Studies of "clean" and "disordered" Bilayer Optical Lattice Systems Circumventing the 'fermionic Coolingproblem'
Abstract
The advancement in the eld of coldatoms has generated a lot of interest in the condensed matter community. Coldatom experiments can simulate clean, disorder/impurity free systems very easily. In these systems, we have a control over various parameters like tuning the interaction between particles by the Feshbach resonance, tuning the hopping between lattice sites by laser intensity and so on. As a result, these systems can be used to mimic various theoretical models, which was hindered because of various experimental limitations. Thus, we have an experimental tool in which we can start with a simple theoretical model and later tune the model experimentally and theoretically to simulate the real materials. This will be helpful in studying the physics of the real materials as we can control interactions as well as the impurities can also be taken care of. But the advancement in the eld of cold atoms has seen a roadblock for the fermions in optical lattices. The super uid and antiferromagnetic phases has not been achieved for fermions in optical lattices due to the \cooling problem" (entropy issues).
In this thesis, we have addressed the issue of the \cooling problem" for fermions in optical lattice systems and studied the system with determinant quantum Monte Carlo technique. We start by giving a general idea of coldatoms and optical lattice potentials, and a brief review of the experimental work going on in the coldatomic systems. Experimental limitations like \fermionic cooling problem" have been discussed in some detail. Then we proposed a bilayer bandinsulator model to circumvent the \entropy problem" and simultaneously increasing the transition temperature for fermions in optical lattices. We have studied the attractive Hubbard model, which is the minimal model for fermions in optical lattices. The techniques that we have used to study the model are mean eld theory, Gaussian uctuation theory and determinant quantum Monte Carlo numerical technique. . Chapter1 : provides a general introduction to the ultracold atoms, optical lattice and Feshbach resonance. In this chapter we have discussed about coldatom experiments in optical lattice systems. Here, we have brie y discussed the control over various parameters in the experiments. The goal of these experiments is to realize or mimic many manybody Hamiltonians in experiments, which until now was just a theoretical tool to describe various manybody physics. In the end we give a brief idea for introducing disorder in the coldatom experiments discuss the limitations of these experiments in realizing the \interesting" super uid and antiferromagnetic phases of fermionic Hubbard model in optical lattices.
Chapter2 : gives a brief idea of \Determinant Quantum MonteCarlo" (DQM C) technique that has been used to study these systems. In this chapter we will discuss the DQM C algorithm and the observables that can be calculated. We will discuss certain limitation of the DQM C algorithm like numerical instability and sign problem. We will brie y discuss how sign problem doesn't occur in the model we studied.
Chapter3 : discusses the way by which we can bypass the \cooling problem" (high entropy state) to get a fermionic super uid state in the cold atom experiments. In this chapter we propose a model whose idea hinges on a lowentropy bandinsulator state, which can be tuned to super uid state by tuning the onsite attractive interaction by Feshbach resonance. We show through Gaussian uctuation theory that the critical temperature achieved is much higher in our model as compared to the singleband Hubbard model. Through detailed variational Monte Carlo calculations, we have shown that the super uid state is indeed the most stable ground state and there is no other competing order. In the end we give a proposal for its realization in the ultracold atom optical lattice systems.
Chapter4 : discusses the DQM C study of the model proposed in chapter
3. Here we have studied the various singleparticle properties like momentum distribution, double occupancies which can be easily measured in coldatom experiments. We also studied the pairpair and the densitydensity correlations in detail through DQM C algorithm and mapped out the full T U phase diagram. We show that the proposed model doesn't favor the charge density wave for the interaction strengths we are interested in.
Chapter5 : gives a brief idea of the e ect of adding an onsite random disorder in our proposed bilayerHubbard model. We study the e ect of random disorder on various singleparticle properties which can be easily veri ed in coldatom experiments. We studied the suppression of the pairpair correlations as we increase the disorder strength in our proposed model. We nd that the critical value of the interaction doesn't change in the weakdisorder limit. We estimated the critical disorder strength needed to destroy the super uid state and argued that the transition from the super uid to Boseglass phase in presence of disorder lies in the universality class of (d + 1) XY model. In the end, we give a schematic U V phase diagram for our system.
Chapter6 : We studied the bilayer attractive Hubbard model in different lattice geometry, the bilayer honeycomb lattice, both in presence and in absence of the onsite random disorder. We discussed how the pairpair and densitydensity correlations behave in the presence and absence of disorder. Through the finitesize scaling analysis we see the coexistence of the super fluid and the charge density wave order at half lling. An in nitesimal disorder destroys the CDW order completely while the super uid phase found to be robust against weakdisorder. We estimated the critical interaction strength, the critical temperature and the critical disorder strength through nitesize scaling, and provide a putative phase diagram for the system considered.
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 Physics (PHY) [324]
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