Renormalization for insulating states of matter

In this thesis, we study three cases of insulating states of matter in terms of the renormalization procedure where the conventional renormalization group scheme is not simply applicable. The first subject is the spectral weight structure of hole-doped Mott insulators. As the mixing between two separate Hubbard bands is dynamically generated, additional charge degrees of freedom is required to give a proper description to the relevant low-energy physics. On this account, we first discuss how the low-energy Hubbard band should be partitioned to account for the extra degrees of freedom. Following the exact integration procedure of the upper Hubbard band, we explicitly demonstrate that the conserved charge cannot be exhausted by counting quasiparticles. In addition, we argue that it is the existence of dynamically generated charge degrees of freedom that gives rise to the coexistence of poles and zeroes in the single-particle Green function. In comparison to the Fermi arc structure, which is intrinsic to cuperate phenomenology, we suggest that the suppression of the spectral weight at the back side of the arc is a consequence of composite excitations, arising from dynamical mixing. The second topic we study is the nature of the transition between two insulating states of matter in a weakly disordered bosonic system. In particular, we investigate the instabilities of the Mott-insulating phase within a renormalization group analysis of the replica field theory obtained by a strong-coupling expansion around the atomic limit. To this end, we identify a new order parameter and associated correlation length scale that are capable of capturing the transition from a state with zero compressibility, the Mott insulator, to another insulating state with finite compressibility, the Bose glass. The order parameter is the relative variance of the disorder-induced mass distribution. From its distinctive behavior on each phase, we find that the divergence of the relative variance in the Bose glass signals the breakdown of self-averaging. Lastly, we also emphasize that the transition at commensurate filling is governed by a different fixed point in the renormalization group flow. The last topic discussed is the thermoelectric properties of the correlated Kondo lattice system at low temperature. Specifically, we explore the periodic Anderson impurity model with spin-orbit interactions, using the slave-particle method. As the thermopower is related to the entropy per carrier, particle-hole asymmetry and a large density of states at the chemical potential make Kondo insulator an ideal platform for thermoelectrics. In this respect, we further explore the possibility to improve the thermoelectric performance by tuning the crystal electric field splitting, the spin-orbit interaction strength, and orbital degeneracy.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Hong, Seungmin

Contributors dc:contributor

• Phillips, Philip W.
• Stone, Michael
• Cooper, S. Lance
• Leigh, Robert G.

• Renormalization
• Hubbard model
• Mott insulator
• Bose glass
• Kondo insulator

Statement dc:rights

• 2013 by Seungmin Hong. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/44258

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/44258