From classical to quantum criticality

Daniel Podolsky, Efrat Shimshoni, Pietro Silvi, Simone Montangero, Tommaso Calarco, Giovanna Morigi, Shmuel Fishman

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We study the crossover from classical to quantum phase transitions at zero temperature within the framework of φ4 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.

Original languageEnglish
Article number214408
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number21
StatePublished - 11 Jun 2014


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