prove that a subclass of Goldilocks QCA, including the QCA implemented experimentally, map to free fermions and therefore can be simulated classically. We support this claim with two proofs, one involving a Jordan-Wigner transformation and one mapping the integrable six-vertex model to QCA. We compute local conserved quantities of these QCA and predict experimentally measurable expectation values. These calculations can be applied to test large digital quantum computers. In contrast, typical Goldilocks QCA have equilibration properties and quasienergy-level statistics that suggest nonintegrability. Still, each of the latter QCA conserves one quantity useful for error mitigation. Our work yields a parametric quantum circuit with tunable integrability properties useful for testing quantum hardware.

quant-ph↗

arXiv2024

Strong zero modes in integrable quantum circuits

It is a classic result that certain interacting integrable spin chains host robust edge modes known as strong zero modes (SZMs). In this work, we extend this result to the Floquet setting of local quantum circuits, focusing on a prototypical model providing an integrable Trotterization for the evolution of the XXZ Heisenberg spin chain. By exploiting the algebraic structures of integrability, we show that an exact SZM operator can be constructed for these integrable quantum circuits in certain regions of parameter space. Our construction, which recovers a well-known result by Paul Fendley in the continuous-time limit, relies on a set of commuting transfer matrices known from integrability, and allows us to easily prove important properties of the SZM, including normalizabilty. Our approach is different from previous methods and could be of independent interest even in the Hamiltonian setting. Our predictions, which are corroborated by numerical simulations of infinite-temperature autocorrelation functions, are potentially interesting for implementations of the XXZ quantum circuit on available quantum platforms.

cond-mat.stat-mech↗

arXiv2023

On correlation functions in models related to the Temperley-Lieb algebra

We deal with quantum spin chains whose Hamiltonian arises from a representation of the Temperley-Lieb algebra, and we consider the mean values of those local operators which are generated by the Temperley-Lieb algebra. We present two key conjectures which relate these mean values to existing literature about factorized correlation functions in the XXZ spin chain. The first conjecture states that the finite volume mean values of the current and generalized current operators are given by the same simple formulas as in the case of the XXZ chain. The second conjecture states that the mean values of products of Temperley-Lieb generators can be factorized: they can expressed as sums of products of current mean values, such that the coefficients in the factorization depend neither on the eigenstate in question, nor on the selected representation of the algebra. The coefficients can be extracted from existing work on factorized correlation functions in the XXZ model. The conjectures should hold for all eigenstates that are non-degenerate with respect to the local charges of the models. We consider concrete representations, where we check the conjectures: the so-called golden chain, the $Q$-state Potts model, and the trace representation. We also explain how to derive the generalized current operators from concrete expressions for the local charges.

nlin.SI↗

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

Integrable Quantum Circuits from the Star-Triangle Relation

The star-triangle relation plays an important role in the realm of exactly solvable models, offering exact results for classical two-dimensional statistical mechanical models. In this article, we construct integrable quantum circuits using the star-triangle relation. Our construction relies on families of mutually commuting two-parameter transfer matrices for statistical mechanical models solved by the star-triangle relation, and differs from previously known constructions based on Yang-Baxter integrable vertex models. At special value of the spectral parameter, the transfer matrices are mapped into integrable quantum circuits, for which infinite families of local conserved charges can be derived. We demonstrate the construction by giving two examples of circuits acting on a chain of $Q-$state qudits: $Q$-state Potts circuits, whose integrability has been conjectured recently by Lotkov et al., and $\mathbb{Z}_Q$ circuits, which are novel to our knowledge. In the first example, we present for $Q=3$ a connection to the Zamolodchikov-Fateev 19-vertex model.

cond-mat.stat-mech↗

arXiv2023

Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study

We consider the quantum quench in the XX spin chain starting from a tilted N\'eel state which explicitly breaks the $U(1)$ symmetry of the post-quench Hamiltonian. Very surprisingly, the $U(1)$ symmetry is not restored at large time because of the activation of a non-Abelian set of charges which all break it. The breaking of the symmetry can be effectively and quantitatively characterised by the recently introduced entanglement asymmetry. By a combination of exact calculations and quasi-particle picture arguments, we are able to exactly describe the behaviour of the asymmetry at any time after the quench. Furthermore we show that the stationary behaviour is completely captured by a non-Abelian generalised Gibbs ensemble. While our computations have been performed for a non-interacting spin chain, we expect similar results to hold for the integrable interacting case as well because of the presence of non-Abelian charges also in that case.

cond-mat.stat-mech↗

arXiv2022

Integrable Digital Quantum Simulation: Generalized Gibbs Ensembles and Trotter Transitions

The Trotter-Suzuki decomposition is a promising avenue for digital quantum simulation (DQS), approximating continuous-time dynamics by discrete Trotter steps of duration $\tau$. Recent work suggested that DQS is typically characterized by a sharp Trotter transition: when $\tau$ is increased beyond a threshold value, approximation errors become uncontrolled at large times due to the onset of quantum chaos. Here we contrast this picture with the case of \emph{integrable} DQS. We focus on a simple quench from a spin-wave state in the prototypical XXZ Heisenberg spin chain, and study its integrable Trotterized evolution as a function of $\tau$. Due to its exact local conservation laws, the system does not heat up to infinite temperature and the late-time properties of the dynamics are captured by a discrete Generalized Gibbs Ensemble (dGGE). By means of exact calculations we find that, for small $\tau$, the dGGE depends analytically on the Trotter step, implying that discretization errors remain bounded even at infinite times. Conversely, the dGGE changes abruptly at a threshold value $\tau_{\rm th}$, signaling a novel type of Trotter transition. We show that the latter can be detected locally, as it is associated with the appearance of a non-zero staggered magnetization with a subtle dependence on $\tau$. We highlight the differences between continuous and discrete GGEs, suggesting the latter as novel interesting nonequilibrium states exclusive to digital platforms.

quant-ph↗

arXiv2022

Symmetry-breaking-induced loss of ergodicity in maps of the simplex with inversion symmetry

Motivated by proving the loss of ergodicity in expanding systems of piecewise affine coupled maps with arbitrary number of units, all-to-all coupling and inversion symmetry, we provide ad-hoc substitutes - namely inversion-symmetric maps of the simplex with arbitrary number of vertices - that exhibit several asymmetric absolutely continuous invariant measures when their expanding rate is sufficiently small. In a preliminary study, we consider arbitrary maps of the multi-dimensional torus with permutation symmetries. Using these symmetries, we show that the existence of multiple invariant sets of such maps can be obtained from their analogues in some reduced maps of a smaller phase space. For the coupled maps, this reduction yields inversion-symmetric maps of the simplex. The subsequent analysis of these reduced maps show that their systematic dynamics is intractable because some essential features vary with the number of units; hence the substitutes which nonetheless capture the coupled maps common characteristics. The construction itself is based on a simple mechanism for the generation of asymmetric invariant union of polytopes, whose basic principles should extend to a broad range of maps with permutation and inversion symmetries.

math.DS↗

arXiv2022

Thermodynamic symmetry resolved entanglement entropies in integrable systems

We develop a general approach to compute the symmetry-resolved R\'enyi and von Neumann entanglement entropies (SREE) of thermodynamic macrostates in interacting integrable systems. Our method is based on a combination of the thermodynamic Bethe ansatz and the G\"artner-Ellis theorem from large deviation theory. We derive an explicit simple formula for the von Neumann SREE, which we show to coincide with the thermodynamic Yang-Yang entropy of an effective macrostate determined by the charge sector. Focusing on the XXZ Heisenberg spin chain, we test our result against iTEBD calculations for thermal states, finding good agreement. As an application, we provide analytic predictions for the asymptotic value of the SREE following a quantum quench.

cond-mat.stat-mech↗