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arXiv:1108.5744 · Physical Review Letters

Boson Pairing and Unusual Criticality in a Generalized XY Model

Yifei Shi, Austen Lamacraft, Paul Fendley

Published Dec 7, 2011• 51 citations
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Abstract

We discuss the unusual critical behavior of a generalized XY model containing both 2π-periodic and π-periodic couplings between sites, allowing for ordinary vortices and half-vortices. The phase diagram of this system includes both single-particle condensate and pair-condensate phases. Using a field theoretic formulation and worm algorithm Monte Carlo simulations, we show that in two dimensions it is possible for the system to pass directly from the disordered (high temperature) phase to the single particle (quasi)condensate via an Ising transition, a situation reminiscent of the "deconfined criticality" scenario.

DOI
10.1103/physrevlett.107.240601

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We discuss the unusual critical behavior of a generalized XY model containing both 2π-periodic and π-periodic couplings between sites, allowing for ordinary vortices and half-vortices. The phase diagram of this system includes both single-particle condensate and pair-condensate phases. Using a field theoretic formulation and worm algorithm Monte Carlo simulations, we show that in two dimensions it is possible for the system to pass directly from the disordered (high temperature) phase to the single particle (quasi)condensate via an Ising transition, a situation reminiscent of the "deconfined criticality" scenario.
Abstract We find the complete phase diagram of a generalised XY model that includes half-vortices. The model possesses superfluid, pair-superfluid and disordered phases, separated by Kosterlitz–Thouless (KT) transitions for both the half-vortices and ordinary vortices, as well as an Ising-type transition. There also occurs an unusual deconfining phase transition, where the disordered to superfluid transition is of Ising rather than KT type. We show by analytical arguments and extensive numerical simulations that there is a point in the phase diagram where the KT transition line meets the deconfining Ising phase transition. We find that the latter extends into the disordered phase not as a phase transition, but rather solely as a deconfinement transition. It is best understood in the dual height model, where on one side of the transition height steps are bound into pairs while on the other they are unbound. We also extend the phase diagram of the dual model, finding both O ( 2 ) loop model and antiferromagnetic Ising transitions.
We study the two-dimensional XY\mathrm{XY}XY model with quenched random phases by Monte Carlo simulation and finite-size scaling analysis. We determine the phase diagram of the model and study its critical behavior as a function of disorder and temperature. If the strength of the randomness is less than a critical value, ${\ensuremath{\sigma}}_{c},$ the system has a Kosterlitz-Thouless (KT) phase transition from the paramagnetic phase to a state with quasi-long-range order. Our data suggest that the latter exists down to T=0T=0T=0 in contradiction with theories that predict the appearance of a low-temperature reentrant phase. At the critical disorder ${T}_{\mathrm{KT}}\ensuremath{\rightarrow}0$ and for $\ensuremath{\sigma}>{\ensuremath{\sigma}}_{c}$ there is no quasiordered phase. At zero temperature there is a phase transition between two different glassy states at ${\ensuremath{\sigma}}_{c}.$ The functional dependence of the correlation length on $\ensuremath{\sigma}$ suggests that this transition corresponds to the disorder-driven unbinding of vortex pairs.
We study, by a Migdal-Kadanoff approximation and Monte Carlo simulations, the phase diagram of a two-dimensional coupled XY-Ising model. This model can describe phase transitions in different systems with underlying continuous and Z2{\mathit{Z}}_{2}Z2​ symmetries. Depending on the parameters, we find separate XY, Ising and first-order transitions. Also, a line of continuous transitions is found with simultaneous loss of XY and Ising order and varying critical exponents. The fully frustrated XY and Josephson-junction systems can be considered to lie along different paths in the model which can result in nonuniversal behavior if the transition is a single one.
A generalisation of the two-dimensional XY model is studied using Monte Carlo simulation. In this model, two-component classical spins interact both ferromagnetically and nematically. Three phases occur as temperature and the two interaction strengths are varied: a high-temperature, disordered phase, and two low-temperature phases with algebraic correlations in, respectively, the ferromagnetic and nematic order parameters. The critical behaviour at the phase boundaries is examined: the high-temperature phase is entered via Kosterlitz-Thouless transitions, whilst the low-temperature phases are separated by an Ising transition.
We study phase transitions of coupled two dimensional XY systems with spatial anisotropy and U(1)×Z2U(1) \times \mathbb{Z}_2U(1)×Z2​ symmetry, motivated by spinless bosonic atoms trapped in square optical lattice on the metastable first excited p−p-p−level orbitals with anisotropic hopping amplitudes. The phase transitions of the system are generally split into an Ising transition and an XY transition, but the sequence and the nature of the transitions depend on the ratio between the anisotropic couplings. In the isotropic limit the XY variables are expected to be disordered before the Ising variables when thermal or quantum fluctuations are turned on gradually. In the anisotropic limit with zero perpendicular hoppings, the finite temperature transition is a Kosterlitz-Thouless transition driven by proliferation of hybrid half vortices, and the zero temperature quantum phase transition is split into a bond order transition and a 3D XY transition, which can be driven by the condensation of either single vortices or half vortices. After the condensation of half vortices the resultant state is a Mott Insulator of paired bosons. A small perpendicular hopping JbJ_bJb​ leads to a 2D Ising transition at low temperature and a 2+1d quantum Ising transition with a small charging energy at zero temperature. Global phase diagrams for both classical and quantum phase transitions are drawn. The analytical results obtained in this work are expected to be checked both numerically and experimentally.
We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram is constructed in terms of the disorder strength and the chemical potential. Via Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where the Mott-insulator-to-superfluid transition occurs, from the strong-disorder regime, where the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-superfluid transition has the dynamical critical exponent $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.35\ifmmode\pm\else\textpm\fi{}0.05$ and the correlation length critical exponent $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.67\ifmmode\pm\else\textpm\fi{}0.03$. We suggest that the proliferation of the particle-hole pairs screens out the weak-disorder effects.