arXiv subjects

Maurizio Fagotti

Publications and source records attributed to Maurizio Fagotti.

At least 37 records · Page 2Linked to original sources

arXiv2021

Macroscopic effects of localised measurements in jammed states of quantum spin chains

A quantum jammed state can be seen as a state where the phase space available to particles shrinks to zero, an interpretation quite accurate in integrable systems, where stable quasiparticles scatter elastically. We consider the integrable dual folded XXZ model, which is equivalent to the XXZ model in the limit of large anisotropy. We perform a jamming-breaking localised measurement in a jammed state. We find that jamming is locally restored, but local observables exhibit nontrivial time evolution on macroscopic, ballistic scales, without ever relaxing back to their initial values.

cond-mat.stat-mech↗

arXiv2021

Measurement catastrophe and ballistic spread of charge density with vanishing current

One of the features of many-body quantum systems with Hilbert-space fragmentation is the existence of stationary states manifesting quantum jamming. It was recently shown that these are "states with memory", in which, e.g., measuring a localised observable has everlasting macroscopic effects. We study such a measurement catastrophe with an example that stands out for its clarity. We show in particular that at late times the expectation value of a charge density becomes a nontrivial function of the ratio between distance and time notwithstanding the corresponding current approaching zero.

quant-ph↗

arXiv2021

Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects

We give a pedagogical introduction to the Generalized Hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.

cond-mat.stat-mech↗

arXiv2021

The Folded Spin-1/2 XXZ Model: II. Thermodynamics and Hydrodynamics with a Minimal Set of Charges

We study the (dual) folded spin-1/2 XXZ model in the thermodynamic limit. We focus, in particular, on a class of local macrostates that includes Gibbs ensembles. We develop a thermodynamic Bethe Ansatz description and work out generalised hydrodynamics at the leading order. Remarkably, in the ballistic scaling limit the junction of two local macrostates results in a discontinuity in the profile of essentially any local observable.

cond-mat.stat-mech↗

arXiv2021

The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties

We study an effective Hamiltonian generating time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, it describes an integrable model with local interactions. We solve it completely by means of a coordinate Bethe Ansatz that manifestly breaks the translational symmetry. We demonstrate the existence of exponentially many jammed states and estimate their stability under the leading correction to the effective Hamiltonian. Some ground state properties of the model are discussed.

cond-mat.stat-mech↗

arXiv2020

Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions

We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

cond-mat.stat-mech↗

arXiv2020

Locally quasi-stationary states in noninteracting spin chains

Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including "quantum corrections").

cond-mat.str-el↗

arXiv2019

Entanglement evolution and generalised hydrodynamics: interacting integrable systems

We investigate the dynamics of bipartite entanglement after the sudden junction of two leads in interacting integrable models. By combining the quasiparticle picture for the entanglement spreading with Generalised Hydrodynamics we derive an analytical prediction for the dynamics of the entanglement entropy between a finite subsystem and the rest. We find that the entanglement rate between the two leads depends only on the physics at the interface and differs from the rate of exchange of thermodynamic entropy. This contrasts with the behaviour in free or homogeneous interacting integrable systems, where the two rates coincide.

cond-mat.stat-mech↗

arXiv2019

On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system

We consider the time evolution of a state in an isolated quantum spin lattice system with energy cumulants proportional to the number of the sites $L^d$. We compute the distribution of the eigenvalues of the time averaged state over a time window $[t_0,t_0+t]$ in the limit of large $L$. This allows us to infer the size of a subspace that captures time evolution in $[t_0,t_0+t]$ with an accuracy $1-ε$. We estimate the size to be $ \frac{\sqrt{2\mathfrak{e}_2}}π\mathrm{erf}^{-1}(1-ε) L^{\frac{d}{2}}t$, where $\mathfrak{e}_2$ is the energy variance per site, and $\mathrm{erf}^{-1}$ is the inverse error function.

quant-ph↗

arXiv2018

Entanglement evolution and generalised hydrodynamics: noninteracting systems

The large-scale properties of homogeneous states after quantum quenches in integrable systems have been successfully described by a semiclassical picture of moving quasiparticles. Here we consider the generalisation for the entanglement evolution after an inhomogeneous quench in noninteracting systems in the framework of generalised hydrodynamics. We focus on the protocol where two semi-infinite halves are initially prepared in different states and then joined together, showing that a proper generalisation of the quasiparticle picture leads to exact quantitative predictions. If the system is initially prepared in a quasistationary state, we find that the entanglement entropy is additive and it can be computed by means of generalised hydrodynamics. Conversely, additivity is lost when the initial state is not quasistationary; yet the entanglement entropy in the large-scale limit can be exactly predicted in the quasiparticle picture, provided that the initial state is low entangled.

cond-mat.stat-mech↗

arXiv2017

Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions

We consider the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joint together. At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time- dependent stationary states. The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamic equations and which signal non-ballistic spin transport. We ascribe this phenomenon to the structure of the local conservation laws and make a prediction for the exact location of the jumps. We find that the jumps propagate at the velocities of the heaviest quasiparticles. By means of tDMRG simulations we show that our theory yields a complete description of the long-time steady profiles of conserved charges, currents, and local correlations.

cond-mat.stat-mech↗

arXiv2017

Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result

We derive a Moyal dynamical equation that describes exact time evolution in generic (inhomogeneous) noninteracting spin-chain models. Assuming quasistationarity, we develop a hydrodynamic theory. The question at hand is whether some large-time corrections are captured by higher-order hydrodynamics. We consider in particular the dynamics after that two chains, prepared in different conditions, are joined together. In these situations a light cone, separating regions with macroscopically different properties, emerges from the junction. In free fermionic systems some observables close to the light cone follow a universal behavior, known as Tracy-Widom scaling. Universality means weak dependence on the system's details, so this is the perfect setting where hydrodynamics could emerge. For the transverse-field Ising chain and the XX model, we show that hydrodynamics captures the scaling behavior close to the light cone. On the other hand, our numerical analysis suggests that hydrodynamics fails in more general models, whenever a condition is not satisfied.

cond-mat.stat-mech↗

arXiv2017

Prethermalization at Low Temperature: the Scent of Long-Range Order

Non-equilibrium time evolution in isolated many-body quantum systems generally results in thermalization. However, the relaxation process can be very slow, and quasi-stationary non-thermal plateaux are often observed at intermediate times. The paradigmatic example is a quantum quench in an integrable model with weak integrability breaking; for a long time, the state can not escape the constraints imposed by the approximate integrability. We unveil a new mechanism of prethermalization, based on the presence of a symmetry of the pre-quench Hamiltonian, which is spontaneously broken at zero temperature and is explicitly broken by the post-quench Hamiltonian. The typical time scale of the phenomenon is proportional to the thermal correlation length of the initial state, which diverges as the temperature is lowered. We show that the prethermal quasi-stationary state can be approximated by a mixed state that violates cluster decomposition property. We consider two examples: the transverse-field Ising chain, where the full time evolution is computed analytically, and the (non integrable) ANNNI model, which is investigated numerically.

cond-mat.stat-mech↗

arXiv2016

Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents

We consider the non-equilibrium time evolution of piecewise homogeneous states in the XXZ spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state can be thought as the result of joining chains with different global properties. Through dephasing, at late times the state becomes locally equivalent to a stationary state which explicitly depends on position and time. We propose a kinetic theory of elementary excitations and derive a continuity equation which fully characterizes the thermodynamics of the model. We restrict ourselves to the gapless phase and consider cases where the chains are prepared: 1) at different temperatures; 2) in the ground state of two different models; 3) in the "domain wall" state. We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on TEBD algorithms. As a corollary, we unveil an exact expression for the expectation values of the charge currents in a generic stationary state.

cond-mat.stat-mech↗

arXiv2016

Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents

We review the structure of the conservation laws in noninteracting spin chains and unveil a formal expression for the corresponding currents. We briefly discuss how interactions affect the picture. In the second part, we explore the effects of a localized defect. We show that the emergence of spontaneous currents near the defect undermines any description of the late-time dynamics by means of a stationary state in a finite chain. In particular, the diagonal ensemble does not work. Finally, we provide numerical evidence that simple generic localized defects are not sufficient to induce thermalization.

cond-mat.stat-mech↗

arXiv2016

Determination of the Nonequilibrium Steady State Emerging from a Defect

We consider the non-equilibrium time evolution of a translationally invariant state under a Hamiltonian with a localized defect. We discern the situations where a light-cone spreads out from the defect and separates the system into regions with macroscopically different properties. We identify the light-cone and propose a procedure to obtain a (quasi-)stationary state describing the late time dynamics of local observables. As an explicit example, we study the time evolution generated by the Hamiltonian of the transverse-field Ising chain with a local defect that cuts the interaction between two sites (a quench of the boundary conditions alongside a global quench). We solve the dynamics exactly and show that the late time properties can be obtained with the general method proposed.

cond-mat.stat-mech↗

arXiv2016

Local conservation laws in spin-1/2 XY chains with open boundary conditions

We revisit the conserved quantities of the spin-1/2 XY model with open boundary conditions. In the absence of a transverse field, we find new families of local charges and show that half of the seeming conservation laws are conserved only if the number of sites is odd. In even chains the set of noninteracting charges is abelian, like in the periodic case when the number of sites is odd. In odd chains the set is doubled and becomes non-abelian, like in even periodic chains. The dependence of the charges on the parity of the chain's size undermines the common belief that the thermodynamic limit of diagonal ensembles exists. We consider also the transverse-field Ising chain, where the situation is more ordinary. The generalization to the XY model in a transverse field is not straightforward and we propose a general framework to carry out similar calculations. We conjecture the form of the bulk part of the local charges and discuss the emergence of quasilocal conserved quantities. We provide evidence that in a region of the parameter space there is a reduction of the number of quasilocal conservation laws invariant under chain inversion. As a by-product, we study a class of block-Toeplitz-plus-Hankel operators and identify the conditions that their symbols satisfy in order to commute with a given block-Toeplitz.

cond-mat.stat-mech↗

arXiv2016

Quench dynamics and relaxation in isolated integrable quantum spin chains

We review the dynamics after quantum quenches in integrable quantum spin chains. We give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the description of the steady state by (gen- eralized) Gibbs ensembles. When then turn to general features in the time evolution of local observables after the quench, using a simple model of free fermions as an example. In the second part we present an overview of recent progress in describing quench dynamics in two key paradigms for quantum integrable models, the transverse field Ising chain and the anisotropic spin-1/2 Heisenberg chain.

cond-mat.quant-gas↗