Phase transitions in effective lattice models for strongly correlated systems

Abstract

In three research articles we have studied the critical properties of effective lattice models for strongly correlated electron systems by Monte Carlo simulations. A similar model is used in a fourth article for investigating thermal fluctuations of vortices in a rotating Bose–Einstein condensate. In the first part of this thesis we review the necessary background and introduce the models one by one. The last part is a collection of the papers.

Paper I [1]: We consider the scaling of the mean square dipole moment in a plasma with logarithmic interactions in a two- and three-dimensional system. In both cases, we establish the existence of a low-temperature regime where the mean square dipole moment does not scale with system size and a hightemperature regime does scale with system size. Thus, there is a nonanalytic change in the polarizability of the system as a function of temperature, and hence a metal-insulator transition in both cases. The relevance of this transition in three dimensions to quantum phase transitions in 2 + 1-dimensional systems is briefly discussed.

Paper II [2]: The existence of a discontinuity in the inverse dielectric constant of the two-dimensional Coulomb gas is demonstrated on purely numerical grounds. This is done by expanding the free energy in an applied twist and performing a finite-size scaling analysis of the coefficients of higher-order terms. The phase transition, driven by unbinding of dipoles, corresponds to the Kosterlitz-Thouless transition in the 2D XY model. The method developed is also used for investigating the possibility of a Kosterlitz-Thouless phase transition in a threedimensional system of point charges interacting with a logarithmic pair-potential, a system related to effective theories of low-dimensional strongly correlated systems. We also contrast the finite-size scaling of the fluctuations of the dipole moments of the two-dimensional Coulomb gas and the three-dimensional logarithmic system to those of the three-dimensional Coulomb gas.

Paper III [3]: We perform large-scale Monte Carlo simulations on an effective gauge theory for an easy plane quantum anti-ferromagnet, including a Berry phase term that projects out the S = 1/2 sector. Without a Berry phase term, the model exhibits a phase transition in the 3DXY universality class associated with proliferation of gauge-charge neutral U(1) vortices. The instantons that eliminate the phase transition in the gauge-charged sector are cancelled by the Berry phases. The result is a first order phase transition. This gauge theory therefore does not exhibit deconfined criticality.

Paper IV [4]: We perform Monte Carlo studies of vortices in three dimensions in a cylindrical confinement, with uniform and nonuniform density. The former is relevant to rotating 4He, the latter is relevant to a rotating trapped Bose condensate. In the former case we find dominant angular thermal vortex fluctuations close to the cylinder wall. For the latter case, a novel effect is that at low temperatures the vortex solid close to the center of the trap crosses directly over to a tension-less vortex tangle near the edge of the trap. At higher temperatures an intermediate tensionful vortex liquid located between the vortex solid and the vortex tangle, may exist.