Publications

Unitary integrable models typically relax to a stationary generalized Gibbs ensemble (GGE), but in experimental realizations dissipation often breaks integrability. In this work, we use the recently introduced time-dependent GGE (t-GGE) approach to describe the open dynamics of a gas of bosons subject to atom losses and gains. We employ tensor network methods to provide numerical evidence of the exactness of the t-GGE in the limit of adiabatic dissipation, and of its accuracy in the regime of weak but finite dissipation. That accuracy is tested for two-point functions via the rapidity distribution, and for more complicated correlations through a non-Gaussianity measure. We combine this description with generalized hydrodynamics and we show that it correctly captures transport at large scales. Our results demonstrate that the t-GGE approach is robust in both homogeneous and inhomogeneous settings.

We show that topological metals lacking time-reversal symmetry have an intrinsic non-quantised component of the anomalous Hall conductivity which is contributed not only by the Berry phase of quasiparticles on the Fermi surface, but also by Fermi-liquid corrections due to the residual interactions among quasiparticles, the Landau f-parameters. These corrections pair up with those that modify the optical mass with respect to the quasiparticle effective one, or the charge compressibility with respect to the quasiparticle density of states. Our result supports recent claims that the correct expressions for topological observables include vertex corrections besides the topological invariants built just upon the Green’s functions. Furthermore, it demonstrates that such corrections are naturally accounted for by Landau’s Fermi liquid theory, here extended to the case in which coherence effects between bands crossing the chemical potential and those that are instead away from it may play a crucial role, as in the anomalous Hall conductivity, and have important implications when those metals are on the verge of a doping-driven Mott transition, as we discuss.

We present a classical kinetically constrained model of interacting particles on a triangular ladder, which displays diffusion and jamming and can be treated by means of a classical-quantum mapping. Interpreted as a theory of interacting fermions, the diffusion coefficient is the inverse of the effective mass of the quasiparticles which can be computed using mean-field theory. At a critical density ρ = 2 / 3 , the model undergoes a dynamical phase transition in which exponentially many configurations become jammed while others remain diffusive. The model can be generalized to two dimensions.

We study the entanglement Hamiltonian of two disjoint blocks in the harmonic chain on the line and in its ground state. In the regime of large mass, the only non-vanishing terms are the on-site and nearest-neighbour ones. Analytic expressions are obtained for their profiles, which are written in terms of piecewise linear functions that can be discontinuous and display sharp transitions as the separation between the blocks changes. In the regime of vanishing mass, where the matrices characterizing the entanglement Hamiltonian contain couplings at all distances, we explore the location of the subdominant terms and some combinations of matrix elements that are useful for the continuum limit, comparing the results with the corresponding ones for a free chiral current. The single-particle entanglement spectrum is also investigated.

We study the dynamics of entanglement asymmetry in random unitary circuits (RUCs). Focusing on a local U(1) charge, we consider symmetric initial states evolved by both local one-dimensional circuits and geometrically nonlocal RUCs made of two-qudit gates. We compute the entanglement asymmetry of subsystems of arbitrary size, analyzing the relaxation timescales. We show that the entanglement asymmetry of the whole system approaches its stationary value in a time independent of the system size for both local and nonlocal circuits. For subsystems, we find qualitative differences depending on their size. When the subsystem is larger than half of the full system, the equilibration timescales are again independent of the system size for both local and nonlocal circuits and the entanglement asymmetry grows monotonically in time. Conversely, when the subsystems are smaller than half of the full system, we show that the entanglement asymmetry is nonmonotonic in time and that it equilibrates in a time proportional to the quantum-information scrambling time, providing a physical intuition. As a consequence, the subsystem-equilibration time depends on the locality of interactions, scaling linearly and logarithmically in the system size, respectively, for local and nonlocal RUCs. Our work confirms the entanglement asymmetry as a versatile and computable probe of symmetry in many-body physics and yields a phenomenological overview of entanglement-asymmetry evolution in typical nonintegrable dynamics.

In the last decades, multifaceted manifestations of the breakdown of the self-consistent perturbation theory have been identified for the many-electron problem. Yet, the investigations have been so far mostly limited to paramagnetic states, where symmetry breaking is not allowed. Here, we extend the analysis to the spontaneously symmetry-broken antiferromagnetic (AF) phase of the repulsive Hubbard model. To this aim, we calculated two-particle quantities using dynamical mean-field theory for the AF-ordered Hubbard model and studied the possible occurrence of divergences of the irreducible vertex functions in the charge and spin sectors. Our calculations pinpoint the divergences in the AF phase diagram, showing that while the onset of AF order mitigates the breakdown of the perturbation expansion, it does not fully prevent it. Moreover, we have been able to link the changes in the dynamical structure of the corresponding generalized susceptibilities to the physical crossover from a weak-coupling (Slater) to a strong-coupling (Heisenberg) antiferromagnet, which takes place as the interaction strength is gradually increased. Finally, we discuss possible physical consequences of the irreducible vertex divergences in triggering phase-separation instabilities within the AF phase and elaborate on the implications of our findings for two-dimensional systems, where the onset of a long-range AF order is prevented by the Mermin-Wagner theorem.

We investigate a phenomenon known as Superactivation of Backflow of Information (SBFI); namely, the fact that the tensor product of a non-Markovian dynamics with itself exhibits Backflow of Information (BFI) from environment to system even if the single dynamics does not. Such an effect is witnessed by the non-monotonic behaviour of the Helstrom norm and emerges in the open dynamics of two independent, but statistically coupled, parties. We physically interpret SBFI by means of the discrete-time non-Markovian dynamics of two open qubits collisionally coupled to an environment described by a classical Markov chain. In such a scenario, SBFI can be ascribed to the decrease of the qubit-qubit-environment correlations in favour of those of the two qubits, only. We further prove that the same mechanism at the roots of SBFI also holds in a suitable continuous-time limit. We also show that SBFI does not require entanglement to be witnessed, but only the quantumness of the Helstrom ensemble.

In two-dimensional conformal field theories (CFT) in Minkowski spacetime, we study the spacetime distance between two events along two distinct modular trajectories. When the spatial line is bipartite by a single interval, we consider both the ground state and the state at finite different temperatures for the left and right moving excitations. For the free massless Dirac field in the ground state, the bipartition of the line given by the union of two disjoint intervals is also investigated. The modular flows corresponding to connected subsystems preserve relativistic causality. Locality along the modular flows of some fields is explored by evaluating their (anti-)commutators. In particular, the bilocal nature of the modular Hamiltonian of two disjoint intervals for the massless Dirac field provide multiple trajectories leading to Dirac delta contributions in the (anti-)commutators even when the initial points belong to different intervals, thus being spacelike separated.

We examine the behavior of the entanglement asymmetry in the ground state of a (1+1)-dimensional conformal field theory with a boundary condition that explicitly breaks a bulk symmetry. Our focus is on the asymmetry of a subsystem A originating from the symmetry-breaking boundary and extending into a semi-infinite bulk. By employing the twist field formalism, we derive a universal expression for the asymmetry, showing that the asymptotic behavior for large subsystems is approached algebraically, with an exponent which is twice the conformal dimension of a boundary condition-changing operator. As a secondary result, we also establish a similar asymptotic behavior for the string order parameter. Our exact analytical findings are validated through numerical simulations in the critical Ising and 3-state Potts models.

The entanglement asymmetry measures the extent to which a symmetry is broken within a subsystem of an extended quantum system. Here, we analyse this quantity in Haar random states for arbitrary compact, semi-simple Lie groups, building on and generalising recent results obtained for the U(1) symmetric case. We find that, for any group, the average entanglement asymmetry vanishes in the thermodynamic limit when the subsystem is smaller than its complement. When the subsystem and its complement are of equal size, the entanglement asymmetry jumps to a finite value, indicating a sudden transition of the subsystem from a fully symmetric state to one devoid of any symmetry. For larger subsystem sizes, the entanglement asymmetry displays a logarithmic scaling with a coefficient fixed by the dimension of the group. We also investigate the fluctuations of the entanglement asymmetry, which tend to zero in the thermodynamic limit. We check our findings against exact numerical calculations for the SU(2) and SU(3) groups. We further discuss their implications for the thermalisation of isolated quantum systems and black hole evaporation.

We study the dynamics of hard-core bosons on ladders, in the presence of strong kinetic constrains akin to those of the Bariev model. We use a combination of analytical methods and numerical simulations to establish the phase diagram of the model. The model displays a paired Tomonaga-Luttinger liquid phase featuring an emergent dipole symmetry, which encodes the local pairing constraint into a global, nonlocal quantity. We scrutinize the effect of such emergent low-energy symmetry during quench dynamics including single-particle defects. We observe that, despite being approximate, the dipole symmetry still leads to very slow relaxation dynamics, which we model via an effective field theory. The model we discuss is amenable to realization in both cold atoms in optical lattices and Rydberg atom arrays with dynamics taking place solely in the Rydberg manifold. To observe the unusual dynamics of excitations in such experimental platforms, we propose a two-step protocol, which starts with the quasi-adiabatic preparation of low-energy states, followed by the local creation of defects and their study under quench dynamics.

Symmetry-resolved entanglement, capturing the refined structure of quantum entanglement in systems with global symmetries, has attracted a lot of attention recently. In this manuscript, introducing the notion of symmetry-resolved generalized entropies, we aim to develop a computational framework suitable for the study of excited state symmetry-resolved entanglement as well as the dynamical evolution of symmetry-resolved entanglement in symmetry-preserving out-of-equilibrium settings. We illustrate our framework using the example of (1+1)-d free massless compact boson theory, and benchmark our results using lattice computation in the XX chain. As a byproduct, our computational framework also provides access to the probability distribution of the symmetry charge contained within a subsystem and the corresponding full counting statistics.

Locality is a transversal principle that governs quantum dynamics of many-body systems. However, for cavity-embedded systems, such a fundamental notion is hindered by the presence of nonlocal cavity modes, leaving space for new possible dynamical behavior. Here, we investigate the real-time dynamics of low-energy excitations in one-dimensional Rydberg atom arrays coupled to a global cavity mode. We derive an effective description in terms of a Tavis-Cummings-Ising model, whose phase diagram features ordered and disordered phases. The nonlocal nature of the cavity mode drastically affects the emergent meson and string dynamics. Mesons hybridize coherently with the cavity photons, leading to composite meson-polariton excitations. Strings, differently from local interacting theories, acquire a finite kinetic energy thanks to nonlocal cavity-mediated interactions between the underlying domain walls. We then conclude by presenting a new concrete experimental blueprint for a cavity QED Rydberg atom array simulator where the physics outlined in this Letter can be realized.

We study the directed transport of bosons along a one dimensional lattice in a dissipative setting, where the hopping is only facilitated by coupling to a Markovian reservoir. By combining numerical simulations with a field-theoretic analysis, we investigate the current fluctuations for this process and determine its asymptotic behavior. These findings demonstrate that dissipative bosonic transport belongs to the Kardar-Parisi-Zhang universality class and therefore, in spite of the drastic difference in the underlying particle statistics, it features the same coarse-grained behavior as the corresponding asymmetric simple exclusion process for fermions. However, crucial differences between the two processes emerge when focusing on the full counting statistics of current fluctuations. By mapping both models to the physics of fluctuating interfaces, we find that dissipative transport of bosons and fermions can be understood as surface growth and erosion processes, respectively. Within this unified description, both the similarities and discrepancies between the full counting statistics of the transport are reconciled. Beyond purely theoretical interest, these findings are relevant for experiments with cold atoms or long-lived quasiparticles in nanophotonic lattices, where such transport scenarios can be realized.

We study a three-orbital Hubbard-Kanamori model relevant for iron-based superconductors using variational wave functions explicitly including spatial correlations and electron pairing. We span the nonmagnetic sector from filling n=4, which is representative of undoped iron-based superconductors, to n=3, where a Mott insulating state with each orbital at half filling is found. In the strong-coupling regime, when the electron density is increased, we find a spontaneous differentiation between the occupation of dxz and dyz orbitals, leading to an orbital-selective state with a nematic character that becomes stronger at increasing density. One of these orbitals stays half filled for all densities while the other one hosts (together with the dxy orbital) the excess of electron density. Most importantly, in this regime long-range pairing correlations appear in the orbital with the largest occupation. Our results highlight a strong link between orbital-selective correlations, nematicity, and superconductivity, which requires the presence of a significant Hund's coupling.

Understanding how entanglement can be reduced through simple operations is crucial for both classical and quantum algorithms. We investigate the entanglement properties of lattice models hosting conformal field theories cooled via local Clifford operations, a procedure we refer to as stabilizer disentangling. We uncover two distinct regimes: a constant gain regime, where disentangling is volume-independent, and a log-gain regime, where disentanglement increases with volume, characterized by a reduced effective central charge. In both cases, disentangling efficiency correlates with the target state magic, with larger magic leading to more effective cooling. The dichotomy between the two cases stems from mutual stabilizer Rényi entropy, which influences the entanglement cooling process. We provide an analytical understanding of such effect in the context of cluster Ising models, that feature disentangling global Clifford operations. Our findings indicate that matrix product states possess subclasses based on the relationship between entanglement and magic, and clarifying the potential of new classes of variational states embedding Clifford dynamics within matrix product states.

We extend the recently introduced Clifford-dressed time-dependent variational principle (TDVP) to efficiently compute many-body wave-function amplitudes in the computational basis. This advancement enhances the study of Loschmidt echoes, which generally require accurate calculations of the overlap between the evolved state and the initial wave function. By incorporating Clifford-disentangling gates during TDVP evolution, our method effectively controls entanglement growth while keeping the computation of these amplitudes accessible. Specifically, it reduces the problem to evaluating the overlap between a matrix product state (MPS) and a stabilizer state, a task that remains computationally feasible within the proposed framework. To demonstrate the effectiveness of this approach, we first benchmark it on the one-dimensional transverse-field Ising model. We then apply it to more challenging scenarios, including a nonintegrable next-to-nearest-neighbor Ising chain and a two-dimensional Ising model. Our results highlight the versatility and efficiency of the Clifford-augmented MPS, showcasing its capability to go beyond the evaluation of simple expectation values. This makes it a powerful tool for exploring various aspects of many-body quantum dynamics.

We study the behavior of the classical XY model on a two-dimensional square lattice, with interactions occurring within a vision cone of each spin. Via Monte Carlo simulations, we explore one non-reciprocal and two reciprocal implementations of these interactions. The corresponding energy involves couplings that depend non-trivially on the system’s configuration, leading to both long-range and quasi-long-range ordered phases at low temperatures. Our results demonstrate that non-reciprocity is not essential for achieving long-range order at low temperatures. Using symmetry arguments, we provide a theoretical framework to explain these findings, and additionally we uncover an unexpected order-by-disorder transition.

We propose an enhanced time-dependent variational principle (TDVP) algorithm for matrix product states that integrates Clifford disentangling techniques to efficiently manage entanglement growth. By leveraging the Clifford group, which maps Pauli strings to other Pauli strings while maintaining low computational complexity, we introduce a Clifford dressed single-site 1-TDVP scheme. During the TDVP integration, we apply a global Clifford transformation as needed to reduce entanglement by iteratively sweeping over two-qubit Clifford unitaries that connect neighboring sites in a checkerboard pattern. We validate the new algorithm numerically using various quantum many-body models, including both integrable and nonintegrable systems. Our results demonstrate that the Clifford dressed TDVP significantly improves entanglement management and computational efficiency, achieving higher accuracy, extended simulation times, and enhanced precision in computed observables compared to standard TDVP approaches. Additionally, we propose incorporating Clifford gates directly within the two-site 2-TDVP scheme.

We present a variational quantum adiabatic theorem, which states that, under certain assumptions, the adiabatic dynamics projected onto a variational manifold follow the instantaneous variational ground state. We focus on low-entanglement variational manifolds and target Hamiltonians with classical ground states. Despite highly entangled intermediate states along the exact adiabatic path, the variational evolution converges to the target ground state. We demonstrate this approach with several examples that align with our theoretical analysis.