Studies on the effect of noise in boundary quantum phase transitions
Boundary quantum phase transitions are abrupt ground state transitions triggered by the change of the boundary conditions at single or multiple (but finite) points.
When boundary effects dominate, understanding boundary quantum phase transitions requires a deeper knowledge of strongly correlated electron systems that is beyond the widely applied mean field treatment.
Meanwhile, with strong boundary effect, most systems with boundary quantum phase transition can generally be considered as effectively zero-dimensional, with reservoir details ignored. Consequently, the critical features of boundary quantum phase transitions only involve long-time correlations instead of long-range ones.
On the other hand, different from the geometrical confinement of boundaries, dissipation or quantum noise widely exists along the entire system.
In bulk quantum phase transitions, dissipation decreases system coherence by reducing the long-range correlations.
This fact makes it plausible that dissipation destroys the critical behavior of the quantum critical points.
The effect of dissipation, however, remains unclear in boundary quantum phase transition systems due to their lack of long-range correlations.
In this thesis I thus focus on the effect of dissipation in boundary quantum phase transitions.
These studies are motivated and encouraged by recent experimental triumphs where dissipation is realized and precisely measured in mesoscopic systems, which provide experimental evidences to check theoretical researches.
This thesis involves multiple dissipative mesoscopic systems, including the dissipative two impurity Kondo, two channel Kondo, resonant level, and Anderson models.
To begin with, the effect of dissipation in two impurity Kondo model has been explored and we find that the presence of dissipation restores the quantum phase transition by reducing the unwanted charge tunneling process. We further provide the phase diagram for the system that has an exotic double-quantum-critical-point feature.
After that, the non-equilibrium $I$-$V$ feature of a dissipative resonant level model is studied.
This model has been experimentally proven to host a boundary quantum phase transition.
With different tuning parameters, we calculate the $I$-$V$ feature at both the quantum critical point and in the crossover regime analytically. The theoretical calculation agrees remarkably with the experimental data.
As the spinful version of the resonant level model, the dissipative Anderson model has multiple unique features, including the experimentally observed peak position shifting and dissipation dependent saturated peak conductance. Through renormalization group studies and mapping the model to the quantum Brownian motion model, we understand these features qualitatively.
As an example of the application of above research achievements, we study the stabilization of a Majorana zero mode with the quantum frustration in a dissipative resonant level model. The Majorana zero mode is known to be unstable against the coupling to its partner at the other end of the Majorana hosted nanowire.
We prove that the Majorana zero mode can be stabilized by coupling its partner to the quantum dot of a frustrated dissipative resonant level model, where an isolated impurity Majorana fermion is produced.
Finally, we study the relation between boundary quantum phase transitions and geometric phases. The calculation is carried out at the Toulouse point of a dissipative resonant level model.
Although it satisfies the criteria of bulk quantum phase transitions to host a non-trivial geometric phase, the dissipative resonant level model has zero geometric phase due to the identical zero geometric curvature. This phenomenon is generally explained by studying the geometric tensor of boundary quantum phase transition-hosted systems.
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
Rights for Collection: Duke Dissertations
Works are deposited here by their authors, and represent their research and opinions, not that of Duke University. Some materials and descriptions may include offensive content. More info