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Studies on Fractionalization and Top...

Hu, Yichen.

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Studies on Fractionalization and Topology in Strongly Correlated Systems from Zero to Two Dimensions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Studies on Fractionalization and Topology in Strongly Correlated Systems from Zero to Two Dimensions./
Author:	Hu, Yichen.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	195 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
Contained By:	Dissertations Abstracts International81-02B.
Subject:	Condensed matter physics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13864305
ISBN:	9781085586467

Studies on Fractionalization and Topology in Strongly Correlated Systems from Zero to Two Dimensions.
Hu, Yichen.

Studies on Fractionalization and Topology in Strongly Correlated Systems from Zero to Two Dimensions. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 195 p.

Source: Dissertations Abstracts International, Volume: 81-02, Section: B.

Thesis (Ph.D.)--University of Pennsylvania, 2019.

This item must not be sold to any third party vendors.

The interplay among symmetry, topology and condensed matter systems has deepened our understandings of matter and lead to tremendous recent progresses in finding new topological phases of matter such as topological insulators, superconductors and semi-metals. Most examples of the aforementioned topological materials are free fermion systems, in this thesis, however, we focus on their strongly correlated counterparts where electron-electron interactions play a major role. With interactions, exotic topological phases and quantum critical points with fractionalized quantum degrees of freedom emerge. In the first part of this thesis, we study the problem of resonant tunneling through a quantum dot in a spinful Luttinger liquid. It provides the simplest example of a (0+1)d system with symmetry-protected phase transitions. We show that the problem is equivalent to a two channel SU(3) Kondo problem and can be mapped to a quantum Brownian motion model on a Kagome lattice. Utilizing boundary conformal field theory, we find the universal peak conductance and compute the scaling behavior of the resonance line-shape.For the second part, we present a model of interacting Majorana fermions that describes a superconducting phase with a topological order characterized by the Fibonacci topological field theory. Our theory is based on a SO(7)1 = SO(7)1/(G2)1 x (G2)1 coset construction and implemented by a solvable two-dimensional network model. In addition, we predict a closely related ''anti-Fibonacci'' phase, whose topological order is characterized by the tricritical Ising model. Finally, we propose an interferometer that generalizes the Z2 Majorana interferometer and directly probes the Fibonacci non-Abelian statistics.For the third part, we argue that a correlated fluid of electrons and holes can exhibit fractional quantum Hall effects at zero magnetic field. We first show that a Chern insulator can be realized as a free fermion model with p-wave(m = 1) excitonic pairing. Its ground state wavefunction is then worked out and generalized to m > 1. We give several pieces of evidence that this conjectured wavefunction correctly describes a topological phase, dubbed ''fractional excitonic insulator'', within the same universality class as the corresponding Laughlin state at filling 1/m. We present physical arguments that gapless states with higher angular momentum pairing between energy bands are conducive to forming the fractional excitonic insulator in the presence of repulsive interactions. Without interactions, these gapless states appear at topological phase transitions which separate the trivial insulator from a Chern insulator with higher Chern number. Since the nonvanishing density of states at these higher angular momentum band inversion transitions can give rise to interesting many-body effects, we introduce a series of minimal lattice models realizations in two dimensions. We also study the effect of rotational symmetry broken electron-hole exciton condensation in our lattice models using mean field theory.

ISBN: 9781085586467Subjects--Topical Terms:

3173567
Condensed matter physics.
Subjects--Index Terms:

Fractionalization

Studies on Fractionalization and Topology in Strongly Correlated Systems from Zero to Two Dimensions.
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245 1 0 $a Studies on Fractionalization and Topology in Strongly Correlated Systems from Zero to Two Dimensions.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 195 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
500 $a Advisor: Kane, Charles L.
502 $a Thesis (Ph.D.)--University of Pennsylvania, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a The interplay among symmetry, topology and condensed matter systems has deepened our understandings of matter and lead to tremendous recent progresses in finding new topological phases of matter such as topological insulators, superconductors and semi-metals. Most examples of the aforementioned topological materials are free fermion systems, in this thesis, however, we focus on their strongly correlated counterparts where electron-electron interactions play a major role. With interactions, exotic topological phases and quantum critical points with fractionalized quantum degrees of freedom emerge. In the first part of this thesis, we study the problem of resonant tunneling through a quantum dot in a spinful Luttinger liquid. It provides the simplest example of a (0+1)d system with symmetry-protected phase transitions. We show that the problem is equivalent to a two channel SU(3) Kondo problem and can be mapped to a quantum Brownian motion model on a Kagome lattice. Utilizing boundary conformal field theory, we find the universal peak conductance and compute the scaling behavior of the resonance line-shape.For the second part, we present a model of interacting Majorana fermions that describes a superconducting phase with a topological order characterized by the Fibonacci topological field theory. Our theory is based on a SO(7)1 = SO(7)1/(G2)1 x (G2)1 coset construction and implemented by a solvable two-dimensional network model. In addition, we predict a closely related ''anti-Fibonacci'' phase, whose topological order is characterized by the tricritical Ising model. Finally, we propose an interferometer that generalizes the Z2 Majorana interferometer and directly probes the Fibonacci non-Abelian statistics.For the third part, we argue that a correlated fluid of electrons and holes can exhibit fractional quantum Hall effects at zero magnetic field. We first show that a Chern insulator can be realized as a free fermion model with p-wave(m = 1) excitonic pairing. Its ground state wavefunction is then worked out and generalized to m > 1. We give several pieces of evidence that this conjectured wavefunction correctly describes a topological phase, dubbed ''fractional excitonic insulator'', within the same universality class as the corresponding Laughlin state at filling 1/m. We present physical arguments that gapless states with higher angular momentum pairing between energy bands are conducive to forming the fractional excitonic insulator in the presence of repulsive interactions. Without interactions, these gapless states appear at topological phase transitions which separate the trivial insulator from a Chern insulator with higher Chern number. Since the nonvanishing density of states at these higher angular momentum band inversion transitions can give rise to interesting many-body effects, we introduce a series of minimal lattice models realizations in two dimensions. We also study the effect of rotational symmetry broken electron-hole exciton condensation in our lattice models using mean field theory.
590 $a School code: 0175.
650 4 $a Condensed matter physics. $3 3173567
650 4 $a Physics. $3 516296
653 $a Fractionalization
653 $a Topology
653 $a Strongly correlated systems
653 $a Zero to two dimensions
690 $a 0611
690 $a 0605
710 2 $a University of Pennsylvania. $b Physics and Astronomy. $3 2101621
773 0 $t Dissertations Abstracts International $g 81-02B.
790 $a 0175
791 $a Ph.D.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13864305