arXiv subjects

Jacopo De Nardis

Publications and source records attributed to Jacopo De Nardis.

At least 55 records · Page 3Linked to original sources

arXiv2023

Squeezed ensembles and anomalous dynamic roughening in interacting integrable chains

It is widely accepted that local subsystems in isolated integrable quantum systems equilibrate to generalized Gibbs ensembles. Here, we demonstrate the failure of canonical generalized thermalization for a particular class of initial states in certain types of interacting integrable models. Particularly, we show that in the easy-axis regime of the quantum XXZ chain, pure non-equilibrium initial states with no magnetic fluctuations instead locally relax to squeezed generalized Gibbs ensembles, referring to exotic equilibrium states governed by non-local equilibrium Hamiltonians with sub-extensive charge fluctuations that violate the self-affine scaling. The behaviour at the isotropic point is exceptional and depends on the initial state. We find that relaxation from the Néel state is governed by extensive fluctuations and a super-diffusive dynamical exponent compatible with the Kardar-Parisi-Zhang universality. On the other hand, there are other non-fluctuating initial states that display diffusive scaling. Our predictions can be directly tested in state-of-the-art cold atomic experimental settings.

cond-mat.quant-gas↗

arXiv2023

Generalized Deep Thermalization for Free Fermions

In non-interacting isolated quantum systems out of equilibrium, local subsystems typically relax to non-thermal stationary states. In the standard framework, information on the rest of the system is discarded, and such states are described by a Generalized Gibbs Ensemble (GGE), maximizing the entropy while respecting the constraints imposed by the local conservation laws. Here we show that the latter also completely characterize a recently introduced projected ensemble (PE), constructed by performing projective measurements on the rest of the system and recording the outcomes. By focusing on the time evolution of fermionic Gaussian states in a tight-binding chain, we put forward a random ensemble constructed out of the local conservation laws, which we call deep GGE (dGGE). For infinite-temperature initial states, we show that the dGGE coincides with a universal Haar random ensemble on the manifold of Gaussian states. For both infinite and finite temperatures, we use a Monte Carlo approach to test numerically the predictions of the dGGE against the PE. We study in particular the $k$-moments of the state covariance matrix and the entanglement entropy, finding excellent agreement. Our work provides a first step towards a systematic characterization of projected ensembles beyond the case of chaotic systems and infinite temperatures.

quant-ph↗

arXiv2023

Purification Timescales in Monitored Fermions

We investigate the crucial role played by a global symmetry in the purification timescales and the phase transitions of monitored free fermionic systems separating a mixed and a pure phase. Concretely, we study Majorana and Dirac circuits with $\mathbb{Z}_2$ and U(1) symmetries, respectively. In the first case, we demonstrate the mixed phase of $L$ sites has a purification timescale that scales as $τ_P\sim L \ln L $. At $1\ll t\ll τ_P$ the system attains a finite residual entropy, that we use to unveil the critical properties of the purification transition. In contrast, free fermions with U(1) manifest a sublinear purification timescale at any measurement rate and an apparent Berezinskii-Kosterlitz-Thouless criticality. We find the mixed phase is characterized by $τ_P\sim L^{α(p)}$, with a continuously varying exponent $α(p)<1$.

cond-mat.stat-mech↗

arXiv2023

A dynamical theory for one-dimensional fermions with strong two-body losses: universal non-Hermitian Zeno physics and spin-charge separation

We study an interacting one-dimensional gas of spin-1/2 fermions with two-body losses. The dynamical phase diagram that characterises the approach to the stationary state displays a wide quantum-Zeno region, identified by a peculiar behaviour of the lowest eigenvalues of the associated non-Hermitian Hamiltonian. We characterise the universal dynamics of this Zeno regime using an approximation scheme based on a effective decoupling of charge and spin degrees of freedom, where the latter effectively evolve in a non-Markovian way according to a non-Hermitian Heisenberg Hamiltonian. We present detailed results for the time evolution from initial states with one particle per site with either incoherent and antiferromagnetic spin order, showing how the two non-equilibrium evolutions build up drastically different charge correlations.

cond-mat.quant-gas↗

arXiv2022

Hydrodynamic gauge fixing and higher order hydrodynamic expansion

Hydrodynamics is a powerful emergent theory for the large-scale behaviours in many-body systems, quantum or classical. It is a gradient series expansion, where different orders of spatial derivatives provide an effective description on different length scales. We here report the first general derivation of third-order, or "dispersive", terms in the hydrodynamic expansion. We obtain fully general Kubo-like expressions for the associated hydrodynamic coefficients, and we determine their expressions in quantum integrable models, introducing in this way purely quantum higher-order terms into generalised hydrodynamics. We emphasise the importance of hydrodynamic gauge fixing at diffusive order, where we claim that it is parity-time-reversal, and not time-reversal, invariance that is at the source of Einstein's relation, Onsager's reciprocal relations, the Kubo formula and entropy production. At higher hydrodynamic orders we introduce a more general, n-th order "symmetric" gauge, which we show implies the validity of the higher-order hydrodynamic description.

cond-mat.stat-mech↗

arXiv2022

Hydrodynamic relaxation of spin helices

Motivated by recent cold atom experiments, we study the relaxation of spin helices in quantum XXZ spin chains. The experimentally observed relaxation of spin helices follows scaling laws that are qualitatively different from linear-response transport. We construct a theory of the relaxation of helices, combining generalized hydrodynamics (GHD) with diffusive corrections and the local density approximation. Although helices are far from local equilibrium (so GHD need not apply a priori), our theory reproduces the experimentally observed relaxational dynamics of helices. In particular, our theory explains the existence of temporal regimes with apparent anomalous diffusion, as well as the asymmetry between positive and negative anisotropy regimes.

cond-mat.quant-gas↗

arXiv2021

Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains

We address spin transport in the easy-axis Heisenberg spin chain subject to integrability-breaking perturbations. We find that spin transport is subdiffusive with dynamical exponent $z=4$ up to a timescale that is parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for large finite anisotropy, one eventually recovers diffusion at late times, but with a diffusion constant independent of the strength of the integrability breaking perturbation. We provide numerical evidence for these findings, and explain them by adapting the generalized hydrodynamics framework to nearly integrable dynamics. Our results show that the diffusion constant of near-integrable interacting spin chains is generically not perturbative in the integrability breaking strength.

cond-mat.stat-mech↗

arXiv2021

Diffusive Hydrodynamics of Inhomogenous Hamiltonians

We derive a large-scale hydrodynamic equation, including diffusive and dissipative effects, for systems with generic static position-dependent driving forces coupling to local conserved quantities. We show that this equation predicts entropy increase and thermal states as the only stationary states. The equation applies to any hydrodynamic system with any number of local, PT-symmetric conserved quantities, in arbitrary dimension. It is fully expressed in terms of elements of an extended Onsager matrix. In integrable systems, this matrix admits an expansion in the density of excitations. We evaluate exactly its 2-particle-hole contribution, which dominates at low density, in terms of the scattering phase and dispersion of the quasiparticles, giving a lower bound for the extended Onsager matrix and entropy production. We conclude with a molecular dynamics simulation, demonstrating thermalisation over diffusive time scales in the Toda interacting particle model with an inhomogeneous energy field.

cond-mat.stat-mech↗

arXiv2021

Stability of superdiffusion in nearly integrable spin chains

Superdiffusive finite-temperature transport has been recently observed in a variety of integrable systems with nonabelian global symmetries. Superdiffusion is caused by giant Goldstone-like quasiparticles stabilized by integrability. Here, we argue that these giant quasiparticles remain long-lived, and give divergent contributions to the low-frequency conductivity $σ(ω)$, even in systems that are not perfectly integrable. We find, perturbatively, that $ σ(ω) \sim ω^{-1/3}$ for translation-invariant static perturbations that conserve energy, and $σ(ω) \sim | \log ω|$ for noisy perturbations. The (presumable) crossover to regular diffusion appears to lie beyond low-order perturbation theory. By contrast, integrability-breaking perturbations that break the nonabelian symmetry yield conventional diffusion. Numerical evidence supports the distinction between these two classes of perturbations.

cond-mat.stat-mech↗

arXiv2021

Variational optimization of continuous matrix product states

Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial dimension. Unlike the quantum spin case however, for which the density matrix renormalization group and related matrix product state algorithms provide robust algorithms for optimizing the variational states, the optimization of cMPS for systems with inhomogeneous external potentials has been problematic. We resolve this problem by constructing a piecewise linear parameterization of the underlying matrix-valued functions, which enables the calculation of the exact reduced density matrices everywhere in the system by high-order Taylor expansions. This turns the variational cMPS problem into a variational algorithm from which both the energy and its backwards derivative can be calculated exactly and at a cost that scales as the cube of the bond dimension. We illustrate this by finding ground states of interacting bosons in external potentials, and by calculating boundary or Casimir energy corrections of continuous many-body systems with open boundary conditions.

quant-ph↗

arXiv2021

Correlation functions and transport coefficients in generalised hydrodynamics

We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well as linear and nonlinear response on top of equilibrium and non-equilibrium states. We consider the problems from the complementary perspectives of the general hydrodynamic theory of many-body systems, including hydrodynamic projections, and form-factor expansions in integrable models, and show how they provide a comprehensive and consistent set of exact methods to extract large scale behaviours. Finally, we overview various applications in integrable spin chains and field theories.

cond-mat.stat-mech↗

arXiv2020

Superuniversality of superdiffusion

Anomalous finite-temperature transport has recently been observed in numerical studies of various integrable models in one dimension; these models share the feature of being invariant under a continuous non-abelian global symmetry. This work offers a comprehensive group-theoretic account of this elusive phenomenon. For an integrable quantum model invariant under a global non-abelian simple Lie group $G$, we find that finite-temperature transport of Noether charges associated with symmetry $G$ in thermal states that are invariant under $G$ is universally superdiffusive and characterized by dynamical exponent $z = 3/2$. This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: we accordingly dub it as superuniversal. The anomalous transport behavior is attributed to long-lived giant quasiparticles dressed by thermal fluctuations. We provide an algebraic viewpoint on the corresponding dressing transformation and elucidate formal connections to fusion identities amongst the quantum-group characters. We identify giant quasiparticles with nonlinear soliton modes of classical field theories that describe low-energy excitations above ferromagnetic vacua. Our analysis of these field theories also provides a complete classification of the low-energy (i.e., Goldstone-mode) spectra of quantum isotropic ferromagnetic chains.

cond-mat.stat-mech↗

arXiv2020

Superdiffusion from emergent classical solitons in quantum spin chains

Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. Using a kinetic theory of transport, we compute the KPZ coupling strength for the Heisenberg chain as a function of temperature, directly from microscopics; the results agree well with density-matrix renormalization group simulations. We establish a rigorous quantum-classical correspondence between the "giant quasiparticles" that govern superdiffusion and solitons in the classical continuous Landau-Lifshitz ferromagnet. We conclude that KPZ universality has the same origin in classical and quantum integrable isotropic magnets: a finite-temperature gas of low-energy classical solitons.

cond-mat.stat-mech↗

arXiv2020

Thermalisation of a trapped one-dimensional Bose gas via diffusion

For a decade the fate of a one-dimensional gas of interacting bosons in an external trapping potential remained mysterious. We here show that whenever the underlying integrability of the gas is broken by the presence of the external potential, the inevitable diffusive rearrangements between the quasiparticles, quantified by the diffusion constants of the gas, eventually lead the system to thermalise at late times. We show that the full thermalising dynamics can be described by the generalised hydrodynamics with diffusion and force terms, and we compare these predictions with numerical simulations. Finally, we provide an explanation for the slow thermalisation rates observed in numerical and experimental settings: the hydrodynamics of integrable models is characterised by a continuity of modes, which can have arbitrarily small diffusion coefficients. As a consequence, the approach to thermalisation can display pre-thermal plateau and relaxation dynamics with long polynomial finite-time corrections.

cond-mat.quant-gas↗

arXiv2020

Diffusion from Convection

We introduce non-trivial contributions to diffusion constant in generic many-body systems arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in the vicinity of equilibrium states in terms of powers of local and quasi-local conserved quantities. We show that only the second-order terms in this expansion carry a finite contribution to diffusive spreading. Our formalism implies that whenever there are at least two coupled modes with degenerate group velocities, the system behaves super-diffusively, in accordance with the non-linear fluctuating hydrodynamics theory. Finally, we show that our expression saturates the exact diffusion constants in quantum and classical interacting integrable systems, providing a general framework to derive these expressions.

cond-mat.stat-mech↗

arXiv2020

Real-time scattering of interacting quasiparticles in quantum spin chains

We develop a method based on tensor networks to create localized single particle excitations on top of strongly-correlated quantum spin chains. In analogy to the problem of creating localized Wannier modes, this is achieved by optimizing the gauge freedom of momentum excitations on top of matrix product states. The corresponding wavepackets propagate almost dispersionless. The time-dependent variational principle is used to scatter two such wavepackets, and we extract the phase shift from the collision data. We also study reflection and transmission coefficients of a wavepacket impinging on an impurity.

cond-mat.str-el↗

arXiv2020

Generalised hydrodynamics with dephasing noise

We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the system based on a hydrodynamic formulation. This results in an additional term to the standard generalized hydrodynamics theory describing diffusive dynamics in the momentum space of the quasiparticles of the system, with a time- and momentum-dependent diffusion constant. Our analytical predictions are then benchmarked in the classical limit by comparison with a microscopic simulation of the non-linear Schrodinger equation, showing perfect agreement. In the quantum case, our predictions agree with state-of-the-art numerical simulations of the anisotropic Heisenberg spin in the accessible regime of times and with bosonization predictions in the limit of small dephasing times and temperatures.

cond-mat.stat-mech↗

arXiv2020

Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies

We report a systematic study of finite-temperature spin transport in quantum and classical one-dimensional magnets with isotropic spin interactions, including both integrable and non-integrable models. Employing a phenomenological framework based on a generalized Burgers' equation in a time-dependent stochastic environment, we identify four different universality classes of spin fluctuations. These comprise, aside from normal spin diffusion, three types of superdiffusive transport: the KPZ universality class and two distinct types of anomalous diffusion with multiplicative logarithmic corrections. Our predictions are supported by extensive numerical simulations on various examples of quantum and classical chains. Contrary to common belief, we demonstrate that even non-integrable spin chains can display a diverging spin diffusion constant at finite temperatures.

cond-mat.stat-mech↗