Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model

Solinas, Paolo; Ribeiro, Pedro; Mosseri, Rémy

doi:10.1103/physreva.78.052329

Cited by 21 publications

(30 citation statements)

References 27 publications

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“…The energy gap measurements show evidence of a nonzero gap at the QCP arising from finite-size effects, and using a carefully tailored slow ramp of the Hamiltonian parameters, we have adiabatically crossed the QCP with no apparent excitation of the system. We hope that this work stimulates similar investigations in related many-body systems, and in particular, we anticipate that the results of this study could directly inform investigations in double-well Bose-Josephson junction systems, (pseudo)spin-1/2 interacting systems (48,49), and the Lipkin-Meshkov-Glick (LMG) model (43,50), which share similar Hamiltonians.…”

Section: Adiabatic Qptmentioning

confidence: 64%

Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition

Hoang

Bharath

Boguslawski

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu-Goldstone modes and massive AndersonHiggs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.adiabatic quenches | amplitude excitations | quantum phase transition T he amplitude mode and phase mode describe two distinct excitation degrees of freedom of a complex order parameter ψ = Ae iϕ appearing in many quantum systems such as the order parameter of the Ginzburg-Laudau superconducting phase transition (1) and the two-component quantum field of the NambuGoldstone-Anderson-Higgs matter field model (2-5). In a zerodimensional system of an interacting spin-1 condensate, the transverse spin, S ⊥ , plays the role of an order parameter in the quantum phase transition (QPT) with S ⊥ being zero in the polar (P) phase and nonzero in the broken axisymmetry (BA) phase (Fig. 1A). Representing the transverse spin vector as a complex number, S ⊥ = S x + iS y , with the real and imaginary parts being expectation values of spin-1 operators, the amplitude mode corresponds to the amplitude oscillation of S ⊥ .The amplitude mode can be studied in different spinor phases by tuning the relative strengths of the quadratic Zeeman energy per particle q ∝ B 2 and spin interaction energy c of the condensate (6) by varying the magnetic field strength B (Fig. 1). In the P phase, both the effective spinor potential energy V and the ground state (GS) spin vector have SO(2) rotational symmetry about the vertical axis (Fig. 1A), and there are two degenerate collective amplitude modes along the radial directions about the GS located at the bottom of the parabolic bowl. These amplitude excitations are gapped modes, which vary both the amplitude of S ⊥ and the energy.In the BA phase, the effective spinor potential energy V acquires a Mexican-hat shape with the GS occupying the minimal energy ring of radius ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4c 2 − q 2 p =ð2jcjÞ. The GS spin vector, S ⊥ (orange arrow in Fig. 1A), spontaneously breaks the SO(2) symmetry and acquires a definite direction (7,8). This broken symmetry induces a massless Na...

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Section: Adiabatic Qptmentioning

confidence: 64%

Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition

Hoang

Bharath

Boguslawski

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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“…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

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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

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“…These parameters can be controlled by adjusting the relevant parameters such as the detunings, Rabi frequencies, and coupling coefficients. (12)) Isotropic LMG model (Equation (14)) One-axis twisting LMG model (Equation (16)) √ N g k (N ≃ 10 12 ) 12 12 12…”

Section: The Modelmentioning

confidence: 99%

“…Although the two-axis counter-twisting Hamiltonian is superior to the one-axis twisting one, the spin-spin interaction with the form of two-axis countertwisting has not been realized in any experiments due to the demanding requirements [19][20][21][22]61]. We will discuss how to prepare spin squeezed states by simulating the two-axis counter-twisting interaction with equation (12) in our scheme. In this system, the coherent coupling strength between a single NV center and the cavity is much less than the cavity dissipation rates (|g i | ≪ κ a,b ), but this collective coupling can be enhanced by increasing the number of the NV centers.…”

Section: The Spin Squeezed Statementioning

confidence: 99%

Simulating the Lipkin-Meshkov-Glick model in a hybrid quantum system

Zhou

et al. 2017

Phys. Rev. A

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We propose an efficient scheme for simulating the Lipkin-Meshkov-Glick (LMG) model with nitrogen-vacancy (NV) center ensembles in diamond magnetically coupled to superconducting coplanar waveguide cavities. With the assistance of external microwave driving fields, we show that the interaction of the NV spins can be easily controlled, and several types of the LMG model can be realized by tuning the different parameters. Under the thermal dynamical limit, the distinct non-equilibrium second order quantum phase transition of the spin ensemble can be achieved at the critical point. Furthermore, we show that the spin squeezed state can be generated by tailoring the LMG Hamiltonian to possess the two-axis counter-twisting form in this hybrid quantum system.Comment: 10 pages, 4 figures, Accepted for publication in PR

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Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model

Cited by 21 publications

References 27 publications

Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition

Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition

Quantum metrology in Lipkin-Meshkov-Glick critical systems

Simulating the Lipkin-Meshkov-Glick model in a hybrid quantum system

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