arXiv subjects

Stefano Scopa

Publications and source records attributed to Stefano Scopa.

33 records · Page 2Linked to original sources

arXiv2022

Generalized hydrodynamics of the repulsive spin-$\frac{1}{2}$ Fermi gas

We study non-homogeneous quantum quenches in a one-dimensional gas of repulsive spin-$1/2$ fermions, as described by the integrable Yang-Gaudin model. By means of generalized hydrodynamics (GHD), we analyze in detail the real-time evolution following a sudden change of the confining potential. We consider in particular release protocols and trap quenches, including a version of the quantum Newton's cradle. At zero temperature, we employ a simplified phase-space hydrodynamic picture to characterize the dynamics of the particle- and spin-density profiles. Away from zero temperatures, we perform a thorough numerical study of the GHD equations, and provide quantitative predictions for different values of the temperature, external magnetic field, and chemical potential. We highlight the qualitative features arising due to the multi-component nature of the elementary excitations, discussing in particular effects of spin-charge separation and dynamical polarization.

cond-mat.stat-mech↗

arXiv2022

Real-time spin-charge separation in one-dimensional Fermi gases from generalized hydrodynamics

We revisit early suggestions to observe spin-charge separation (SCS) in cold-atom settings {in the time domain} by studying one-dimensional repulsive Fermi gases in a harmonic potential, where pulse perturbations are initially created at the center of the trap. We analyze the subsequent evolution using generalized hydrodynamics (GHD), which provides an exact description, at large space-time scales, for arbitrary temperature $T$, particle density, and interactions. At $T=0$ and vanishing magnetic field, we find that, after a nontrivial transient regime, spin and charge dynamically decouple up to perturbatively small corrections which we quantify. In this limit, our results can be understood based on a simple phase-space hydrodynamic picture. At finite temperature, we solve numerically the GHD equations, showing that for low $T>0$ effects of SCS survive and {characterize} explicitly the value of $T$ for which the two distinguishable excitations melt.

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arXiv2022

Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench

We investigate the non-equilibrium dynamics of the symmetry-resolved Rényi entropies in a one-dimensional gas of non-interacting spinless fermions by means of quantum generalised hydrodynamics, which recently allowed to obtain very accurate results for the total entanglement in inhomogeneous quench settings. Although our discussion is valid for any quench setting accessible with quantum generalised hydrodynamics, we focus on the case of a quantum gas initially prepared in a bipartite fashion and subsequently let evolve unitarily with a hopping Hamiltonian. For this system, we characterise the symmetry-resolved Rényi entropies as function of time $t$ and of the entangling position $x$ along the inhomogeneous profile. We observe an asymptotic logarithmic growth of the charged moments at half system and an asymptotic restoration of equipartition of entropy among symmetry sectors with deviations which are proportional to the square of the inverse of the total entropy.

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arXiv2022

Entanglement dynamics of a hard-core quantum gas during a Joule expansion

We study the entanglement dynamics of a one-dimensional hard-core quantum gas initially confined in a box of size $L$ with saturated density $ρ=1$. The gas is suddenly released into a region of size $2L$ by moving one of the box edges. We show that the analytic prediction for the entanglement entropy obtained from quantum fluctuating hydrodynamics holds quantitatively true even after several reflections of the gas against the box edges. We further investigate the long time limit $t/L\gg 1$ where a Floquet picture of the non-equilibrium dynamics emerges and hydrodynamics eventually breaks down.

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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.

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arXiv2022

Entanglement dynamics in confining spin chains

The confinement of elementary excitations induces distinctive features in the non-equilibrium quench dynamics. One of the most remarkable is the suppression of entanglement entropy which in several instances turns out to oscillate rather than grow indefinitely. While the qualitative physical origin of this behavior is clear, till now no quantitative understanding away from the field theory limit was available. Here we investigate this problem in the weak quench limit, when mesons are excited at rest, hindering entropy growth and exhibiting persistent oscillations. We provide analytical predictions of the entire entanglement dynamics based on a Gaussian approximation of the many-body state, which captures numerical data with great accuracy and is further simplified to a semiclassical quasiparticle picture in the regime of weak confinement. Our methods are valid in general and we apply explicitly to two prototypical models: the Ising chain in a tilted field and the experimentally relevant long-range Ising model.

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arXiv2021

Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion

We consider the non-equilibrium dynamics of the entanglement entropy of a one-dimensional quantum gas of hard-core particles, initially confined in a box potential at zero temperature. At $t=0$ the right edge of the box is suddenly released and the system is let free to expand. During this expansion, the initially correlated region propagates with a non-homogeneous profile, leading to the growth of entanglement entropy. This setting is investigated in the hydrodynamic regime, with tools stemming from semi-classical Wigner function approach and with recent developments of quantum fluctuating hydrodynamics. Within this framework, the entanglement entropy can be associated to a correlation function of chiral twist-fields of the conformal field theory that lives along the Fermi contour and it can be exactly determined. Our predictions for the entanglement evolution are found in agreement with and generalize previous results in literature based on numerical calculations and heuristic arguments.

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arXiv2020

One-particle density matrix of a trapped Lieb-Liniger anyonic gas

We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum systems. We first revisit homogeneous anyonic gases with point-wise interactions. In the harmonic Luttinger liquid expansion of the one-particle density matrix for finite interaction strength, the non-universal field amplitudes were not yet known. We extract them from the Bethe Ansatz formula for the field form factors, providing an exact asymptotic expansion of this correlation function, thus extending the available results in the Tonks-Girardeau limit. Next, we analyse trapped gases with non-trivial density profiles. By applying recent analytic and numerical techniques for inhomogeneous Luttinger liquids,we provide exact expansions for the one-particle density matrix. We present our results for different confining potentials, highlighting the main differences with respect to bosonic gases.

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arXiv2020

Determinant formula for the field form factor in the anyonic Lieb-Liniger model

We derive an exact formula for the field form factor in the anyonic Lieb-Liniger model, valid for arbitrary values of the interaction $c$, anyonic parameter $κ$, and number of particles $N$. Analogously to the bosonic case, the form factor is expressed in terms of the determinant of a $N\times N$ matrix, whose elements are rational functions of the Bethe quasimomenta but explicitly depend on $κ$. The formula is efficient to evaluate, and provide an essential ingredient for several numerical and analytical calculations. Its derivation consists of three steps. First, we show that the anyonic form factor is equal to the bosonic one between two special off-shell Bethe states, in the standard Lieb-Liniger model. Second, we characterize its analytic properties and provide a set of conditions that uniquely specify it. Finally, we show that our determinant formula satisfies these conditions.

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arXiv2018

Dynamical off-equilibrium scaling across magnetic first-order phase transitions

We investigate the off-equilibrium dynamics of a classical spin system with $O(n)$ symmetry in $2< D <4$ spatial dimensions and in the limit $n\to \infty$. The system is set up in an ordered equilibrium state is and subsequently driven out of equilibrium by slowly varying the external magnetic field $h$ across the transition line $h_c=0$ at fixed temperature $T\leq T_c$. We distinguish the cases $T = T_c$ where the magnetic transition is continuous and $T<T_c$ where the transition is discontinuous. In the former case, we apply a standard Kibble-Zurek approach to describe the non-equilibrium scaling and formally compute the correlation functions and scaling relations. For the discontinuous transition we develop a scaling theory which builds on the coherence length rather than the correlation length since the latter remains finite for all times. Finally, we derive the off-equilibrium scaling relations for the hysteresis loop area during a round-trip protocol that takes the system across its phase transition and back. Remarkably, our results are valid beyond the large-$n$ limit.

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arXiv2018

Exact solution of time-dependent Lindblad equations with closed algebras

Time-dependent Lindblad master equations have important applications in areas ranging from quantum thermodynamics to dissipative quantum computing. In this paper we outline a general method for writing down exact solutions of time-dependent Lindblad equations whose superoperators form closed algebras. We focus on the particular case of a single qubit and study the exact solution generated by both coherent and incoherent mechanisms. We also show that if the time-dependence is periodic, the problem may be recast in terms of Floquet theory. As an application, we give an exact solution for a two-levels quantum heat engine operating in a finite-time.

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arXiv2018

Lindblad-Floquet description of finite-time quantum heat engines

The operation of autonomous finite-time quantum heat engines rely on the existence of a stable limit cycle in which the dynamics becomes periodic. The two main questions that naturally arise are therefore whether such a limit cycle will eventually be reached and, once it has, what is the state of the system within the limit cycle. In this paper we show that the application of Floquet's theory to Lindblad dynamics offers clear answers to both questions. By moving to a generalized rotating frame, we show that it is possible to identify a single object, the Floquet Liouvillian, which encompasses all operating properties of the engine. First, its spectrum dictates the convergence to a limit cycle. And second, the state within the limit cycle is precisely its zero eigenstate, therefore reducing the problem to that of determining the steady-state of a time-independent master equation. To illustrate the usefulness of this theory, we apply it to a harmonic oscillator subject to a time-periodic work protocol and time-periodic dissipation, an open-system generalization of the Ermakov-Lewis theory. The use of this theory to implement a finite-time Carnot engine subject to continuous frequency modulations is also discussed.

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arXiv2018

Exact dynamics of a one dimensional Bose gas in a periodic time-dependent harmonic trap

We study the unitary dynamics of a one-dimensional gas of hard-core bosons trapped into a harmonic potential which varies periodically in time with frequency $ω(t)$. Such periodic systems can be classified into orbits of different monodromies corresponding to two different physical situations, namely the case in which the bosonic cloud remains stable during the time-evolution and the case where it turns out to be unstable. In the present work we derive in the large particle number limit exact results for the stroboscopic evolution of the energy and particle densities in both physical situations.

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arXiv2017

One-dimensional Bose gas driven by a slow time-dependent harmonic trap

We consider the unitary time evolution of a one-dimensional cloud of hard-core bosons loaded on a harmonic trap potential which is slowly released in time with a general ramp $g(t)$. After the identification of a typical length scale $\ell(t)$, related to the time ramp, we focus our attention on the dynamics of the density profile within a first order time-dependent perturbation scheme. In the special case of a linear ramp, we compare the first order predictions to the exact solution obtained through Ermakov-Lewis dynamical invariants. We also obtain an exact analytical solution for a cloud released from a harmonic trap with an amplitude that varies as the inverse of time. In such situation, the typical size of the cloud grows with a power law governed by an exponent that depends continuously on the initial trap frequency. At high enough initial trap amplitude, the exponent acquires an imaginary part that leads to the emergence of a log-periodic modulation of the cloud expansion.

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arXiv2016

Off-equilibrium scaling driven by a time-dependent magnetic field in O(N) vector models

We investigate the off-equilibrium dynamics of a spin system with O($N$) symmetry in $2 < d < 4$ spatial dimensions arising by the presence of a slowly varying time-dependent magnetic field $h(t,t_s) \sim t/t_s$, $t_s$ is a time scale, at the critical temperature $T = T_c$ and below it $T < T_c$. After showing the general theory, we demonstrate the off-equilibrium scaling and we formally compute the correlation functions in the limit of large $N$. We derive the off-equilibrium scaling relations for the hysteresis loop area and for the magnetic work done by the system when the magnetic field $h(t,t_s)$ is varied across the phase transitions cyclically in time. We also investigate the first deviations from the equilibrium behavior in the correlation functions checking the consistence for an exponential approach.

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