Novel Quantum Phase Transitions in Low-Dimensional Systems

Abstract

We study a number of quantum phase transitions, which are exotic in their nature and separates non-trivial phases of matter. Since quantum fluctuations, which drive these phase transitions, are stronger in low-dimensions, we concentrate on low-dimensional systems. We consider two different two-dimensional systems in this thesis and study their phase transition. First, we investigate a phase transition in graphene, one of the most famous two-dimensional systems in condensed matter. For a suspended bilayer graphene in ν = 0 quantum Hall regime, the conductivity data and mean-field analysis suggests a phase transition from an antiferromagnetic (AF) state to a valence bond solid (VBS) state, when perpendicular electric field is increased. This AF to VBS phase transition is reminiscent of deconfined criticality, which is a novel phase transition that cannot be explained by Landau’s theory of symmetry breaking. We show that in the strong coupling regime of bilayer graphene, the AF state is destabilized by the transverse electric field, likely resulting in a VBS state. We also consider monolayer and bilayer graphene in the large cyclotron gap limit and show that the effective action for the AF and VBS order parameters have a topological Wess-Zumino-Witten term, supporting that the phase transition observed in experiments is in the deconfined criticality class. Second, we study the model systems of cuprate superconductor, which is effectively a two-dimensionalal system in the CuO_2 plane. The proposal that the pseudogap metal is a fractionalized Fermi liquid described by a quantum dimer model is extended using the density matrix renormalization group. Measuring the Friedel oscillations in the open boundaries reveals that the fermionic dimers have dispersion minima near (π/2,π/2), which is compatible with the Fermi arcs in photoemission. Moreover, investigating the entanglement entropy suggests that the dimer model with low fermion density is similar to the free fermion system above the Lifshitz transition. We also study the phase transition from a metal with SU(2) spin symmetry to an AF metal. By applying the functional renormalization group to the two-band spin-fermion model, we establish the existence of a strongly coupled fixed point and calculate critical exponents of the fixed point.