Exact solutions for the LMG model Hamiltonian based on the Bethe ansatz

How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this Letter, we analyze and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-1=2 particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions for the long-time nonintegrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of manybody dephasing.

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“…is called Lipkin-Meshkov-Glick model [59], which is integrable [60,61] since there exist N conserved quantities. For example, ⃗…”

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confidence: 99%

Many-Body Dephasing in a Trapped-Ion Quantum Simulator

et al. 2020

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“…The fact that Schrödinger function is dependent on a unit circle S 1 , however, makes a crucial role for construction of infinite-dimensional fermions. 40 Contrary to PD and the present paper, we do not use any bosonization and infinite-dimensional techniques and hence have no restrictions on interaction strengths of LMG Hamiltonian. 8, it turns out that the fully parametrized -dependent SCF Hamiltonian is made up of only the -dependent Hamiltonian H F ϱ ;HF on infinite-dimensional Fock space F ϱ .…”

Section: Discussionmentioning

confidence: 97%

Self-consistent-field method and τ-functional method on group manifold in soliton theory. II. Laurent coefficients of soliton solutions for sl̂n and for sûn

Nishiyama

Providência

Komatsu

2007

Journal of Mathematical Physics

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Block correlated coupled cluster method with a complete-active-space self-consistent-field reference function: The formula for general active spaces and its applications for multibond breaking systemsWe consider a finite many fermion system with n single-particle states. Let c ␣ and c ␣ † ͑␣ =1, ... ,n͒ be the annihilation-creation operators of the fermion. Owing to the anticommutation relations1͒ fermion pair operators e ␣␤ ϵ c ␣ † c ␤ satisfy a Lie commutation relation 053502-2 Nishiyama, da Providência, and Komatsu J. Math. Phys. 48, 053502 ͑2007͒ This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.12.233.101 On: Tue, 02 Dec 2014 17:16:58 053502-3 Laurent coefficients of soliton solutions J. Math. Phys. 48, 053502 ͑2007͒ * : + C · 1 ͑␣,␤ = 1,2;Tr a r = 0,a r sl 2 ͒, 053502-11 Laurent coefficients of soliton solutions J. Math. Phys. 48, 053502 ͑2007͒

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“…In the isotropic (XX) case the Hamiltonian of this effective model is a polynomial in J 2 and J z , where J is the the total spin operator, and can thus be exactly solved for arbitrary N . The general (non-isotropic) LMG model can be solved in principle via the Bethe ansatz [20,21], though in practice this is less efficient than brute-force numerical diagonalization. In the thermodynamic limit, however, the density of states of the latter model in the highest spin sector (J = N/2) has been derived by means of a spin-coherent-state formalism [22,23].…”

Section: Introductionmentioning

confidence: 99%

Generalized Lipkin–Meshkov–Glick models of Haldane–Shastry type

Carrasco¹,

Finkel²,

González‐López³

2017

J. Stat. Mech.

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Abstract. We introduce a class of generalized Lipkin-Meshkov-Glick (gLMG) models with su(m) interactions of Haldane-Shastry type. We have computed the partition function of these models in closed form by exactly evaluating the partition function of the restriction of a spin chain Hamiltonian of Haldane-Shastry type to subspaces with well-defined magnon numbers. As a byproduct of our analysis, we have obtained strong numerical evidence of the Gaussian character of the level density of the latter restricted Hamiltonians, and studied the distribution of the spacings of consecutive unfolded levels. We have also discussed the thermodynamic behavior of a large family of su(2) and su(3) gLMG models, showing that it is qualitatively similar to that of a two-level system.Keywords: integrable spin chains and vertex models, solvable lattice models arXiv:1706.08751v2 [cond-mat.stat-mech]

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Exact solutions for the LMG model Hamiltonian based on the Bethe ansatz

Cited by 24 publications

References 20 publications

Many-Body Dephasing in a Trapped-Ion Quantum Simulator

Many-Body Dephasing in a Trapped-Ion Quantum Simulator

Self-consistent-field method and τ-functional method on group manifold in soliton theory. II. Laurent coefficients of soliton solutions for sl̂n and for sûn

Generalized Lipkin–Meshkov–Glick models of Haldane–Shastry type

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