From classical to quantum criticality

Abstract

We study the crossover from classical to quantum phase transitions at zero temperature within the framework of ${\varphi }^4$ theory. The classical transition at zero temperature can be described by the Landau theory, turning into a quantum Ising transition with the addition of quantum fluctuations. We perform a calculation of the transition line in the regime where the quantum fluctuations are weak. The calculation is based on a renormalization group analysis of the crossover between classical and quantum transitions, and is well controlled even for space-time dimensionality $D$ below 4. In particular, for $D=2$ we obtain an analytic expression for the transition line which is valid for a wide range of parameters, as confirmed by numerical calculations based on the Density Matrix Renormalization Group. This behavior could be tested by measuring the phase diagram of the linear-zigzag instability in systems of trapped ions or repulsively-interacting dipoles.

7 pages, 3 figures

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Cited by in corpus (16)

• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Crossover from the classical to the quantum Kibble-Zurek scaling
• Anisotropic Long-Range Spin Systems
• Quantum sensors for the generating functional of interacting quantum field theories
• Finite temperature spectrum at the symmetry-breaking linear-zigzag transition
• Odd-parity superconductivity near inversion breaking quantum critical point in one dimension
• Lindblad dynamics of a quantum spherical spin
• Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson
• Ion-crystal demonstration of structural phase transition induced solely by temperature
• Non-equilibrium quantum thermodynamics in Coulomb crystals
• Buckling transitions and clock order of two-dimensional Coulomb crystals
• Dynamical Ginzburg criterion for the quantum-classical crossover of the Kibble-Zurek mechanism
• Multi-mode Bose-Hubbard model for quantum dipolar gases in confined geometries
• Operator-based derivation of phonon modes and characterization of correlations for trapped ions at zero and finite temperature
• Long-range Ising interactions mediated by $\lambda {\varphi }^4$ fields: probing the renormalisation of sound in crystals of trapped ions
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $\lambda {\varphi }^4$ model