arXiv subjects

Michele Mazzoni

Publications and source records attributed to Michele Mazzoni.

15 recordsLinked to original sources

arXiv2026

Entanglement Asymmetry in Random Quantum Automata

We investigate the subsystem entanglement asymmetry in random quantum automaton ensembles, which are generated by permuting the basis states in the Hilbert space and applying global phase shifts. We compute the ensemble average of the $U(1)$ subsystem asymmetry in different connectivity geometries, showing that the late-time limit of the ensemble associated to a 2-local circuit geometry coincides with the all-to-all ensemble average. By focusing on different subsystem sizes, we demonstrate that, similarly to Haar-random circuits, the system locally symmetrizes. However, in sharp contrast to the Haar-random setting, the scale at which symmetrization happens depends on the initial state, a phenomenon we associate with the interplay of conservation of the participation entropy and the uniform exploration of charge sectors. Additionally, we connect the growth of the subsystem asymmetry to the subsystem coherence and show that their growth is characterized by the same symmetrization scale.

cond-mat.stat-mech↗

arXiv2026

Generalized hydrodynamics of free fermions under extensive-charge monitoring

We study transport dynamics of free fermions subject to the external monitoring of a conserved charge over an extensive region. Focusing on bipartition protocols, we consider monitoring the total particle number over half of the system, and study the profiles of local charges and currents at hydrodynamic scales. While the Lindbladian describing the averaged dynamics is non-local, we show that the profiles can be understood in terms of localized impurities. We present a general framework based on the generalized hydrodynamics (GHD) picture, allowing for a hybrid numerical-analytic solution of the quench dynamics at hydrodynamic scales. We illustrate our approach for domain-wall initial states, showing that monitoring leads to discontinuities in the profiles that become more pronounced as the rate increases and that lead to the absence of transport in the Zeno limit of infinite monitoring rates. Our GHD framework could be naturally extended to interacting systems, paving the way for a systematic study of transport of integrable models subject to extensive-charge measurements.

cond-mat.stat-mech↗

arXiv2026

An asymmetry lower bound on fermionic non-Gaussianity

Fermionic Gaussian states are a fundamental tool in many-body physics, faithfully representing non-interacting quantum systems and allowing for efficient numerical simulations. Given a many-body wave function, it is therefore interesting to ask how much it differs from that of a Gaussian state, as quantified by the notion of non-Gaussianity. In this work, we relate measures of non-Gaussianity with the Shannon entropy of the particle-number distribution, coinciding with the particle-number asymmetry for pure states. We derive a lower bound on the relative entropy of non-Gaussianity in terms of the exponential of the Shannon entropy, and study numerically its tightness for large system sizes. Our bound is non-trivial for large values of the asymmetry and relies on the concentration of the particle-number distribution of (mixed) fermionic Gaussian states. Since the Shannon entropy of the particle-number distribution is often efficient to compute or experimentally measure, our results can be viewed as a practical way to lower bound non-Gaussianity, highlighting a non-trivial interplay with particle-number asymmetry.

quant-ph↗

arXiv2025

Breaking global symmetries with locality-preserving operations

In the general framework of quantum resource theories, one typically only distinguishes between operations that can or cannot generate the resource of interest. In many-body settings, one can further characterize quantum operations based on underlying geometrical constraints, and a natural question is to understand the power of resource-generating operations that preserve locality. In this work, we address this question within the resource theory of asymmetry, which has recently found applications in the study of many-body symmetry-breaking and symmetry-restoration phenomena. We consider symmetries corresponding to both abelian and non-abelian compact groups with a homogeneous action on the space of $N$ qubits, focusing on the prototypical examples of $U(1)$ and $SU(2)$. We study the so-called $G$-asymmetry $\Delta S^{G}_N$, and present two main results. First, we derive a general bound on the asymmetry that can be generated by locality-preserving operations acting on product states. We prove that, in any spatial dimension, $\Delta S^{G}_N\leq (1/2)\Delta S^{G, \rm max}_N[1+o(1)]$, where $\Delta S^{G, \rm max}_N$ is the maximum value of the $G$-asymmetry in the full many-body Hilbert space. Second, we show that locality-preserving operations can generate maximal asymmetry, $\Delta S^{G}_N\sim\Delta S^{G, \rm max}_N$, when applied to symmetric states featuring long-range entanglement. Our results provide a unified perspective on recent studies of asymmetry in many-body physics, highlighting a non-trivial interplay between asymmetry, locality, and entanglement.

quant-ph↗

arXiv2025

Entanglement dynamics and Page curves in random permutation circuits

The characterization of ensembles of many-qubit random states and their realization via quantum circuits are crucial tasks in quantum-information theory. In this work, we study the ensembles generated by quantum circuits that randomly permute the computational basis, thus acting classically on the corresponding states. We focus on the averaged entanglement and present two main results. First, we derive generically tight upper bounds on the entanglement that can be generated by applying permutation circuits to arbitrary initial states. We show that the late-time ``entanglement Page curves'' are bounded in terms of the initial state participation entropies and its overlap with the ``maximally antilocalized'' state. Second, comparing the averaged R\'enyi-$2$ entropies generated by $(i)$ an infinitely deep random circuit of two-qubit gates and $(ii)$ global random permutations, we show that the two quantities are different for finite $N$ but the corresponding Page curves coincide in the thermodynamic limit. We also discuss how these conclusions are modified by additional random phases or considering circuits of $k$-local gates with $k\geq 3$. Our results are exact and highlight the implications of classical features on entanglement generation in many-body systems.

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 content of kink excitations

Quantum one-dimensional systems in their ordered phase admit kinks as elementary excitations above their symmetry-broken vacua. While the scattering properties of the kinks resemble those of quasiparticles, they have distinct locality features that are manifest in their entanglement content. In this work, we study the entanglement entropy of kink excitations. We first present detailed calculations for specific states of a spin-1/2 chain to highlight the salient features of these excitations. Second, we provide a field-theoretic framework based on the algebraic relations between the twist fields and the semilocal fields associated with the excitations, and we compute the R\'enyi entropies in this framework. We obtain universal predictions for the entropy difference between the excited states with a finite number of kinks and the symmetry-broken ground states, which do not depend on the microscopic details of the model in the limit of large regions. Finally, we discuss some consequences of the Kramers-Wannier duality, which relates the ordered and disordered phases of the Ising model, and we explain why, counterintuitively, no explicit relations between those phases are found at the level of entanglement.

cond-mat.str-el↗

arXiv2024

Generalised Hydrodynamics of $\mathrm{T\bar{T}}$-Deformed Integrable Quantum Field Theories

In this paper we evaluate the averages of conserved densities and currents associated to charges of generic spin in (1+1)-dimensional massive integrable Quantum Field Theories perturbed by the irrelevant $\mathrm{T\bar{T}}$ operator. By making use of the Thermodynamic Bethe Ansatz approach and of the theory of Generalised Hydrodynamics, we study the non-equilibrium steady state averages of conserved densities and currents in a partitioning protocol. We show that in particular limits, averages can be evaluated exactly in terms of quantities known from the unperturbed theory. In the massless limit we recover known results for the energy and momentum currents and generalise those to any higher spin conserved quantities. We extend some of our results to perturbations of the generalised $\mathrm{T\bar{T}}$ type. For the massive free fermion theory, we find an analytic expression for the effective inverse temperature after at $\mathrm{T\bar{T}}$ perturbation in terms of the bare inverse temperature by making use of Lambert's $W$ function.

hep-th↗

arXiv2024

Expectation Values of Conserved Charges in Integrable Quantum Field Theories out of Thermal Equilibrium

In this work we present a computation of the averages of conserved charge densities and currents of (1+1)-dimensional Integrable Quantum Field Theories in Generalised Gibbs Ensembles. Our approach is based on the quasi-particle description provided by the Thermodynamic Bethe Ansatz combined with the principles of Generalised Hydrodynamics, and we focus on Non-Equilibrium Steady State averages. When considering the ultraviolet (i.e. high temperature) limit of such averages, we recover the famous result by Bernard and Doyon (2012) for the energy current and density in Conformal Field Theories, and we extend it to conserved quantities with spin $s > 1$. We show that their averages are proportional to $T_L^{s+1}\pm T_R^{s+1}$, with $T_L$, $T_R$ the temperatures of two asymptotic thermal reservoirs. The same power law is obtained when considering some non-thermal generalised Gibbs states. In Conformal Field Theory, the power law is a consequence of the transformation properties of conserved charge operators, while the proportionality coefficient depends on the spin of the operator and on the central charge of the theory. We present an exact analytic expression for this coefficient in the case of a massive free fermion. At equilibrium, proportionality of spin-$s$ density averages to $T^{s+1}$ can be thought of as a generalisation of Stefan-Boltzmann's law, which states that the energy per unit surface area radiated by a black body scales as $T^4$.

hep-th↗

arXiv2023

Entanglement asymmetry in the ordered phase of many-body systems: the Ising Field Theory

Global symmetries of quantum many-body systems can be spontaneously broken. Whenever this mechanism happens, the ground state is degenerate and one encounters an ordered phase. In this study, our objective is to investigate this phenomenon by examining the entanglement asymmetry of a specific region. This quantity, which has recently been introduced in the context of $U(1)$ symmetry breaking, is extended to encompass arbitrary finite groups $G$. We also establish a field theoretic framework in the replica theory using twist operators. We explicitly demonstrate our construction in the ordered phase of the Ising field theory in 1+1 dimensions, where a $\mathbb{Z}_2$ symmetry is spontaneously broken, and we employ a form factor bootstrap approach to characterise a family of composite twist fields. Analytical predictions are provided for the entanglement asymmetry of an interval in the Ising model as the length of the interval becomes large. We also propose a general conjecture relating the entanglement asymmetry and the number of degenerate vacua, expected to be valid for a large class of states, and we prove it explicitly in some cases.

cond-mat.stat-mech↗

arXiv2023

Symmetry Resolved Entanglement of Excited States in Quantum Field Theory III: Bosonic and Fermionic Negativity

In two recent works, we studied the symmetry resolved Rényi entropies of quasi-particle excited states in quantum field theory. We found that the entropies display many model-independent features which we discussed and analytically characterised. In this paper we extend this line of investigation by providing analytical and numerical evidence that a similar universal behavior arises for the symmetry resolved negativity. In particular, we compute the ratio of charged moments of the partially transposed reduced density matrix as an expectation value of twist operators. These are ``fused" versions of the more traditionally used branch point twist fields and were introduced in a previous work. The use of twist operators allows us to perform the computation in an arbitrary number of spacial dimensions. We show that, in the large-volume limit, only the commutation relations between the twist operators and local fields matter, and computations reduce to a purely combinatorial problem. We address some specific issues regarding fermionic excitations, whose treatment requires the notion of partial time-reversal transformation, and we discuss the differences and analogies with their bosonic counterpart. We find that although the operation of partial transposition requires a redefinition for fermionic theories, the ratio of the negativity moments between an excited state and the ground state is universal and identical for fermions and bosons as well as for a large variety of very different states, ranging from simple qubit states to the excited states of free quantum field theories. Our predictions are tested numerically on a 1D Fermi chain.

hep-th↗

arXiv2023

Two-Point Functions of Composite Twist Fields in the Ising Field Theory

All standard measures of bipartite entanglement in one-dimensional quantum field theories can be expressed in terms of correlators of branch point twist fields, here denoted by $\mathcal{T}$ and $\mathcal{T}^\dagger$. These are symmetry fields associated to cyclic permutation symmetry in a replica theory and having the smallest conformal dimension at the critical point. Recently, other twist fields (composite twist fields), typically of higher dimension, have been shown to play a role in the study of a new measure of entanglement known as the symmetry resolved entanglement entropy. In this paper we give an exact expression for the two-point function of a composite twist field that arises in the Ising field theory. In doing so we extend the techniques originally developed for the standard branch point twist field in free theories as well as an existing computation due to Horváth and Calabrese of the same two-point function which focused on the leading large-distance contribution. We study the ground state two-point function of the composite twist field $\mathcal{T}_μ$ and its conjugate $\mathcal{T}_μ^\dagger$. At criticality, this field can be defined as the leading field in the operator product expansion of $\mathcal{T}$ and the disorder field $μ$. We find a general formula for $\log \langle \mathcal{T}_μ(0) \mathcal{T}^\dagger_μ(r)\rangle$ and for (the derivative of) its analytic continuation to positive real replica numbers greater than 1. We check our formula for consistency by showing that at short distances it exactly reproduces the expected conformal dimension

hep-th↗

arXiv2022

Symmetry Resolved Entanglement of Excited States in Quantum Field Theory II: Numerics, Interacting Theories and Higher Dimensions

In a recent paper we studied the entanglement content of zero-density excited states in complex free quantum field theories, focusing on the symmetry resolved entanglement entropy (SREE). By zero-density states we mean states consisting of a fixed, finite number of excitations above the ground state in an infinite-volume system. The SREE is defined for theories that possess an internal symmetry and provides a measure of the contribution to the total entanglement of each symmetry sector. In our work, we showed that the ratio of Fourier-transforms of the SREEs (i.e. the ratio of charged moments) takes a very simple and universal form for these states, which depends only on the number, statistics and symmetry charge of the excitations as well as the relative size of the entanglement region with respect to the whole system's size. In this paper we provide numerical evidence for our formulae by computing functions of the charged moments in two free lattice theories: a 1D Fermi gas and a complex harmonic chain. We also extend our results in two directions: by showing that they apply also to excited states of interacting theories (i.e. magnon states) and by developing a higher dimensional generalisation of the branch point twist field picture, leading to results in (interacting) higher-dimensional models.

hep-th↗

arXiv2022

Symmetry Resolved Entanglement of Excited States in Quantum Field Theory I: Free Theories, Twist Fields and Qubits

The excess entanglement resulting from exciting a finite number of quasiparticles above the ground state of a free integrable quantum field theory has been investigated quite extensively in the literature. It has been found that it takes a very simple form, depending only on the number of excitations and their statistics. There is now mounting evidence that such formulae also apply to interacting and even higher-dimensional quantum theories. In this paper we study the entanglement content of such zero-density excited states focusing on the symmetry resolved entanglement, that is on 1+1D quantum field theories that possess an internal symmetry. The ratio of charged moments between the excited and grounds states, from which the symmetry resolved entanglement entropy can be obtained, takes a very simple and universal form, which in addition to the number and statistics of the excitations, now depends also on the symmetry charge. Using form factor techniques, we obtain both the ratio of moments and the symmetry resolved entanglement entropies in complex free theories which possess $U(1)$ symmetry. The same formulae are found for simple qubit states.

hep-th↗

arXiv2021

The Staircase Model: Massless Flows and Hydrodynamics

The staircase model is a simple generalization of the sinh-Gordon model, obtained by complexifying the coupling constant. This produces a new theory with many interesting features. Chief among them is the fact that scaling functions such as Zamolodchikov's $c$-function display "roaming" behaviour, that is, they visit the vicinity of an infinite number of conformal fixed points, the unitary minimal models of conformal field theory. This rich structure also makes the model an interesting candidate for study using the generalized hydrodynamic approach to integrable quantum field theory (IQFT). By studying hydrodynamic quantities such as the effective velocities of quasiparticles we can develop a more physical picture of interaction in the theory, both at and away from equilibrium. Indeed, we find that in the staircase model the effective velocity displays monotonicity features not found in any other IQFT. These admit a natural interpretation when investigated in the context of the massless theories known as $\mathcal{M}A_k^{(+)}$ models, which provide an effective description of massless flows between consecutive unitary minimal models. Remarkably, we find that the effective velocity in the staircase model can be reconstructed by a "cut and paste" procedure involving the equivalent functions associated to the massless excitations of suitable $\mathcal{M}A_k^{(+)}$ models. We also investigate the average currents and densities of higher spin conserved quantities in the partitioning protocol.

hep-th↗