Computing Quantum Phase Transitions

Abstract

A phase transition occurs when the thermodynamic properties of a material display a singularity as a function of the external parameters. Imagine, for instance, taking a piece of ice out of the freezer. Initially, its properties change only slowly with increasing temperature. However, at 0°C, a sudden and dramatic change occurs. The thermal motion of the water molecules becomes so strong that it destroys the crystal structure. The ice melts, and a new phase of water forms, the liquid phase. At the phase transition temperature of 0°C the solid (ice) and the liquid phases of water coexist. A finite amount of heat, the so-called latent heat, is required to transform the ice into liquid water. Phase transitions involving latent heat are called first-order transitions. Another well known example of a phase transition is the ferromagnetic transition of iron. At room temperature, iron is ferromagnetic, i.e., it displays a spontaneous magnetization. With rising temperature, the magnetization decreases continuously due to thermal fluctuations of the spins.At the transition temperature (the so-called Curie point) of 770°C, the magnetization vanishes, and iron is paramagnetic at higher temperatures. In contrast to the previous example, there is no phase coexistence at the transition temperature; the ferromagnetic and paramagnetic phases rather become indistinguishable. Consequently, there is no latent heat. This type of phase transition is called continuous (second-order) transition or critical point.

Quantum criticality in a dissipative (2+1)-dimensionalXYmodel of circulating currents in high-Tccuprates

“…This is not observed in our results. We have also verified explicitly, by an appropriate modification of the scaling, 35 that our results are not consistent with activated dynamical scaling.…”

“…21, which predicts a strictly infinite z for ξ τ ∼ ξ z so that ξ is strictly vanishing at criticality. Another conceivable sense in which z → ∞ is by activated dynamical scaling, 35 i.e., scaling on the form ln ξ τ ∼ ξ ψ . In this case, as we expect also in the first case, locality would manifest itself in our simulations as a strongly increasing value of z > 1 as the thermodynamical limit was approached.…”

Monte Carlo simulations of dissipative quantum Ising models

“…If, on the other hand, one has z → ∞ in the sense of activated dynamical scaling, the method is in principle feasible. 19 Before continuing the discussion of the bond dissipation, we comment further on the relation between the real space representation of q 2 |ω| and the form of the bond dissipation used in Eq. (7).…”

Ordered magnetism in the intrinsically decorated jeff=12α−CoV3O8

“…These concentration gradients were noted in dilute model antiferromagnets 1,159,161,[167][168][169] . Such a combination of significant dilution and disorder would be expected to have a significant effect on the dynamics 1,11,12,20,49,51,116,[170][171][172] . In this sense, it is surprising that there seems to be little effect on the magnetic dynamics in α-CoV 3 O 8 , where the magnetic excitations are consistent with a fully ordered cation arrangement.…”