Alexandria Digital Research Library

The magical geometry of 1D quantum liquids

Author:
Plamadeala, Eugeniu
Degree Supervisor:
Chetan Nayak
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2016
Issued Date:
2016
Topics:
Theoretical physics and Condensed matter physics
Keywords:
Unimodular lattice
Hyperconductor
Topological phases
Perfect metal
Quantum critical point
Quantum wire
Genres:
Online resources and Dissertations, Academic
Degree Grantor:
University of California, Santa Barbara. Physics
Dissertation:
Ph.D.--University of California, Santa Barbara, 2016
Description:

We investigate the edge properties of Abelian topological phases in two spatial dimensions. We discover that many of them support multiple fully chiral edge phases, with surprising and measurable experimental consequences. Using the machinery of conformal field theory and integral quadratic forms we establish that distinct chiral edge phases correspond to genera of positive-definite integral lattices. This completes the notion of bulk-boundary correspondence for topological phases. We establish that by tuning inter-channel interactions the system can be made to transition between the different edge phases without closing the bulk gap.

Separately we construct a family of one-dimensional models, called Perfect Metals, with no relevant mass-generating operators. These theories describe stable quantum critical phases of interacting fermions, bosons or spins in a quantum nanowire. These models rigorously answer a long-standing question about the existence of stable metallic phases in one and two spatial dimensions in the presence of generic disorder. Separately, they are the first example of a stable phase of an infinite parallel array of coupled Luttinger liquids.

We perform a detailed study of the transport properties of Perfect Metals and show that in addition to violating the Wiedemann-Franz law, they naturally exhibit low power-law dependence of electric and thermal conductivities on temperature all the way to zero temperature. We dub this phenomenological set of properties a hyperconductor because in some sense, hyperconductors are better conductors that superconductors, which may have thermal conductivities that are exponentially small in temperature.

Physical Description:
1 online resource (260 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3rb74r7
ISBN:
9781369339550
Catalog System Number:
990047189830203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Eugeniu Plamadeala
File Description
Access: Public access
Plamadeala_ucsb_0035D_13003.pdf pdf (Portable Document Format)