New methods in the theory of quantum spin systems

We study a three-mode Hamiltonian modelling a heteronuclear molecular BoseEinstein condensate. Two modes are associated with two distinguishable atomic constituents, which can combine to form a molecule represented by the third mode. Beginning with a semi-classical analogue of the model, we conduct an analysis to determine the phase space fixed points of the system. Bifurcations of the fixed points naturally separate the coupling parameter space into different regions. Two distinct scenarios are found, dependent on whether the imbalance between the number operators for the atomic modes is zero or non-zero. This result suggests the ground-state properties of the model exhibit an unusual sensitivity on the atomic imbalance. We then test this finding for the quantum mechanical model. Specifically we use Bethe ansatz methods, ground-state expectation values, the character of the quantum dynamics, and ground-state wavefunction overlaps to clarify the nature of the ground-state phases. The character of the transition is smoothed due to quantum fluctuations, but we may nonetheless identify the emergence of a quantum phase boundary in the limit of zero atomic imbalance.

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“…The concept of mapping the spectrum of many-body systems into those of one-body Schrödinger equations has been discussed in detail in [23].…”

Section: Substituting Into the Schrödinger Equation Gives The Followimentioning

confidence: 99%

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

et al. 2007

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“…This model is often used to describe the magnetic properties of molecules such as Mn 12 acetate 4 . However, it also captures the physics of interacting bosons in a double-well-like structure 5,6 and is thus relevant to (two-mode) Bose-Einstein condensates 7 as well as Josephson junctions. It has also been recently used in optical cavity quantum electrodynamics in its dissipative version 8,9 for studying the decoherence of a single spin coupled to a spin bath 10,11 or quench dynamics 12 .…”

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confidence: 99%

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

2008

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The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin-coherent-state formalism. In the first step, a classical analysis allows one to distinguish between four distinct regions in the parameter space according to the nature of the singularities arising in the classical energy surface; these correspond to spectral critical points. The eigenfunctions are then analyzed more precisely in terms of the associated roots of the Majorana polynomial, leading to exact expressions for the density of states in the thermodynamic limit. Finitesize effects are also analyzed, leading in particular to logarithmic corrections near the singularities occurring in the spectrum. Finally, we also compute expectation values of the spin operators in a semiclassical analysis in order to illustrate some subtle effects occurring in one region of the parameter space.

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“…The generating function [21] (ϕ) can be constructed in terms of the conventional eigenstates ofŜ z such that…”

mentioning

confidence: 99%

“…Thus, we have periodic wavefunctions for even N and anti-periodic wavefunctions for odd N. The explicit form of the spin operator acting on the wavefunction (ϕ) is seen [21] to bê…”

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confidence: 99%

Unconventional quantum phase transition in the finite-size Lipkin–Meshkov–Glick model

Chen

Liang

2006

New J. Phys.

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New methods in the theory of quantum spin systems

Cited by 155 publications

References 75 publications

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

Unconventional quantum phase transition in the finite-size Lipkin–Meshkov–Glick model

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