Quantum criticality of the Lipkin-Meshkov-Glick model in terms of fidelity susceptibility

Kwok, Ho-Man; Ning, Wei; Gu, Shi-Jian; Lin, Hai–Qing

doi:10.1103/physreve.78.032103

Cited by 90 publications

(59 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It also found applications in several different fields, leading to a variety of results in terms of entanglement properties of its ground state [23][24][25] and spin squeezing [26]. For finite-size chains LMG have been characterized in terms of fidelity susceptibility [27][28][29] and adiabatic dynamics [30][31][32]. Although the LMG model cannot be solved analytically for a generic chain size, some of its extensions are amenable to an exact solution [33].…”

Section: Introductionmentioning

confidence: 99%

Quantum metrology in Lipkin-Meshkov-Glick critical systems

2014

View full text Add to dashboard Cite

The Lipkin-Meshkov-Glick (LMG) model describes critical systems with interaction beyond the first-neighbor approximation. Here we address the characterization of LMG systems, i.e. the estimation of anisotropy, and show how criticality may be exploited to improve precision. In particular, we provide exact results for the Quantum Fisher Information of small-size LMG chains made of $N=2, 3$ and $4$ lattice sites and analyze the same quantity in the thermodynamical limit by means of a zero-th order approximation of the system Hamiltonian. We then show that the ultimate bounds to precision may be achieved by tuning the external field and by measuring the total magnetization of the system. We also address the use of LMG systems as quantum thermometers and show that: i) precision is governed by the gap between the lowest energy levels of the systems, ii) field-dependent level crossing provides a resource to extend the operating range of the quantum thermometer.Comment: 11 pages, 5 figure

show abstract

Section: Introductionmentioning

confidence: 99%

Quantum metrology in Lipkin-Meshkov-Glick critical systems

2014

View full text Add to dashboard Cite

show abstract

“…The ground state phase diagram consists of two distinct regions and exhibits a second order quantum phase transition when hðtÞ ¼ 1 [16,24]. In the limit of weak interaction, the LMG model can be solved exactly by mapping it to N bosons in a double well, while in the thermodynamic limit, N → ∞, it can be solved through the Holstein-Primakoff (HP) transformation [15,25,26]. The latter approach is also a good approximation for N ≫ 1, although with some limitations [27], and in the Supplemental Material [28] we illustrate this mapping explicitly.…”

mentioning

confidence: 99%

Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model

et al. 2015

View full text Add to dashboard Cite

We study transitionless quantum driving in an infinite-range many-body system described by the LipkinMeshkov-Glick model. Despite the correlation length being always infinite the closing of the gap at the critical point makes the driving Hamiltonian of increasing complexity also in this case. To this aim we develop a hybrid strategy combining a shortcut to adiabaticity and optimal control that allows us to achieve remarkably good performance in suppressing the defect production across the phase transition. DOI: 10.1103/PhysRevLett.114.177206 PACS numbers: 75.10.Jm, 05.30.Rt, 64.60.Ht, 73.43.Nq The dynamical evolution of a quantum system often has to be tailored so that a given initial state is transformed into a suitably chosen target one. In cases such as this, the use of techniques for quantum optimal control can be key in engineering an efficient protocol. Over the years, formal control methods have been devised, both in the classical and quantum scenario [1]. To date, optimal control has been proven beneficial in a multitude of fields, ranging from molecular physics to quantum information processing or high precision measurements [2]. Only very recently, however, this framework has been extended so as to cope with the rich phenomenology and complexity of quantum many-body systems [3,4]. In this context, quantum optimal control has been shown to be crucial for the design of schemes for the preparation of many-body quantum states [3,5,6], the exploration of the experimentally achievable limits in quantum interferometry [7], and the cooling of quantum systems [8].Needless to say, quantum optimal control is not the only way to design the dynamical evolution of a quantum system, and one could consider simpler (suboptimal) ways to drive the desired dynamics. For instance, using the adiabatic theorem we are able to constrain a quantum system to remain in an eigenstate during any evolution. However, in order for such a technique to be accurate, it should operate on a rather long time scale. Unwanted transitions between the state we would like to confine the system into and other ones in its spectrum, which are induced by the unavoidably finite-speed nature of an evolution and ultimately limit the precision of the adiabatic dynamics, can be suppressed by adding suitable corrections to the Hamiltonian guiding the evolution [9,10]. This form of quantum control, named the shortcut to adiabaticity (STA), has been considered in a variety of different situations, and recently reviewed in Ref. [11]. An experimental implementation using cold atomic gases has been reported in Ref. [12].Recently, the idea of a STA has been extended to quantum many-body systems, a context where it can be potentially very beneficial. The STA was first employed in the suppression of defects produced when crossing a quantum phase transition in the paradigm model embodied by the one-dimensional Ising model [13]. Despite such potential, a crucial feature that emerges from the use of a STA in many-body scenarios is the inherent complexity of the ...

show abstract

“…It exhibits a universal behavior for any large number of particles, as it was shown in [29], although in our case a different interaction term of the LMG model Hamiltonian was considered.…”

Section: Discussionmentioning

confidence: 59%

“…This implies the determination of the second derivative of the fidelity as follows which expresses the answer of the physical system to the interaction term associated to the control parameter γ, and for that reason it has been called the fidelity susceptibility. The maximum of the fidelity susceptibility determines the exact localization of the quantum phase transition together with critical exponents of the quantum phase transition associated to the corresponding interaction term of the Hamiltonian [29]. This new concept can be used to determine the scaling behavior and universality of the quantum phase transition [4,29].…”

Section: Fidelitymentioning

confidence: 99%

“…The maximum of the fidelity susceptibility determines the exact localization of the quantum phase transition together with critical exponents of the quantum phase transition associated to the corresponding interaction term of the Hamiltonian [29]. This new concept can be used to determine the scaling behavior and universality of the quantum phase transition [4,29]. Following the procedure indicated in [15] the LMG model Hamiltonian can be expanded in terms of powers of N −1 , N 1/2 and N 0 by means of the HolsteinPrimakoff representation of the angular momentum generators and determine exact expressions for the fidelity susceptibility in both sides of the quantum phase transition.…”

Section: Fidelitymentioning

confidence: 99%

See 1 more Smart Citation

Quantum phase transitions in the LMG model by means of quantum information concepts

Castaños

López‐Peña

Nahmad-Achar

et al. 2012

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Abstract.Quantum phase transitions are currently studied in several fields of physics, as examples one finds: in nuclear physics the shape phase transitions within the Interacting Boson Model; in quantum optics two level atoms interacting with a one mode electromagnetic radiation in a cavity; and in condensed matter in the analysis of the behavior of spin systems. In this contribution we employ the fidelity and its susceptibility, two concepts widely used in quantum information theory, to determine the quantum phase transitions of the Lipkin-Meshkov-Glick (LMG) model together with its scaling properties. By means of these concepts, we propose a quantum method to determine the crossings and anti-crossings present in a model Hamiltonian as a function of the control parameters of the model. A review of the separatrix of the LMG model is done to compare the results obtained by means of quantum information concepts with those related with the singular behavior of the energy surface of the model, which is the expectation value of the Hamiltonian with respect to spin coherent states. IntroductionThe quantum phase transitions of many body systems are characterized by a sudden change in the ground state properties. They are different to the thermal phase transitions because they are due entirely to quantum fluctuations. They are described typically as due to a non-analytic behavior of the ground state properties when the Hamiltonian system crosses a transition point. Although one of the most important manifestations of a quantum phase transition occurs in the energy spectra of the physical systems, it can be observed also in many other observables.The crossing of levels in the spectrum of physical system is an indication of a first order transition, while the second order ones correspond to other causes and they are continuous. This latter type of transitions can be characterized by means of the spontaneous symmetry breaking formalism developed by Ginzburg, Landau and Wilson, where the order parameters play a crucial role. In particular the Ginzburg-Landau theory is related with the phase transitions of a material between the superconductor state to the normal one [1]. A manner to relate a variety of different phenomena in condensed matter theory is through the renormalization group, which originated to reconcile divergences in continuos theories with the finite experimental results. This is done by means of a cutoff procedure which in the modern vision lets us separate the modes of the physical system [2].The study of complex systems can be simplified by analyzing their static and dynamic entanglement properties. When a physical system approximates a critical point, the structure

show abstract

Quantum criticality of the Lipkin-Meshkov-Glick model in terms of fidelity susceptibility

Cited by 90 publications

References 37 publications

Quantum metrology in Lipkin-Meshkov-Glick critical systems

Quantum metrology in Lipkin-Meshkov-Glick critical systems

Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model

Quantum phase transitions in the LMG model by means of quantum information concepts

Contact Info

Product

Resources

About