Publications

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.

We study the dynamics of the quenched Anderson model at finite temperature using matrix product states (MPSs). Exploiting a chain mapping for the electron bath, we investigate the entanglement structure in the MPS for various orderings of the two chains, which emerge from the thermofield transformation employed to deal with nonzero temperature. We show that merging both chains can significantly lower the entanglement at finite temperatures as compared to an intuitive nearest-neighbor implementation of the Hamiltonian. Analyzing the population of the free bath modes - possible when simulating the full dynamics of impurity plus bath - we find clear signatures of the Kondo effect in the quench dynamics.

Abstract: We study the dynamics of charge and energy currents in a Coulomb-coupled double quantum dot system, when only one of the two dots is adiabatically driven by a time-periodic gate that modulates its energy level. Although the Coulomb coupling does not allow for electron transfer between the dots, it enables an exchange of energy between them which induces a time variation of charge in the undriven dot. We describe the effect of electron interactions at low temperature using a time-dependent slave-spin 1 formulation within mean field that efficiently captures the main effects of the strong correlations as well as the dynamical nature of the driving. We find that the currents induced in the undriven dot due to the mutual friction between inter-dot electrons are of the same order as those generated in the adiabatically driven dot. Interestingly, up to 43% of the energy injected by the ac sources can be transferred from the driven dot to the undriven one. We complete our analysis by studying the impact of the Coulomb interaction on the resistance of the quantum dot that is driven by the gate. Graphic abstract: [Figure not available: see fulltext.].

Engineered dynamical maps combining coherent and dissipative transformations of quantum states with quantum measurements have demonstrated a number of technological applications, and promise to be a crucial tool in quantum thermodynamic processes. Here we exploit the control on the effective open spin qutrit dynamics of a nitrogen-vacancy center to experimentally realize an autonomous feedback process (Maxwell's demon) with tunable dissipative strength. The feedback is enabled by random measurement events that condition the subsequent dissipative evolution of the qutrit. The efficacy of the autonomous Maxwell's demon is quantified by means of a generalized Sagawa-Ueda-Tasaki relation for dissipative dynamics. To achieve this, we experimentally characterize the fluctuations of the energy exchanged between the system and its the environment. This opens the way to the implementation of a new class of Maxwell's demons, which could be useful for quantum sensing and quantum thermodynamic devices.

We study the entanglement dynamics of thermofield double (TFD) states in integrable spin chains and quantum field theories. We show that, for a natural choice of the Hamiltonian eigenbasis, the TFD evolution may be interpreted as a quantum quench from an initial state which is low-entangled in the real-space representation and displays a simple quasiparticle structure. Based on a semiclassical picture analogous to the one developed for standard quantum quenches, we conjecture a formula for the entanglement dynamics, which is valid for both discrete and continuous integrable field theories, and expected to be exact in the scaling limit of large space and time scales. We test our conjecture in two prototypical examples of integrable spin chains, where numerical tests are possible. First, in the XY-model, we compare our predictions with exact results obtained by mapping the system to free fermions, finding excellent agreement. Second, we test our conjecture in the interacting XXZ Heisenberg model, against numerical iTEBD calculations. For the latter, we generally find good agreement, although, for some range of the system parameters and within the accessible simulation times, some small discrepancies are visible, which we attribute to finite-time effects.

We study the leading and sub-leading magnetic perturbations of the thermal E7 integrable deformation of the tricritical Ising model. In the low-temperature phase, these magnetic perturbations lead to the confinement of the kinks of the model. The resulting meson spectrum can be obtained using the semi-classical quantisation, here extended to include also mesonic excitations composed of two different kinks. An interesting feature of the integrable sub-leading magnetic perturbation of the thermal E7 deformation of the model is the possibility to swap the role of the two operators, i.e. the possibility to consider the model as a thermal perturbation of the integrable A3 model associated to the sub-leading magnetic deformation. Due to the occurrence of vacuum degeneracy unrelated to spontaneous symmetry breaking in A3, the confinement pattern shows novel features compared to previously studied models. Interestingly enough, the validity of the semi-classical description in terms of the A3 endpoint extends well beyond small fields, and therefore the full parameter space of the joint thermal and sub-leading magnetic deformation is well described by a combination of semi-classical approaches. All predictions are verified by comparison to finite volume spectrum resulting from truncated conformal space.

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional E7 Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, σ(x) and σ0(x), in either phase are accompanied by associated disorder operators, µ(x) and µ0(x). Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For σ(x) and σ0(x), the equations are identical in form and are parameterised by the values of the one-particle form factors of the two lightest Z2 odd particles. Similarly, the equations for µ(x) and µ0(x) have identical form and are parameterised by two elementary form factors. Using the clustering property, we show that these four sets of solutions are eventually not independent; instead, the parameters of the solutions for σ(x)/σ0(x) are fixed in terms of those for µ(x)/µ0(x). We use the truncated conformal space approach to confirm numerically the derived expressions of the matrix elements as well as the validity of the ∆-sum rule as applied to the off-critical correlators. We employ the derived form factors of the order and disorder operators to compute the exact dynamical structure factors of the theory, a set of quantities with a rich spectroscopy which may be directly tested in future inelastic neutron or Raman scattering experiments.

We study the spatiotemporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. Such emission channels can be synthesized with tunable spatial profiles in lossy cavity QED experiments using a magnetic field gradient and a Raman drive with multiple sidebands. We consider systems initially in an uncorrelated state, and find that correlations widen and contract in a novel pattern intimately related to both the dissipative nature of the dynamical channel and its spatial profile. Additionally, we make a methodological contribution by generalizing nonequilibrium spin-wave theory to the case of dissipative systems and derive equations of motion for any translationally invariant spin chain whose dynamics can be described by a combination of Hamiltonian interactions and dissipative Lindblad channels. Our work aims at extending the study of correlation dynamics to purely dissipative quantum simulators and compare them with the established paradigm of correlations spreading in Hamiltonian systems.

We study the nonequilibrium relaxational dynamics of a probe particle linearly coupled to a thermally fluctuating scalar field and subject to a harmonic potential, which provides a cartoon for an optically trapped colloid immersed in a fluid close to its bulk critical point. The average position of the particle initially displaced from the position of mechanical equilibrium is shown to feature long-time algebraic tails as the critical point of the field is approached, the universal exponents of which are determined in arbitrary spatial dimensions. As expected, this behavior cannot be captured by adiabatic approaches which assumes fast field relaxation. The predictions of the analytic, perturbative approach are qualitatively confirmed by numerical simulations.

The presence of a global internal symmetry in a quantum many-body system is reflected in the fact that the entanglement between its subparts is endowed with an internal structure, namely it can be decomposed as a sum of contributions associated to each symmetry sector. The symmetry resolution of entanglement measures provides a formidable tool to probe the out-of-equilibrium dynamics of quantum systems. Here, we study the time evolution of charge-imbalance-resolved negativity after a global quench in the context of free-fermion systems, complementing former works for the symmetry-resolved entanglement entropy. We find that the charge-imbalance-resolved logarithmic negativity shows an effective equipartition in the scaling limit of large times and system size, with a perfect equipartition for early and infinite times. We also derive and conjecture a formula for the dynamics of the charged Renyi logarithmic negativities. We argue that our results can be understood in the framework of the quasiparticle picture for the entanglement dynamics, and provide a conjecture that we expect to be valid for generic integrable models.

We introduce and study generalized Rényi entropies defined through the traces of products of TrB(| Ψi⟩⟨Ψj|) where ∣Ψi⟩ are eigenstates of a two-dimensional conformal field theory (CFT). When ∣Ψi⟩ = ∣Ψj⟩ these objects reduce to the standard Rényi entropies of the eigenstates of the CFT. Exploiting the path integral formalism, we show that the second generalized Rényi entropies are equivalent to four point correlators. We then focus on a free bosonic theory for which the mode expansion of the fields allows us to develop an efficient strategy to compute the second generalized Rényi entropy for all eigenstates. As a byproduct, our approach also leads to new results for the standard Rényi and relative entropies involving arbitrary descendent states of the bosonic CFT.

We propose a spatiotemporal characterization of the entanglement dynamics in many-body localized (MBL) systems, which exhibits a striking resemblance to dynamical heterogeneity in classical glasses. Specifically, we find that the relaxation times of local entanglement, as measured by the concurrence, are spatially correlated yielding a dynamical length scale for quantum entanglement. As a consequence of this spatiotemporal analysis, we observe that the considered MBL system is made up of dynamically correlated clusters with a size set by this entanglement length scale. The system decomposes into compartments of different activity such as active regions with fast quantum entanglement dynamics and inactive regions where the dynamics is slow. We further find that the relaxation times of the on-site concurrence become broadly distributed and more spatially correlated, as disorder increases or the energy of the initial state decreases. Through this spatiotemporal characterization of entanglement, our work unravels a previously unrecognized connection between the behavior of classical glasses and the genuine quantum dynamics of MBL systems.

In this paper, we apply the form factor bootstrap approach to branch point twist fields in the q-state Potts model for q ≤ 3. For q = 3 this is an integrable interacting quantum field theory with an internal discrete ℤ3 symmetry and therefore provides an ideal starting point for the investigation of the symmetry resolved entanglement entropies. However, more generally, for q ≤ 3 the standard Rényi and entanglement entropies are also accessible through the bootstrap programme. In our work we present form factor solutions both for the standard branch point twist field with q ≤ 3 and for the composite (or symmetry resolved) branch point twist field with q = 3. In both cases, the form factor equations are solved for two particles and the solutions are carefully checked via the ∆-sum rule. Using our analytic predictions, we compute the leading finite-size corrections to the entanglement entropy and entanglement equipartition for a single interval in the ground state.

Recent developments in quantum machine learning have seen the introduction of several models to generalize the classical perceptron to the quantum regime. The capabilities of these quantum models need to be determined precisely in order to establish if a quantum advantage is achievable. Here we use a statistical physics approach to compute the pattern capacity of a particular model of quantum perceptron realized by means of a continuous variable quantum system.

We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and nonlocal terms gives rise to a phase diagram with liquid phases with dominant cluster, spin-, and density-wave quasi-long-range ordering. These phases are separated by Berezinskii-Kosterlitz-Thouless, Gaussian, and supersymmetric (SUSY) quantum critical transitions. For the latter, we provide a phenomenological description of coupled SUSY conformal field theories, whose predictions are confirmed by matrix product state simulations. Our results are motivated by, and directly relevant to, recent experiments with Rydberg-dressed atoms in optical lattices, where ladder dynamics has already been demonstrated, and emphasize the capabilities of these setups to investigate exotic quantum phenomena such as cluster liquids and coupled SUSY conformal field theories.

The competition and interplay between charge-density wave and superconductivity have become a central subject for quasi-two-dimensional compounds. Some of these materials, such as the transition-metal dichalcogenides, exhibit strong electron-phonon coupling, an interaction that may favor both phases, depending on the external parameters, such as hydrostatic pressure. In view of this, here we analyze the single-band t-t′ Holstein model in the square lattice, adding a next-nearest neighbor hopping t′ in order to play the role of the external pressure. To this end, we perform unbiased quantum Monte Carlo simulations with an efficient inversion sampling technique appropriately devised for this model. Such a methodology drastically reduces the autocorrelation time and increases the efficiency of the Monte Carlo approach. By investigating the charge-charge correlation functions, we obtain the behavior of the critical temperature as a function of t′ and, from compressibility analysis, we show that a first-order metal-to-insulator phase transition occurs. We also provide a low-temperature phase diagram for the model.

In the context of ground states of quantum many-body systems, the locality of entanglement between connected regions of space is directly tied to the locality of the corresponding entanglement Hamiltonian: the latter is dominated by local, few-body terms. In this work, we introduce the negativity Hamiltonian as the (non-Hermitian) effective Hamiltonian operator describing the logarithm of the partial transpose of a many-body system. This allows us to address the connection between entanglement and operator locality beyond the paradigm of bipartite pure systems. As a first step in this direction, we study the structure of the negativity Hamiltonian for fermionic conformal field theories and a free-fermion chain: in both cases, we show that the negativity Hamiltonian assumes a quasilocal functional form, that is captured by simple functional relations.

We explore the dynamical phases of unitary Clifford circuits with variable-range interactions, coupled to a monitoring environment. We investigate two classes of models, distinguished by the action of the unitary gates, which either are organized in clusters of finite-range two-body gates, or are pair-wise interactions randomly distributed throughout the system with a power-law distribution. We find the range of the interactions plays a key role in characterizing both phases and their measurement-induced transitions. For the cluster unitary gates we find a transition between a phase with volume-law scaling of the entanglement entropy and a phase with area-law entanglement entropy. Our results indicate that the universality class of the phase transition is compatible to that of short range hybrid Clifford circuits. Oppositely, in the case of power-law distributed gates, we find the universality class of the phase transition changes continuously with the parameter controlling the range of interactions. In particular, for intermediate values of the control parameter, we find a non-conformal critical line which separates a phase with volume-law scaling of the entanglement entropy from one with sub-extensive scaling. Within this region, we find the entanglement entropy and the logarithmic negativity present a cross-over from a phase with algebraic growth of entanglement with system size, and an area-law phase.

We study the relaxation of the local ferromagnetic order in the transverse field quantum Ising chain with power-law decaying interactions ∼ 1/rα. We prepare the system in the GHZ state and study the time evolution of the probability distribution function (PDF) of the order parameter within a block of when quenching the transverse field. The model is known to support long range order at finite temperature for α ≤ 2.0. In this regime, quasi-localized topological magnetic defects are expected to strongly affect the equilibration of the full probability distribution. We highlight different dynamical regimes where gaussification mechanism may be slowed down by confinement and eventually breaks. We further study the PDF dynamics induced by changing the effective dimensionality of the system; we mimic this by quenching the range of the interactions. As a matter of fact, the behavior of the system crucially depends on the value of α governing the unitary evolution.

We present EDIpack, an exact diagonalization package to solve generic quantum impurity problems. The algorithm includes a generalization of the look-up method introduced in Ref. [1] and enables a massively parallel execution of the matrix-vector linear operations required by Lanczos and Arnoldi algorithms. We show that a suitable Fock basis organization is crucial to optimize the inter-processors communication in a distributed memory setup and to reach sub-linear scaling in sufficiently large systems. We discuss the algorithm in details indicating how to deal with multiple orbitals and electron-phonon coupling. Finally, we outline the download, installation and functioning of the package. Program summary: Program title: EDIpack CPC Library link to program files: https://doi.org/10.17632/2hxhw9zjg9.1 Code Ocean capsule: https://codeocean.com/capsule/3537659 Licensing provisions: GPLv3 Programming language: Fortran, Python External dependencies: CMake (>=3.0.0), Scifortran, MPI Nature of problem: The solution of multi-orbital quantum impurity systems at zero or low temperatures, including the effective description of lattice models of strongly correlated electrons, are difficult to determine. Solution method: Use parallel exact diagonalization algorithm to compute the low lying spectrum and evaluate dynamical correlation functions.