arXiv subjects

Giuseppe E. Santoro

Publications and source records attributed to Giuseppe E. Santoro.

At least 55 records · Page 3Linked to original sources

arXiv2016

Entanglement entropy in a periodically driven Ising chain

In this work we study the entanglement entropy of a uniform quantum Ising chain in transverse field undergoing a periodic driving of period $τ$ . By means of Floquet theory we show that, for any subchain, the entanglement entropy tends asymptotically to a value $τ$ - periodic in time. We provide a semi-analytical formula for the leading term of this asymptotic regime: It is constant in time and obeys a volume law. The entropy in the asymptotic regime is always smaller than the thermal one: because of integrability the system locally relaxes to a Generalized Gibbs Ensemble (GGE) density matrix. The leading term of the asymptotic entanglement entropy is completely determined by this GGE density matrix. Remarkably, the asymptotic entropy shows marked features in correspondence to some non-equilibrium quantum phase transitions undergone by a Floquet state analog of the ground state.

quant-ph↗

arXiv2016

CDW slips and giant frictional dissipation peaks at the NbSe$_2$ surface

Accessing, controlling and understanding nanoscale friction and dissipation is a crucial issue in nanotechnology, where moving elements are central. Recently, ultra-sensitive noncontact pendulum Atomic Force Microscope (AFM) succeeded in detecting the electronic friction drop caused by the onset of superconductivity in Nb, raising hopes that a wider variety of mechanisms of mechanical dissipation arising from electron organization into different collective phenomena will become accessible through this unconventional surface probe. Among them, the driven phase dynamics of charge-density-waves (CDWs) represents an outstanding challenge as a source of dissipation. Here we report a striking multiplet of AFM dissipation peaks arising at nanometer distances above the surface of NbSe$_2$ - a layered compound exhibiting an incommensurate CDW. Each peak appears at a well defined tip-surface interaction force of the order of a nN, and persists until T=70K where CDW short-range order is known to disappear. A theoretical model is presented showing that the peaks are connected to tip-induced local 2$π$ CDW phase slips. Under the attractive potential of the approaching tip, the local CDW surface phase landscape deforms continuously until a series of 2$π$ jumps occur between different values of the local phase. As the tip oscillates to and fro, each slip gives rise to a hysteresis cycle, appearing at a selected distance, the dissipation corresponding to "pumping" in and out a local slip in the surface CDW phase of NbSe$_2$.

cond-mat.mes-hall↗

arXiv2016

Quantum annealing speedup over simulated annealing on random Ising chains

We show clear evidence of a quadratic speedup of a quantum annealing (QA) Schroedinger dynamics over a Glauber master-equation simulated annealing (SA) for a random Ising model in one dimension, via an equal-footing exact deterministic dynamics of the Jordan-Wigner fermionized problems. This is remarkable, in view of the arguments of Katzgraber et al., PRX 4, 021008 (2014), since SA does not encounter any phase transition, while QA does. We also find a second remarkable result: that a "quantum-inspired" imaginary-time Schroedinger QA provides a further exponential speedup, i.e., an asymptotic residual error decreasing as a power-law $τ^{-μ}$ of the annealing time $τ$.

quant-ph↗

arXiv2015

Asymptotic work statistics of periodically driven Ising chains

We study the work statistics of a periodically-driven integrable closed quantum system, addressing in particular the role played by the presence of a quantum critical point. Taking the example of a one-dimensional transverse Ising model in the presence of a spatially homogeneous but periodically time-varying transverse field of frequency $ω_0$, we arrive at the characteristic cumulant generating function $G(u)$, which is then used to calculate the work distribution function $P(W)$. By applying the Floquet theory we show that, in the infinite time limit, $P(W)$ converges, starting from the initial ground state, towards an asymptotic steady state value whose small-$W$ behaviour depends only on the properties of the small-wave-vector modes and on a few important ingredients: the time-averaged value of the transverse field, $h_0$, the initial transverse field, $h_{\rm i}$, and the equilibrium quantum critical point $h_c$, which we find to generate a sequence of non-equilibrium critical points $h_{*l}=h_c+lω_0/2$, with $l$ integer. When $h_{\rm i}\neq h_c$, we find a "universal" edge singularity in $P(W)$ at a threshold value of $W_{\rm th}=2|h_{\rm i}-h_c|$ which is entirely determined by $h_{\rm i}$. The form of that singularity --- Dirac delta derivative or square root --- depends on $h_0$ being or not at a non-equilibrium critical point $h_{*l}$. On the contrary, when $h_{\rm i}=h_c$, $G(u)$ decays as a power-law for large $u$, leading to different types of edge singularity at $W_{\rm th}=0$. Generalizing our calculations to the case in which we initialize the system in a finite temperature density matrix, the irreversible entropy generated by the periodic driving is also shown to reach a steady state value in the infinite time limit.

quant-ph↗

arXiv2015

Subharmonic Shapiro steps of sliding colloidal monolayers in optical lattices

We investigate theoretically the possibility to observe dynamical mode locking, in the form of Shapiro steps, when a time-periodic potential or force modulation is applied to a two-dimensional (2D) lattice of colloidal particles that are dragged by an external force over an optically generated periodic potential. Here we present realistic molecular dynamics simulations of a 2D experimental setup, where the colloid sliding is realized through the motion of soliton lines between locally commensurate patches or domains, and where the Shapiro steps are predicted and analyzed. Interestingly, the jump between one step and the next is seen to correspond to a fixed number of colloids jumping from one patch to the next, across the soliton line boundary, during each AC cycle. In addition to ordinary "integer" steps, coinciding here with the synchronous rigid advancement of the whole colloid monolayer, our main prediction is the existence of additional smaller "subharmonic" steps due to localized solitonic regions of incommensurate layers executing synchronized slips, while the majority of the colloids remains pinned to a potential minimum. The current availability and wide parameter tunability of colloid monolayers makes these predictions potentially easy to access in an experimentally rich 2D geometrical configuration.

cond-mat.mes-hall↗

arXiv2015

Thermalization in a periodically driven fully-connected quantum Ising ferromagnet

By means of a Floquet analysis, we study the quantum dynamics of a fully connected Lipkin-Ising ferromagnet in a periodically driven transverse field showing that thermalization in the steady state is intimately connected to properties of the $N\to \infty$ classical Hamiltonian dynamics. When the dynamics is ergodic, the Floquet spectrum obeys a Wigner-Dyson statistics and the system satisfies the eigenstate thermalization hypothesis (ETH): Independently of the initial state, local observables relax to the $T=\infty$ thermal value, and Floquet states are delocalized in the Hilbert space. On the contrary, if the classical dynamics is regular no thermalization occurs. We further discuss the relationship between ergodicity and dynamical phase transitions, and the relevance of our results to other fully-connected periodically driven models (like the Bose-Hubbard), and possibilities of experimental realization in the case of two coupled BEC.

cond-mat.stat-mech↗

arXiv2015

How to calculate quantum quench distributions with a weighted Wang-Landau Monte Carlo

We present here an extension of the Wang-Landau Monte Carlo method which allows us to get very accurate estimates of the full probability distributions of several observables after a quantum quench for large systems, whenever the relevant matrix elements are calculable, but the full exponential complexity of the Hilbert space would make an exhaustive enumeration impossible beyond very limited sizes. We apply this method to quenches of free-fermion models with disorder, further corroborating the fact that a generalized Gibbs ensemble fails to capture the long-time average of many-body operators when disorder is present.

cond-mat.stat-mech↗

arXiv2014

Non-contact dissipation on the surface of charge density wave materials

Bulk electrical dissipation caused by charge-density-wave (CDW) depinning and sliding is a classic subject. We present a novel local, nanoscale mechanism describing the occurrence of mechanical dissipation peaks in the dynamics of an atomic force microscope tip oscillating above the surface of a CDW material. Local surface 2$π$ slips of the CDW phase are predicted to take place giving rise to mechanical hysteresis and large dissipation at discrete tip surface distances. The results of our static and dynamic numerical simulations are believed to be relevant to recent experiments on NbSe$_2$; other candidate systems in which similar effects should be observable are also discussed.

cond-mat.mes-hall↗

arXiv2014

Charge density wave surface phase slips and non-contact nanofriction

cond-mat.mes-hall↗

arXiv2014

Loschmidt echo and dynamical fidelity in periodically driven quantum systems

We study the dynamical fidelity $\mathcal{F} (t)$ and the Loschmidt echo $\mathcal{L} (t)$, following a periodic driving of the transverse magnetic field of a quantum Ising chain (back and forth across the quantum critical point) by calculating the overlap between the initial ground state and the state reached after $n$ periods $τ$. We show that $\log{\mathcal{F}}(nτ)/L$ (the logarithm of the fidelity per-site) reaches a steady value in the asymptotic limit $n\to \infty$, and we derive an exact analytical expression for this quantity. Remarkably, the steady state value of $[\log{\mathcal{F}}(nτ\to \infty)]/L$ shows memory of non-trivial phase information which is instead hidden in the case of thermodynamic quantities; this conclusion, moreover, is not restricted to 1-dimensional models.

quant-ph↗

arXiv2013

Linear response as a singular limit for a periodically driven closed quantum system

We address the issue of the validity of linear response theory for a closed quantum system subject to a periodic external driving. Linear response theory (LRT) predicts energy absorption at frequencies of the external driving where the imaginary part of the appropriate response function is different from zero. Here we show that, for a fairly general non-linear many-body system on a lattice subject to an extensive perturbation, this approximation should be expected to be valid only up to a time $t^*$ depending on the strength of the driving, beyond which the true coherent Schrödinger evolution departs from the linear response prediction and the system stops absorbing energy form the driving. We exemplify this phenomenon in detail with the example of a quantum Ising chain subject to a time-periodic modulation of the transverse field, by comparing an exact Floquet analysis with the standard results of LRT. In this context, we also show that if the perturbation is just local, the system is expected in the thermodynamic limit to keep absorbing energy, and LRT works at all times. We finally argue more generally the validity of the scenario presented for closed quantum many-body lattice systems with a bound on the energy-per-site spectrum, discussing the experimental relevance of our findings in the context of cold atoms in optical lattices and ultra-fast spectroscopy experiments.

quant-ph↗

arXiv2013

Relaxation and Thermalization after a Quantum Quench: Why Localization is Important

We study the unitary dynamics and the thermalization properties of free-fermion-like Hamiltonians after a sudden quantum quench, extending the results of S. Ziraldo et al. [Phys. Rev. Lett. 109, 247205 (2012)]. With analytical and numerical arguments, we show that the existence of a stationary state and its description with a generalized Gibbs ensemble (GGE) depend crucially on the observable considered (local versus extensive) and on the localization properties of the final Hamiltonian. We present results on two one-dimensional (1D) models, the disordered 1D fermionic chain with long-range hopping and the disordered Ising/XY spin chain. We analytically prove that, while time averages of one-body operators are perfectly reproduced by GGE (even for finite-size systems, if time integrals are extended beyond revivals), time averages of many-body operators might show clear deviations from the GGE prediction when disorder-induced localization of the eigenstates is at play.

cond-mat.dis-nn↗

arXiv2012

Relaxation Dynamics of Disordered Spin Chains: Localization and the Existence of a Stationary State

We study the unitary relaxation dynamics of disordered spin chains following a sudden quench of the Hamiltonian. We give analytical arguments, corroborated by specific numerical examples, to show that the existence of a stationary state depends crucially on the spectral and localization properties of the final Hamiltonian, and not on the initial state. We test these ideas on integrable one-dimensional models of the Ising or XY class, but argue more generally on their validity for more complex (nonintegrable) models.

cond-mat.dis-nn↗

arXiv2012

Periodic steady state and interference in a periodically driven quantum system

We study the coherent dynamics of a quantum many-body system subject to a time-periodic driving. We argue that in many cases, destructive interference in time makes most of the quantum averages time-periodic, after an initial transient. We discuss in detail the case of a quantum Ising chain periodically driven across the critical point, finding that, as a result of quantum coherence, the system never reaches an infinite temperature state. Floquet resonance effects are moreover observed in the frequency dependence of the various observables, which display a sequence of well-defined peaks or dips. Extensions to non-integrable systems are discussed.

cond-mat.stat-mech↗

arXiv2012

Matrix Product State representation for Slater Determinants and Configuration Interaction States

Slater determinants are product states of filled quantum fermionic orbitals. When they are expressed in a configuration space basis chosen a priori, their entanglement is bound and controlled. This suggests that an exact representation of Slater determinants as finitely-correlated states is possible. In this paper we analyze this issue and provide an exact Matrix Product representation for Slater determinant states. We also argue possible meaningful extensions that embed more complex configuration interaction states into the description.

quant-ph↗

arXiv2012

Many-body localization and thermalization in the full probability distribution function of observables

We investigate the relation between thermalization following a quantum quench and many-body localization in quasiparticle space in terms of the long-time full distribution function of physical observables. In particular, expanding on our recent work [E. Canovi {\em et al.}, Phys. Rev. B {\bf 83}, 094431 (2011)], we focus on the long-time behavior of an integrable XXZ chain subject to an integrability-breaking perturbation. After a characterization of the breaking of integrability and the associated localization/delocalization transition using the level spacing statistics and the properties of the eigenstates, we study the effect of integrability-breaking on the asymptotic state after a quantum quench of the anisotropy parameter, looking at the behavior of the full probability distribution of the transverse and longitudinal magnetization of a subsystem. We compare the resulting distributions with those obtained in equilibrium at an effective temperature set by the initial energy. We find that, while the long time distribution functions appear to always agree {\it qualitatively} with the equilibrium ones, {\it quantitative} agreement is obtained only when integrability is fully broken and the relevant eigenstates are diffusive in quasi-particle space.

cond-mat.stat-mech↗

arXiv2011

Crossover from adiabatic to antiadiabatic quantum pumping with dissipation

Quantum pumping, in its different forms, is attracting attention from different fields, from fundamental quantum mechanics, to nanotechnology, to superconductivity. We investigate the crossover of quantum pumping from the adiabatic to the anti-adiabatic regime in the presence of dissipation, and find general and explicit analytical expressions for the pumped current in a minimal model describing a system with the topology of a ring forced by a periodic modulation of frequency omega. The solution allows following in a transparent way the evolution of pumped DC current from much smaller to much larger omega values than the other relevant energy scale, the energy splitting introduced by the modulation. We find and characterize a temperature-dependent optimal value of the frequency for which the pumped current is maximal.

quant-ph↗

arXiv2011

Applicability of the generalized Gibbs ensemble after a quench in the quantum Ising chain

We investigate the out-of-equilibrium dynamics of the one-dimensional quantum Ising model after a sudden quench of the transverse magnetic field. While for a translationally invariant system the statistical description of the asymptotic order parameter correlations after the quench can be performed in terms of the generalized Gibbs ensemble, we show that a breaking of translational invariance, e.g., by perturbing the boundary conditions, disrupts its validity. This effect, which of course vanishes in the thermodynamic limit, is shown to be very important in the presence of disorder.

cond-mat.stat-mech↗