Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

Caneva, Tommaso; Fazio, Rosario; Santoro, Giuseppe E.

doi:10.1103/physrevb.78.104426

Cited by 95 publications

(113 citation statements)

References 57 publications

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“…However, at least in the static case, the behaviour of entanglement (and more specifically of entanglement entropy) has an universal character so that it can be used as an estimator of quantum correlations 10 and to detect as well as to classify quantum phase transitions also in fully interacting models [11][12][13][14][15][16] . Thus, it is natural to ask whether the dynamical behaviour of a closed quantum system, especially when crossing a phase transition, can be described by looking at the dynamics of entanglement entropy and entanglement spectrum, a topic on which there are only a few general results [17][18][19][20] .…”

Section: Introductionmentioning

confidence: 99%

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

et al. 2014

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We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the transversefield Ising model with a time-dependent magnetic field, which is linearly tuned on a time scale τ . The time evolution of the entanglement entropy displays different regimes depending on the value of τ , showing also oscillations which depend on the instantaneous energy spectrum. The entanglement spectrum is characterized by a rich dynamics where multiple crossings take place with a gap-dependent frequency. Moreover, we investigate the Kibble-Zurek scaling of entanglement entropy and Schmidt gap.

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Section: Introductionmentioning

confidence: 99%

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

et al. 2014

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“…The Dicke states |S = N/2, S z with S z = −N/2, ..., N/2 provide a convenient basis spanning the subspace accessible through the dynamics. Indeed the entanglement entropy S L,N can be easily evaluated noticing that, since the maximum value of the total spin can be achieved only with maximum value of the spin in each bipartition, the following decomposition holds [43,49]:…”

Section: Entanglement Entropy Maximizationmentioning

confidence: 99%

“…As target state we chose the gs of H[Γ = 0] (ferromagnetic phase). We focused our attention on the case γ = 0, representative of the class γ < 1 (for γ = 1 the dynamics is trivial due to the symmetry of H) [43]. For this model indeed a lot of physical information is available: the gap between the ground state and the first excited state closes polynomially with the size at the critical point [32], ∆ ∼ N −1/3 .…”

Section: Lipkin-meshkov-glick Modelmentioning

confidence: 99%

Chopped random-basis quantum optimization

2011

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In this work we describe in detail the Chopped RAndom Basis (CRAB) optimal control technique recently introduced to optimize t-DMRG simulations [1]. Here we study the efficiency of this control technique in optimizing different quantum processes and we show that in the considered cases we obtain results equivalent to those obtained via different optimal control methods while using less resources. We propose the CRAB optimization as a general and versatile optimal control technique. PACS numbers:Realizing artificial, controllable quantum systems has represented one of the most promising challenge in physics for the last thirty years [2]. On one side such systems could unveil unexplored features of Nature, when employed as universal quantum simulators [3]; on the other side this technology could be exploited to realize a new generation of extremely powerful devices, like quantum computers [4]. Along with the impressive progress marked recently in the construction of tunable quantum systems [5,6], there is a renewed and increasing interest in quantum optimal control (OC) theory, the study of the optimization techniques aimed at improving the outcome of a quantum process [2]. Indeed OC can prove to be crucial under several respects for the development of quantum devices: first, it can be generally employed to speed up a quantum process to make it less prone to decoherence or noise effects induced by the unavoidable interaction with the external environment. Second, considering a realistic experimental setup in which just few parameters are tunable or, in the most difficult situations, only partially tunable, OC can provide an answer about the optimal use of the available resources.Traditionally OC has been exploited in atomic and molecular physics [7][8][9]. More recently, with the advent of quantum information, the requirement of accurate control of quantum systems has become unavoidable to build quantum information processors [10][11][12][13][14][15][16]. However, the above mentioned methods often result in optimal driving fields that require a level of tunability incompatible with current experimental capabilities and in general, the calculation of the optimal fields requires an exact description of the system (either analytical or numerical). The field of application of these methods is severely limited also by the need to have access to huge amount of information about the system, e.g. computing gradients of the control fields, expectation values of observables as a function of time. Moreover, standard OC algorithms define a set of Euler-Lagrange equations that have to be solved to find the optimal control pulse [2], where the equation for the correction to the driving field is highly dependent on the constraints imposed on the system and on the figures of merit considered. This implies that considering different figures of merit and/or constraints on the system needs a redefinition of the corresponding Euler-Lagrange equations, hindering a straightforward adaptation of the optimization procedure to different s...

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“…The Kibble-Zurek scaling has been verified in various exactly solvable spin models and systems of interacting bosons [4,13,16,17,11,5]; it has been generalized to quenching through a multicritical point [31], across a gapless phase [20,23], and along a gapless line [26,28], and to systems with quenched disorder [14], white noise [18], infinite-range interactions [27], and edge states [30]. Studies have also been made to estimate the defect density for quenching with a non-linear form [21], an oscillatory variation of an applied magnetic field [32] or under a reversal of the magnetic field [33].…”

Section: Introductionmentioning

confidence: 99%

“…The non-equilibrium dynamics of a quantum system when quenched very fast [3] or slowly across a quantum critical point [4,5] has attracted the attention of several groups recently. The possibility of experimental realizations of quantum dynamics in spin-1 Bose condensates [6] and atoms trapped in optical lattices [7,8] has led to an upsurge in studies of related theoretical models [3,4,5,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33].…”

mentioning

confidence: 99%

Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line

Divakaran

Mukherjee

Dutta

et al. 2010

Lecture Notes in Physics

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The exciting physics of quantum phase transitions has been explored extensively in the last few years [1,2]. The non-equilibrium dynamics of a quantum system when quenched very fast [3] or slowly across a quantum critical point [4,5] has attracted the attention of several groups recently. The possibility of experimental realizations of quantum dynamics in spin-1 Bose condensates [6] and atoms trapped in optical lattices [7,8] has led to an upsurge in studies of related theoretical models [3,4,5,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33].In this review, we concentrate on the dynamics of quantum spin chains swept across a quantum critical or multicritical point or along a gapless line by a slow (adiabatic) variation of a parameter appearing in the Hamiltonian of the system. Our aim is to find the scaling form of the density of defects (which, in our case, is the density of wrongly oriented spins) in the final state which is reached after the system is prepared in an initial ground state and then slowly quenched through a quantum critical point. The dynamics in the vicinity of a quantum critical point is necessarily non-adiabatic due to the divergence of the relaxation time of the underlying quantum system which forces the system to be infinitely sluggish; thus the system fails to respond to a change in a parameter of the Hamiltonian no matter how slow that rate of change may be! We first recall the Kibble-Zurek argument [34,35] which predicts a scaling form for the defect density following a slow quench through a quantum critical point. We assume that a parameter g of the Hamiltonian is varied in a linear fashion such that g − g c ∼ t/τ, where g = g c denotes the value of g at the quantum critical point and τ is the quenching time. Our interest is in the adiabatic limit, τ → ∞. The energy gap of the quantum Hamiltonian vanishes at the critical point as (g − g c ) νz whereas the relaxation time ξ τ , which is inverse of the gap, diverges at the critical point. It is clear that non-adiabaticity becomes important at a timet when the characteristic time scale of the quantum system (i.e., the relaxation time) is of the order of the inverse of the rate of change of the Hamiltonian; this yields

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Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

Cited by 95 publications

References 57 publications

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

Chopped random-basis quantum optimization

Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line

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