Defects in dimer model
||Defects in dimer model|
||Eddy Ardonne <email@example.com>|
||2014-02-28 – 2015-02-01|
The low temperature physics of a large fraction of equilibrium condensed matter systems is described as broken symmetry phases or unique ground states. A third possibility is that the system is ‘frustrated’. ‘Frustration’ occurs in systems where interaction has pieces that are mutually ‘contradicting’ such that a unique low temperature configuration does not exist. Instead, these systems are described by a manifold of ground states. This large degeneracy allows the local degrees of freedom to fluctuate, while still being constrained to lie within a ground state manifold. Such non-trivial constraints and large degeneracies pose interesting theoretical challenges.
The constrained fluctuations cause subtle correlations that lead to several interesting emergent phenomena such as fractionalization, topological order, topological defects, unconventional phase transitions etc. Recent experiments in rare earth compounds like pyrochlores demonstrate several of these phenomena in real materials.
One example of a classical model that demonstrates similar physics is the cubic dimer model. The cubic dimer model describes a system whose degrees of freedom are ‘dimers’ sitting on the links of a cubic lattice, subject to the constraint that each lattice point is connected to one and only one dimer. Fluctuations of the system subject to these constraints make it similar to frustrated systems described above and can be used to study several related questions. A phase transition of this system from an ordered phase to a dimer `liquid’ phase is thought to be described by a deconfined critical point. Deconfined criticality is a model for an unconventional phase transition where the phase transition can be described by emergent fractional degrees of freedom interacting with an emergent electromagnetic field.
Through a study performed using resources from SNIC project number # 001/12-231 we explored the effect of relaxation of the constraints by introducing a very dilute set of defects. The results of the calculations showed clear agreement with predictions of the deconfined criticality ( Physical Review B 89, 014404 (2014) ) .
This previous study focused on effects of ‘charge 1’ defects. The charge indicates the extent of relaxation of the constraint at each defect. In the present proposal we plan to analyse the relevance of defects which have higher charge. The result of this study will provide further tests of deconfined criticality.
The computations will use Monte Carlo methods based on a directed loop algorithm. The directed loop algorithm has been extensively used for studying the cubic dimer model in the fully constrained regime. The algorithm can be modified to allow generation of a thermodynamic equilibrium density of charge 1 defects. This was developed and used in the calculations performed as a part of the previous SNIC project. Ideas developed during this work allowed us to devise new techniques to study higher charge defects - in particular charge two and three. The codes required has been written and tested and could be used as soon as an allocation is granted.
In addition to answering the questions from physics, we hope to further explore and develop useful numerical techniques during this work.