arXiv subjects

Federico Rottoli

Publications and source records attributed to Federico Rottoli.

17 recordsLinked to original sources

arXiv2026

Out-of-equilibrium inhomogeneous XX chains: Exact results and the hydrodynamic limit

We study the out-of-equilibrium dynamics in the XX chain with step-like magnetic field, which maps to an inhomogeneous tight-binding chain after Jordan-Wigner transformation. We obtain exact analytic expressions for the fermionic two-point correlation function after a quantum quench from several initial product states, both homogeneous and inhomogeneous ones. This is achieved by using a combination of Fourier and Laplace transforms, which al low us to map the problem to a standard Riemann-Hilbert problem on the unit circle. For arbitrary positions and times the correlators are not expressed in terms of elementary functions. However, in the hydrodynamic limit $x,y,t\to\infty$ with fixed ratios, we provide explicit formulas that depend only on the effective transmission coefficient across the origin. We benchmark our analytic predictions against exact numerical simulations and find excellent agreement in the hydrodynamic limit, apart from finite-time corrections.

cond-mat.stat-mech↗

arXiv2026

Entanglement dynamics after quenches with inhomogeneous Hamiltonians

We investigate entanglement dynamics in bipartite systems governed by inhomogeneous Hamiltonians of the form $H = H_L + H_R$, where $H_{L/R}$ acts only on the left or right region and is homogeneous within each region. Focusing on the XX chain and the transverse-field Ising chain, we derive analytical formulas for the entanglement entropy between the two regions in the hydrodynamic limit of long times. In this regime, fermions incident on the interface undergo scattering, generating entanglement between reflected and transmitted modes. The resulting quasiparticle picture is controlled by the transmission coefficient, which we obtain analytically by solving the stationary lattice Schr\"odinger equation. Due to the bounded dispersion, strong inhomogeneity suppresses both transport and entanglement growth. We benchmark our analytical predictions against numerical simulations in paradigmatic setups. Finally, we extend the analysis to the interacting XXZ chain using tDMRG. The numerical data show qualitative agreement with the quadratic case: entanglement growth remains suppressed in the strongly inhomogeneous limit. Notably, however, entanglement continues to increase even when transport is suppressed, at least at intermediate times.

cond-mat.stat-mech↗

arXiv2026

Entanglement Hamiltonians in dissipative free fermions and the time-dependent GGE

We investigate the dynamics of Entanglement Hamiltonians (EHs) in dissipative free-fermionic systems using a recent operator-based formulation of the quasiparticle picture. Focusing on gain and loss dissipation, we study the post-quench evolution and derive explicit expressions for the EH at the ballistic scale. In the long-time and weak-dissipation regime, the EH is shown to take the form of a time-dependent Generalized Gibbs Ensemble (t-GGE), with a structure that is universal across different initial states of the quench protocol. Within this framework, the emergence of the t-GGE is fully accounted for by the quasiparticle picture, and we argue that this description remains valid whenever the Lindbladian admits an appropriate coarse-grained representation.

cond-mat.stat-mech↗

arXiv2025

Universality of equilibration dynamics after quantum quenches

We investigate the distribution of the eigenvalues of the reduced density matrix (entanglement spectrum) after a global quantum quench. We show that in an appropriate scaling limit the lower part of the entanglement spectrum exhibits ``universality''. In the scaling limit and at asymptotically long times the distribution of the entanglement spectrum depends on two parameters that can be determined from the R\'enyi entropies. We show that two typical scenarios occur. In the first one, the distribution of the entanglement spectrum levels is similar to the one describing the ground-state entanglement spectrum in Conformal Field Theories. In the second scenario, the lower levels of the entanglement spectrum are highly degenerate and their distribution is given by a series of Dirac deltas. We benchmark our analytical results in free-fermion chains, such as the transverse field Ising chain and the XX chain, in the rule 54 chain, and in Bethe ansatz solvable spin models.

cond-mat.stat-mech↗

arXiv2025

Eigenstate Thermalization Hypothesis (ETH) for off-diagonal matrix elements in integrable spin chains

We investigate off-diagonal matrix elements of local operators in integrable spin chains, focusing on the isotropic spin-$1/2$ Heisenberg chain ($XXX$ chain). We employ state-of-the-art Algebraic Bethe Ansatz results, which allow us to efficiently compute matrix elements of operators with support up to two sites between generic energy eigenstates. We consider both matrix elements between eigenstates that are in the same thermodynamic macrostate, as well as eigenstates that belong to different macrostates. In the former case, focusing on thermal states we numerically show that matrix elements are compatible with the exponential decay as $\exp(-L |{M}^{\scriptscriptstyle{\mathcal{O}}}_{ij}|)$. The probability distribution functions of ${M}_{ij}^{\scriptscriptstyle{\mathcal{O}}}$ depend on the observable and on the macrostate, and are well described by Gumbel distributions. On the other hand, matrix elements between eigenstates in different macrostates decay faster as $\exp(-|{M'}_{ij}^{\scriptscriptstyle{\mathcal{O}}}|L^2)$, with ${M'}_{ij}^{\scriptscriptstyle \mathcal{O}}$, again, compatible with a Gumbel distribution.

cond-mat.stat-mech↗

arXiv2025

Time Evolution of the Symmetry Resolved Entanglement Entropy after a Mass Quench

In this paper we investigate the properties of the symmetry resolved entanglement entropy after a mass quench in the Ising field theory. Since the theory is free and the post-quench state known explicitly, the one-point function of the relevant (composite) branch point twist field can be computed using form factor techniques, similar to previous work on the branch point twist field and the magnetisation, respectively. We find that the symmetry resolved entropy grows linearly in time at the same rate as the total entropy, and that there are sub-leading oscillatory corrections. This result provides the first explicit computation of the out-of-equilibrium dynamics of the symmetry resolved entropy employing twist fields in quantum field theory and is consistent with existing results based on the quasiparticle picture.

hep-th↗

arXiv2024

Entanglement Hamiltonians and the quasiparticle picture

The entanglement Hamiltonian (EH) provides the most comprehensive characterization of bipartite entanglement in many-body quantum systems. Ground states of local Hamiltonians inherit this locality, resulting in EHs that are dominated by local, few-body terms. Unfortunately, in non-equilibrium situations, analytic results are rare and largely confined to continuous field theories, which fail to accurately describe microscopic models. To address this gap, we present an analytic result for the EH following a quantum quench in non-interacting fermionic models, valid in the ballistic scaling regime. The derivation adapts the celebrated quasiparticle picture to operators, providing detailed insights into its physical properties. The resulting analytic formula serves as a foundation for engineering EHs in quantum optics experiments.

quant-ph↗

arXiv2024

Entanglement Hamiltonian in the non-Hermitian SSH model

Entanglement Hamiltonians provide the most comprehensive characterisation of entanglement in extended quantum systems. A key result in unitary quantum field theories is the Bisognano-Wichmann theorem, which establishes the locality of the entanglement Hamiltonian. In this work, our focus is on the non-Hermitian Su-Schrieffer-Heeger (SSH) chain. We study the entanglement Hamiltonian both in a gapped phase and at criticality. In the gapped phase we find that the lattice entanglement Hamiltonian is compatible with a lattice Bisognano-Wichmann result, with an entanglement temperature linear in the lattice index. At the critical point, we identify a new imaginary chemical potential term absent in unitary models. This operator is responsible for the negative entanglement entropy observed in the non-Hermitian SSH chain at criticality.

quant-ph↗

arXiv2023

Entanglement entropy along a massless renormalisation flow: the tricritical to critical Ising crossover

We study the R\'enyi entanglement entropies along the massless renormalisation group flow that connects the tricritical and critical Ising field theories. Similarly to the massive integrable field theories, we derive a set of bootstrap equations, from which we can analytically calculate the twist field form factors in a recursive way. Additionally, we also obtain them as a non-trivial roaming limit of the sinh-Gordon theory. Then the R\'enyi entanglement entropies are obtained as expansions in terms of the form factors of these branch point twist fields. We find that the form factor expansion of the entanglement entropy along the flow organises in two different kind of terms. Those that couple particles with the same chirality, and reproduce the entropy of the infrared Ising theory, and those that couple particles with different chirality, which provide the ultraviolet contributions. The massless flow under study possesses a global $\mathbb{Z}_2$ spin-flip symmetry. We further consider the composite twist fields associated to this group, which enter in the study of the symmetry resolution of the entanglement. We derive analytical expressions for their form factors both from the bootstrap equations and from the roaming limit of the sinh-Gordon theory.

hep-th↗

arXiv2023

Finite temperature negativity Hamiltonians of the massless Dirac fermion

The negativity Hamiltonian, defined as the logarithm of a partially transposed density matrix, provides an operatorial characterisation of mixed-state entanglement. However, so far, it has only been studied for the mixed-state density matrices corresponding to subsystems of globally pure states. Here, we consider as a genuine example of a mixed state the one-dimensional massless Dirac fermions in a system at finite temperature and size. As subsystems, we consider an arbitrary set of disjoint intervals. The structure of the corresponding negativity Hamiltonian resembles the one for the entanglement Hamiltonian in the same geometry: in addition to a local term proportional to the stress-energy tensor, each point is non-locally coupled to an infinite but discrete set of other points. However, when the lengths of the transposed and non-transposed intervals coincide, the structure remarkably simplifies and we retrieve the mild non-locality of the ground state negativity Hamiltonian. We also conjecture an exact expression for the negativity Hamiltonian associated to the twisted partial transpose, which is a Hermitian fermionic matrix. We finally obtain the continuum limit of both the local and bi-local operators from exact numerical computations in free-fermionic chains.

hep-th↗

arXiv2023

Entanglement and negativity Hamiltonians for the massless Dirac field on the half line

We study the ground-state entanglement Hamiltonian of several disjoint intervals for the massless Dirac fermion on the half-line. Its structure consists of a local part and a bi-local term that couples each point to another one in each other interval. The bi-local operator can be either diagonal or mixed in the fermionic chiralities and it is sensitive to the boundary conditions. The knowledge of such entanglement Hamiltonian is the starting point to evaluate the negativity Hamiltonian, i.e. the logarithm of the partially transposed reduced density matrix, which is an operatorial characterisation of entanglement of subsystems in a mixed states. We find that the negativity Hamiltonian inherits the structure of the corresponding entanglement Hamiltonian. We finally show how the continuum expressions for both these operators can be recovered from exact numerical computations in free-fermion chains.

cond-mat.stat-mech↗

arXiv2023

Domain wall melting across a defect

We study the melting of a domain wall in a free-fermionic chain with a localised impurity. We find that the defect enhances quantum correlations in such a way that even the smallest scatterer leads to a linear growth of the entanglement entropy contrasting the logarithmic behaviour in the clean system. Exploiting the hydrodynamic approach and the quasiparticle picture, we provide exact predictions for the evolution of the entanglement entropy for arbitrary bipartitions. In particular, the steady production of pairs at the defect gives rise to non-local correlations among distant points. We also characterise the subleading logarithmic corrections, highlighting some universal features.

cond-mat.stat-mech↗

arXiv2022

Entanglement Hamiltonian during a domain wall melting in the free Fermi chain

We study the unitary time evolution of the entanglement Hamiltonian of a free Fermi lattice gas in one dimension initially prepared in a domain wall configuration. To this aim, we exploit the recent development of quantum fluctuating hydrodynamics. Our findings for the entanglement Hamiltonian are based on the effective field theory description of the domain wall melting and are expected to exactly describe the Euler scaling limit of the lattice gas. However, such field theoretical results can be recovered from high-precision numerical lattice calculations only when summing appropriately over all the hoppings up to distant sites.

cond-mat.stat-mech↗

arXiv2022

Gauge fixing and metric independence in topological quantum theories

We consider topological gauge theories in three dimensions which are defined by metric independent lagrangians. It has been claimed that the functional integration necessarily depends nontrivially on the gauge-fixing metric. We demonstrate that the partition function and the mean values of the gauge invariant observables do not really depend on the gauge-fixing metric.

hep-th↗

arXiv2021

Coupling Yang-Mills with Causal Dynamical Triangulations

We discuss the algorithmic problem of minimal coupling gauge fields of the Yang-Mills type to Quantum Gravity in the approach known as Causal Dynamical Triangulations (CDT) as a step towards studying, ultimately, systems of gravity coupled with bosonic and fermionic matter. We first describe the algorithm for general dimensions and gauge groups and then focus on the results obtained from simulations of 2d CDT coupled to gauge fields with U{(1)} and SU{(2)} gauge groups, where we studied both observables related to gravity and gauge fields, and compared them with analogous simulations in the static flat case.

hep-lat↗

arXiv2020

Compact Gauge Fields on Causal Dynamical Triangulations: a 2D case study

We discuss the discretization of Yang-Mills theories on Dynamical Triangulations in the compact formulation, with gauge fields living on the links of the dual graph associated with the triangulation, and the numerical investigation of the minimally coupled system by Monte Carlo simulations. We provide, in particular, an explicit construction and implementation of the Markov chain moves for 2D Causal Dynamical Triangulations coupled to either $U(1)$ or $SU(2)$ gauge fields; the results of exploratory numerical simulations on a toroidal geometry are also presented for both cases. We study the critical behavior of gravity related observables, determining the associated critical indices, which turn out to be independent of the bare gauge coupling: we obtain in particular $ν= 0.496(7)$ for the critical index regulating the divergence of the correlation length of the volume profiles. Gauge observables are also investigated, including holonomies (torelons) and, for the $U(1)$ gauge theory, the winding number and the topological susceptibility. An interesting result is that the critical slowing down of the topological charge, which affects various lattice field theories in the continuum limit, seems to be strongly suppressed (i.e., by orders of magnitude) by the presence of a locally variable geometry: that may suggest possible ways for improvement also in other contexts.

hep-lat↗

arXiv2020

Perturbative BF theory

We consider a superrenomalizable gauge theory of topological type, in which the structure group is equal to the inhomogeneous group ISU(2). The generating functional of the correlation functions of the gauge fields is derived and its connection with the generating functional of the Chern-Simons theory is discussed. The complete renomalization of this model defined in R^3 is presented. The structure of the ISU(2) conjugacy classes is determined. Gauge invariant observables are defined by means of appropriately normalized traces of ISU(2) holonomies associated with oriented, framed and coloured knots. The perturbative evaluation of the Wilson lines expectation values is investigated and the up-to-third-order contributions to the perturbative expansion of the observables, which correspond to knot invariants, are produced. The general dependence of the knot observables on the framing is worked out.

hep-th↗