Off-equilibrium relaxational dynamics with improved Ising Hamiltonian

We study the off-equilibrium relaxational dynamics at criticality in the three-dimensional Blume-Capel model whose static critical behaviour belongs to the 3d-Ising universality class. Using "improved" Hamiltonian (the leading corrections to scaling have vanishing amplitude) we perform Monte Carlo simulations of the relaxational dynamics after a quench from $T=\infty$ to $T_c$. Analysing the off-equilibrium dynamics at $T_c$ we obtain an estimate of the dynamical critical exponent $z=2.020(8)$ that is perfectly consistent with the Field Theory predictions.Comment: 14 pages, 7 figures, references added, to appear in J. Stat. Mec

Relaxation of the order-parameter statistics in the Ising quantum chain

We study the out-of-equilibrium probability distribution function of the local order parameter in the transverse field Ising quantum chain. Starting from a fully polarised state, the relaxation of the ferromagnetic order is analysed: we obtain a full analytical description of the late-time stationary distribution by means of a remarkable relation to the partition function of a 3-states classical model. Accordingly, depending on the phase whereto the post-quench Hamiltonian belongs, the probability distribution may locally retain memories of the initial long-range order. When quenching deep in the broken-symmetry phase, we show that the stationary order-parameter statistics is indeed related to that of the ground state. We highlight this connection by inspecting the ground-state equilibrium properties, where we propose an effective description based on the block-diagonal approximation of the n-point spin correlation functions

Critical quench dynamics in confined systems

We analyze the coherent quantum evolution of a many-particle system after slowly sweeping a power-law confining potential. The amplitude of the confining potential is varied in time along a power-law ramp such that the many-particle system finally reaches or crosses a critical point. Under this protocol we derive general scaling laws for the density of excitations created during the non-adiabatic sweep of the confining potential. It is found that the mean excitation density follows an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential. We confirm our scaling laws by first order adiabatic calculation and exact results on the Ising quantum chain with a varying transverse field.Comment: To appear in Phys. Rev. Let

Entanglement spreading and quasiparticle picture beyond the pair structure

The quasi-particle picture is a powerful tool to understand the entanglement spreading in many-body quantum systems after a quench. As an input, the structure of the excitations' pattern of the initial state must be provided, the common choice being pairwise-created excitations. However, several cases exile this simple assumption. In this work, we investigate weakly-interacting to free quenches in one dimension. This results in a far richer excitations' pattern where multiplets with a larger number of particles are excited. We generalize the quasi-particle ansatz to such a wide class of initial states, providing a small-coupling expansion of the Renyi entropies. Our results are in perfect agreement with iTEBD numerical simulations

Quantum Magic via Perfect Sampling of Matrix Product States

We introduce a novel breakthrough approach to evaluate the nonstabilizerness of an $N$-qubits Matrix Product State (MPS) with bond dimension $\chi$. In particular, we consider the recently introduced Stabilizer R\'enyi Entropies (SREs). We show that the exponentially hard evaluation of the SREs can be achieved by means of a simple perfect sampling of the many-body wave function over the Pauli string configurations. The MPS representation enables such a sampling in an efficient way with a computational cost $O(N\chi^3)$, no matter the R\'enyi index $n\in\mathbb{R}^{+}$. The accuracy, being size-independent, can be arbitrarily improved with the number of samples. We benchmark our method over randomly generated magic states, as well as in the ground-state of the quantum Ising chain. Exploiting the extremely favourable scaling, we easily have access to the non-equilibrium dynamics of the SREs after a quantum quench

Thermalization of long range Ising model in different dynamical regimes: a full counting statistics approach

We study thermalization of transverse field Ising chain with power law decaying interaction $\sim 1/r^{\alpha}$ following a global quantum quench of the transverse field to two different dynamical regimes. We quantify the thermalization behavior by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the Gibbs canonical ensemble (GCE). To this end, we use matrix product state (MPS) based time dependent variational principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all the interaction strength $\alpha$ considered whereas thermalization occurs in the region with weak confinement.Comment: 23 pages, 5 figures update1: changed some wording

Dinamica di rilassamento fuori equilibrio nel modello di Ising

In questo lavoro ci siamo occupati della dinamica di rilassamento nel modello di Ising nei primi istanti temporali dell’evoluzione (dinamica critica fuori equilibrio): per fissare le idee, immaginiamo di effettuare sul sistema in esame un repentino abbassamento di temperatura da T = ∞ a T = Tc. Dal punto di vista teorico, il comportamento fuori equilibrio è indotto dalle condizioni iniziali e non è generico. Difatti, se il raffreddamento viene fatto ad una temperatura appena al di sotto della temperatura critica il sistema termalizza in un tempo finito t_eq ∼ ξ^z (essendo z l’esponente critico associato alla dinamica) e raggiunge uno stato di equilibrio caratterizzato dalla funzione di distribuzione canonica associata all’hamiltoniana mesoscopica H. Al punto critico, viceversa, gli effetti delle condizioni iniziali persistono per un tempo infinito e danno origine ad un comportamento critico fuori equilibrio che presenta alcune caratteristiche universali. Abbiamo studiato dunque la dinamica di puro rilassamento (modello A) alla criticità in un sistema di Ising tridimensionale; in particolare si è usato una hamiltoniana tipo Blume-Capel con parametri “improved” per ridurre al minimo le correzioni allo scaling. Ciò ha permesso di effettuare simulazioni Monte Carlo su reticoli cubici di dimensione relativamente piccola (L = 32, 48, 64, 96) in corrispondenza dei parametri critici βc = 0.3856717, D∗ = 0.641. Per ciascun reticolo, a seconda delle dimensioni, abbiamo effettuato una media su N = 100000 − 200000 catene di Markov differenti; per ciascuna di tali catene siamo partiti da configurazioni disordinate (T = ∞) differenti e abbiamo effettuato 400 sweeps reticolari (700 per L=96) usando l’algoritmo Metropolis. Il sito reticolare sul quale effettuare la proposta di upgrade viene scelto usando il checkerboard. Così facendo, abbiamo osservato l’andamento temporale nei primi stadi della dinamica (fuori equilibrio) della suscettività χ(t, L) e della lunghezza di correlazione ξ (t, L)

Real-time-dynamics quantum simulation of (1+1)-dimensional lattice QED with Rydberg atoms

We show how to implement a Rydberg-atom quantum simulator to study the nonequilibrium dynamics of an Abelian (1+1)-dimensional lattice gauge theory. The implementation locally codifies the degrees of freedom of a Z3 gauge field, once the matter field is integrated out by means of the Gauss local symmetries. The quantum simulator scheme is based on currently available technology and thus is scalable to considerable lattice sizes. It allows, within experimentally reachable regimes, us to explore different string dynamics and to infer information about the Schwinger U(1) model

Quantum quench in a harmonically trapped one-dimensional Bose gas

We study the nonequilibrium dynamics of a one-dimensional Bose gas trapped by a harmonic potential for a quench from zero to infinite interaction. The different thermodynamic limits required for the equilibrium pre- and post-quench Hamiltonians are the origin of a few unexpected phenomena that have no counterparts in the translational-invariant setting. We find that the dynamics is perfectly periodic with breathing time related to the strength of the trapping potential. For very short times, we observe a sudden expansion leading to an extreme dilution of the gas and to the emergence of slowly decaying tails in the density profile. The haste of the expansion induces an undertow-like effect with a pronounced local minimum of the density at the center of the trap. At half period there is a refocusing phenomenon characterized by a sharp central peak of the density, juxtaposed to algebraically decaying tails. We finally show that the time-averaged density is correctly captured by a generalized Gibbs ensemble built with the conserved mode occupations

Work statistics, quantum signatures and enhanced work extraction in quadratic fermionic models

In quadratic fermionic models we determine a quantum correction to the work statistics after a sudden and a time-dependent driving. Such a correction lies in the non-commutativity of the initial quantum state and the time-dependent Hamiltonian, and is revealed via the Kirkwood-Dirac quasiprobability (KDQ) approach to two-times correlators. Thanks to the latter, one can assess the onset of non-classical signatures in the KDQ distribution of work, in the form of negative and complex values that no classical theory can reveal. By applying these concepts on the one-dimensional transverse-field Ising model, we relate non-classical behaviours of the KDQ statistics of work in correspondence of the critical points of the model. Finally, we also prove the enhancement of the extracted work in non-classical regimes where the non-commutativity takes a role