arXiv subjects

Lorenzo Gotta

Publications and source records attributed to Lorenzo Gotta.

11 recordsLinked to original sources

arXiv2026

Enhancing entanglement asymmetry in fragmented quantum systems

Entanglement asymmetry provides a quantitative measure of symmetry breaking in many-body quantum states. Focusing on inhomogeneous $U(1)$ charges, such as dipole and multipole moments, we show that the typical asymmetry is bounded by a universal fraction of its maximal value. Multipole charges naturally arise in systems with Hilbert-space fragmentation, where the dynamics splits into exponentially many disconnected sectors. Using the commutant algebra formalism, we generalize entanglement asymmetry to account for fragmentation. While the asymmetry grows logarithmically for conventional symmetries, it can scale extensively in fragmented systems and distinguish classical from quantum fragmentation. We derive general upper bounds for the asymmetry and identify states that saturate them. To study the typical behavior of the asymmetry, we consider the ensemble of random matrix product states. By identifying the bond dimension with an effective time parameter, we qualitatively reproduce recent results on asymmetry dynamics in random quantum circuits, suggesting a universal behavior for the asymmetry of $U(1)$ charges in local ergodic systems.

cond-mat.stat-mech↗

arXiv2026

Towers of quantum many-body scars under stochastic resetting

Towers of quantum many-body scars are sets of highly-excited eigenstates of nonintegrable Hamiltonians whose dynamics shows athermal behavior and persistent oscillations in time. The preparation of such states is, however, challenging due to their entanglement content. In this work, we show that local properties of such states can be prepared by interspersing the scarred dynamics with stochastic resets to much simpler unentangled product states. Stochastic resetting amounts to reinitializing the many-body wavefunction of the system at random times to a predefined state, which we choose to be in the scarred subspace. We derive several analytical results for the ensuing dynamics, e.g., for the time evolution of the fidelity and of local observables. Resetting damps the scarred oscillations and generates spatial off-diagonal long-range order in the ensuing stationary state. The latter shows mixedness that scales logarithmically as a function of the system size, which follows from the structure of the scarred eigenstates. We prove that such stationary states are locally equivalent, in the sparse-resetting limit, to a single pure scarred eigenstate, which is determined by the reset state. This protocol thereby might represent a route to the experimental preparation of the local properties of correlated and entangled states through resetting.

cond-mat.stat-mech↗

arXiv2025

Open-system quantum many-body scars: a theory

In this work, we undertake the problem of formally introducing a notion of quantum many-body scarring in open quantum systems governed by the Lindblad equation. To this goal, we rely on the commutant-algebra framework for the description of strong symmetries to introduce the unconventional strong-symmetry structure leading to the existence of anomalous stationary states, which we dub open-system quantum many-body scars (OSQMBS), besides a typical infinite-temperature state. We provide several benchmarks of the theoretical predictions on the stationary-state manifold and on convergence to stationarity, as well as describe the time-evolution of off-diagonal coherences among the Hilbert space symmetry sectors identified by OSQMBS and their orthogonal complement. Moreover, we investigate the existence of asymptotic OSQMBS (AOSQMBS), the latter being states that, despite converging to the typical infinite-temperature state in the large-time limit, display anomalously-large relaxation time scales, which we thoroughly describe by means of the behavior of their fidelity as a function of time through proper scaling Ansaetze.

quant-ph↗

arXiv2025

Exceptional stationary state in a dephasing many-body open quantum system

We study a dephasing many-body open quantum system that hosts, together with the infinite-temperature state, another additional stationary state. The latter is exceptional in many respects, as it is pure and retains memory of the initial condition, whereas any orthogonal state evolves towards the infinite-temperature state erasing any information on the initial state. We discuss the approach to stationarity of the model focusing in particular on the fate of interfaces between the two states; a simple classical model based on a membrane picture helps developing an effective hydrodynamic theory even if the dynamics does not feature any conserved quantity. The fact that the model reaches stationary properties on timescales that depend on the system size while the asymptotic decay rate is finite is duly highlighted. We point out the reasons for considering these exceptional stationary states as quantum many-body scars in the open system framework.

quant-ph↗

arXiv2024

Dirac Impurity in a Luttinger liquid

We consider a linearly-dispersing quantum impurity interacting through a contact density-density term with a one-dimensional (1D) superfluid described by the Tomonaga-Luttinger liquid theory. Using a linked cluster expansion we characterize the impurity dynamics by calculating approximate expressions for the single-particle Green's function and for the time evolution of the density profile. We show the existence of two different dynamical regimes: (i) a $\textit{quasiparticle}$ regime, dominated by the presence of a finite lifetime for the host impurity, and (ii) an $\textit{infrared-dominated}$ regime, where the impurity causes a Anderson's orthogonality catastrophe of the 1D bath. We discuss the possible experimental consequences of these findings for cold atoms experiments.

cond-mat.str-el↗

arXiv2023

Asymptotic Quantum Many-Body Scars

We consider a quantum lattice spin model featuring exact quasiparticle towers of eigenstates with low entanglement at finite size, known as quantum many-body scars (QMBS). We show that the states in the neighboring part of the energy spectrum can be superposed to construct entire families of low-entanglement states whose energy variance decreases asymptotically to zero as the lattice size is increased. As a consequence, they have a relaxation time that diverges in the thermodynamic limit, and therefore exhibit the typical behavior of exact QMBS although they are not exact eigenstates of the Hamiltonian for any finite size. We refer to such states as \textit{asymptotic} QMBS. These states are orthogonal to any exact QMBS at any finite size, and their existence shows that the presence of an exact QMBS leaves important signatures of non-thermalness in the rest of the spectrum; therefore, QMBS-like phenomena can hide in what is typically considered the thermal part of the spectrum. We support our study using numerical simulations in the spin-1 XY model, a paradigmatic model for QMBS, and we conclude by presenting a weak perturbation of the model that destroys the exact QMBS while keeping the asymptotic QMBS.

cond-mat.str-el↗

arXiv2022

Exact many-body scars based on pairs or multimers in a chain of spinless fermions

We construct a 1D model Hamiltonian of spinless fermions for which the spinless analogue of $η$-pairing states are quantum many-body scars of the model. These states are excited states and display subvolume entanglement entropy scaling; they form a tower of states that are equally spaced in energy (resulting in periodic oscillations in the Loschmidt echo and in the time evolution of observables for initial states prepared in a superposition of them) and are atypical in the sense that they weakly break the eigenstate thermalization hypothesis, while the other excited states are thermal. We extend the approach by presenting models with a tower of scar states generated by multimers located at the edge of the Brillouin zone.

cond-mat.str-el↗

arXiv2021

Kinetic formation of trimers in a spinless fermionic chain

We show the stabilization of two trimer phases in a chain of spinless fermions with a correlated hopping term. A trimer fluid forms due to a gain in trimer kinetic energy and competes with a fluid of unbound fermions. Furthermore, we observe two intermediate phases where these two fluids coexist and do not spatially separate. Depending on the way trimers are created out of the Fermi sea, hybridization can occur, in which case the onset of correlations between the two fluids is well captured by a generalized BCS ansatz. These results are finally extended to the formation of larger multimers, which highlights the peculiarities of pair and trimer formation.

cond-mat.str-el↗

arXiv2021

Two-fluid coexistence and phase separation in a one dimensional model with pair hopping and density interactions

We compute the phase diagram of a one-dimensional model of spinless fermions with pair-hopping and nearest-neighbor interaction, first introduced by Ruhman and Altman, using the density-matrix renormalization group combined with various analytical approaches. Although the main phases are a Luttinger liquid of fermions and a Luttinger liquid of pairs, we also find remarkable phases in which only a fraction of the fermions are paired. In such case, two situations arise: either fermions and pairs coexist spatially in a two-fluid mixture, or they are spatially segregated leading to phase separation. These results are supported by several analytical models that describe in an accurate way various relevant cuts of the phase diagram. Last, we identify relevant microscopic observables that capture the presence of these two fluids: while originally introduced in a phenomenological way, they support a wider application of two-fluid models for describing pairing phenomena.

cond-mat.str-el↗

arXiv2021

Pairing in spin chains and spinless fermions with next-nearest neighbour interactions

We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest neighbour range. In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbour and next-nearest-neighbour interactions. Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations. The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles. In relation with recent studies, we show several emergent transition lines with a central charge $c = 3/2$ between the Luttinger-liquid and the cluster Luttinger liquid phases. These results could be experimentally investigated using highly-tunable quantum simulators.

cond-mat.quant-gas↗

arXiv2020

Two-fluid coexistence in a spinless fermions chain with pair hopping

We show that a simple one-dimensional model of spinless fermions with pair hopping displays a phase in which a Luttinger liquid of paired fermions coexists with a Luttinger liquid of unpaired fermions. Our results are based on extensive numerical density-matrix renormalisation group calculations and are supported by a two-fluid model that captures the essence of the coexistence region.

cond-mat.str-el↗