January 2-6, 2015, GIS NTU Convention Center, Taipei, Taiwan
 
Programme
1/2 Fri.
Time
Speaker
Title
8:45-9:15
Registration
Chair: Chuan-Tsung Chan
9:15-9:30
Feng-Li Ling
Opening Remarks

9:30-11:00

Zhengcheng Gu
Emergence of p+ip superconductivity in 2D strongly correlated Dirac fermions
Searching for p+ip superconducting(SC) state has become a fascinating subject in condensed matter physics, as a dream application awaiting in topological quantum computation. In this paper, we report a theoretical discovery of a p+ip SC ground state (coexisting with ferromagnetic order) in honeycomb lattice Hubbard model with infinite repulsive interaction at low doping(δ<0.2), by using both the state-of-art Grassmann tensor product state(GTPS) approach and a quantum field theory approach. Our discovery suggests a new mechanism for p+ip SC state in generic strongly correlated systems and opens a new door towards experimental realization. The p+ip SC state has an instability towards a potential non-Fermi liquid with a large but finite U. However, a small Zeeman field term stabilizes the p+ip SC state. Relevant realistic materials are also proposed.

Slide, Video I, II, III, IV
11:00-11:15
----- Break -----
11:15-12:00
Ching-Yu Huang
The detection of topologically ordered phases
Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry enriched topological (SET) phases. We introduce simple methods to detect the SET order directly from a complete set of topologically degenerate ground state wave functions. In particular, we first show how to directly determine the characteristic symmetry fractionalization of the quasiparticles from the reduced density matrix of the minimally entangled states. Second, we show how a simple generalization of a string order parameter can be measured to detect SET. The selection rules will get a characterization of SET. This way is more physical, and can be used by other methods, e.g., quantum Monte Carlo methods or potentially measured experimentally. We demonstrated the usefulness of this approach by considering a spin-1 model on the honeycomb lattice and the resonating valence bond state on a kagome lattice. On the other hand, in the tensor network approach to simulate strongly interacting systems, the quantum state renormalization algorithm has been shown to be effective in identifying intrinsic topological orders. We demonstrate the effectiveness of this algorithm with examples of nontrivial symmetry-protected topological (SPT) phases with internal symmetry in 1D and internal and translation symmetry in 2D.

Slide, Video I, II
12:00-13:30
----- Lunch (not catered)-----
Chair: Chi-Ken Lu
13:30-15:00
Tzu-Chieh Wei
Topological entanglement and minimally entangled states via the geometric measure of entanglement I
I will introduce a geometric measure of entanglement (GE) and use it to quantify entanglement in toric code ground states in certain basis. It turns out that the geometric entanglement exhibits a bulk law and an additional constant, the latter being the identical to the topological entanglement entropy. The entanglement itself can actually be used to obtain the four minimally entangled states (MES), which form a special basis in the ground space and can be used to obtain the modular matrices. Next, I will examine how the topological entanglement via GE can be used to detect the transition from the Z_2 topological phase to a trivial phase by applying a string tension to the toric code. Such a string tension frustrates large loop configurations in the toric code ground state, and when it is sufficiently large, the wavefunction becomes a trivial product state. Somewhere between the exact toric code ground state and the trivial product state, there must exist a phase transition. I will present numerical results to extract the "topological" part of the geometric entanglement as the string tension varies. In the large system limit, it is indeed constant inside the topological phase and sharply drops to zero in the trivial phase, and it correctly identifies the transition point. It turns out that the transition point can be obtained analytically by mapping to the classical 2D Ising model and agrees with the numerics.

Slide, Video I, II, III
15:00-15:15
----- Break -----
15:15-16:00
Chi-Ken Lu
From zero mode to topological superconductivity in graphene
Correlated electronic states in graphene is the subject that many theorists and experimentalists pursue. The vanishing density of state at the charge neutral point has been shown to prevent gap opening at Dirac point. Nevertheless, the presence of magnetic field may help develop the correlated states. In this talk, the textured excitation of massive (chiral) Dirac electrons are discussed. I shall make a connection of zero mode to the topological term in a general context. The implication of topological term is the charged mass Skyrmion. I shall also discuss a phase transition from the Skyrmion into the superconducting state.

Slide, Video I, II


1/3 Sat.
Time
Speaker
Title
Chair: Ying-Jer Kao

9:30-11:00

Xiao-Gang Wen
Symmetry protected topological order and group cohomology theory I
Symmetry protected topological (SPT) states are a new kind of gapped states that do not break any symmetry and have no topological order. Despite having no symmetry breaking order and having no topological order (ie no fractionalized topological excitations and no robust gapless boundary excitations), SPT states can still be non-trivial new states of matter. I will present
(1) a systematic theory of SPT order based on non-linear sigma model and its topological terms.
(2) ways to probe/measure SPT orders, and the connection to anomalies
(3) mechanism to generate SPT orders

Slide, Video I, II, III, IV
11:00-11:30
----- Break -----
11:30-12:15
Tzu-Chieh Wei
Topological entanglement and minimally entangled states via the geometric measure of entanglement II
I will introduce a geometric measure of entanglement (GE) and use it to quantify entanglement in toric code ground states in certain basis. It turns out that the geometric entanglement exhibits a bulk law and an additional constant, the latter being the identical to the topological entanglement entropy. The entanglement itself can actually be used to obtain the four minimally entangled states (MES), which form a special basis in the ground space and can be used to obtain the modular matrices. Next, I will examine how the topological entanglement via GE can be used to detect the transition from the Z_2 topological phase to a trivial phase by applying a string tension to the toric code. Such a string tension frustrates large loop configurations in the toric code ground state, and when it is sufficiently large, the wavefunction becomes a trivial product state. Somewhere between the exact toric code ground state and the trivial product state, there must exist a phase transition. I will present numerical results to extract the "topological" part of the geometric entanglement as the string tension varies. In the large system limit, it is indeed constant inside the topological phase and sharply drops to zero in the trivial phase, and it correctly identifies the transition point. It turns out that the transition point can be obtained analytically by mapping to the classical 2D Ising model and agrees with the numerics.

Slide, Video I, II
12:15-13:30
----- Lunch (not catered)-----
Chair: Mikio Nakahara
13:30-14:15
Tzu-Chieh Wei
Topological entanglement and minimally entangled states via the geometric measure of entanglement III
I will introduce a geometric measure of entanglement (GE) and use it to quantify entanglement in toric code ground states in certain basis. It turns out that the geometric entanglement exhibits a bulk law and an additional constant, the latter being the identical to the topological entanglement entropy. The entanglement itself can actually be used to obtain the four minimally entangled states (MES), which form a special basis in the ground space and can be used to obtain the modular matrices. Next, I will examine how the topological entanglement via GE can be used to detect the transition from the Z_2 topological phase to a trivial phase by applying a string tension to the toric code. Such a string tension frustrates large loop configurations in the toric code ground state, and when it is sufficiently large, the wavefunction becomes a trivial product state. Somewhere between the exact toric code ground state and the trivial product state, there must exist a phase transition. I will present numerical results to extract the "topological" part of the geometric entanglement as the string tension varies. In the large system limit, it is indeed constant inside the topological phase and sharply drops to zero in the trivial phase, and it correctly identifies the transition point. It turns out that the transition point can be obtained analytically by mapping to the classical 2D Ising model and agrees with the numerics.

Slide, Video I, II
14:15-14:30
----- Break -----
14:30-16:00
Zhengcheng Gu
Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
Bosonic topological insulators (BTI) in three spatial dimensions are symmetry protected topological (SPT) phases with U(1)⋊ZT2 symmetry, where U(1) is boson particle number conservation, and ZT2 is time-reversal symmetry with T2=1. BTI were first proposed based on the group cohomology theory which suggests two distinct root states, each carrying a Z2 index. Soon after, surface anomalous topological orders were proposed to identify different root states of BTI, leading to a new BTI root state beyond the group cohomology classification. Nevertheless, it is still unclear what is the universal physical mechanism for BTI phases and what kinds of microscopic Hamiltonians can realize them. In this paper, we answer the first question by proposing a universal physical mechanism via vortex-line condensation in a superfluid, which can potentially be realized in realistic systems, e.g., helium-4 or cold atoms in optical lattices. Using such a simple physical picture, we find three root phases, of which two of them are classified by group cohomology theory while the other is beyond group cohomology classification. The physical picture also leads to a "natural" bulk dynamic topological quantum field theory (TQFT) description for BTI phases and gives rise to a possible physical pathway towards experimental realizations. Finally, we generalize the vortex-line condensation picture to other symmetries and find that in three dimensions, even for a unitary Z2 symmetry, there could be a nontrivial Z2 SPT phase beyond the group cohomology classification.

Slide, Video I, II, III


1/4 Sun.
Time
Speaker
Title
Chair: Pochung Chen

9:30-11:00

Xiao-Gang Wen
Symmetry protected topological order and group cohomology theory II
Symmetry protected topological (SPT) states are a new kind of gapped states that do not break any symmetry and have no topological order. Despite having no symmetry breaking order and having no topological order (ie no fractionalized topological excitations and no robust gapless boundary excitations), SPT states can still be non-trivial new states of matter. I will present
(1) a systematic theory of SPT order based on non-linear sigma model and its topological terms.
(2) ways to probe/measure SPT orders, and the connection to anomalies
(3) mechanism to generate SPT orders

Video I, II, III, IV
11:00-11:30
----- Break -----
11:30-12:15
Cenke Xu
Field theory description and classification of "Almost" topological states I
In these lectures we will discuss quantum field theory description and classification of "almost" topological states of matter, which include bosonic symmetry protected topological states, and more generally short range entangled states which do not require any symmetry. These states all have a trivially gapped and nondegenerate bulk spectrum, but protected gapless or degenerate boundary spectrum. Field theory serves as a convenient and intuitive formalism for understanding these states, it gives us both the boundary properties and bulk wave function of these states. We will also discuss topological insulators under strong interaction, and its possible connection to the Standard Model and Grand Unified Theories.

Slide, Video I, II
12:15-14:00
----- Lunch (not catered)-----
Chair: Wei-Feng Tsai
14:00-14:45
Cenke Xu
Field theory description and classification of "Almost" topological states II
In these lectures we will discuss quantum field theory description and classification of "almost" topological states of matter, which include bosonic symmetry protected topological states, and more generally short range entangled states which do not require any symmetry. These states all have a trivially gapped and nondegenerate bulk spectrum, but protected gapless or degenerate boundary spectrum. Field theory serves as a convenient and intuitive formalism for understanding these states, it gives us both the boundary properties and bulk wave function of these states. We will also discuss topological insulators under strong interaction, and its possible connection to the Standard Model and Grand Unified Theories.

Slide, Video I, II
14:45-15:00
----- Break -----
15:00-16:30
Ling-Yan Hung
Anyon condensation and boundary conditions of non-chiral topological order in 2+1 dimensions
We will review previous work on the classification of boundary conditions of Abelian topological order in 2+1 dimensions. We will discuss their connection with anyon condensation, and also review the basics of anyon condensation. We will then generalize our discussion to obtaining boundary conditions of non-Abelian topological phases, and compute ground state degeneracy of non-Abelian topological order on open surfaces.

Video I, II, III

16:30-17:15

Xiao-Gang Wen
Symmetry protected topological order and group cohomology theory III
Symmetry protected topological (SPT) states are a new kind of gapped states that do not break any symmetry and have no topological order. Despite having no symmetry breaking order and having no topological order (ie no fractionalized topological excitations and no robust gapless boundary excitations), SPT states can still be non-trivial new states of matter. I will present
(1) a systematic theory of SPT order based on non-linear sigma model and its topological terms.
(2) ways to probe/measure SPT orders, and the connection to anomalies
(3) mechanism to generate SPT orders

Video I, II, III


1/5 Mon.
Time
Speaker
Title
Chair: Tze Chieh Wei

9:30-11:00

Cenke Xu
Field theory description and classification of "Almost" topological states III
In these lectures we will discuss quantum field theory description and classification of "almost" topological states of matter, which include bosonic symmetry protected topological states, and more generally short range entangled states which do not require any symmetry. These states all have a trivially gapped and nondegenerate bulk spectrum, but protected gapless or degenerate boundary spectrum. Field theory serves as a convenient and intuitive formalism for understanding these states, it gives us both the boundary properties and bulk wave function of these states. We will also discuss topological insulators under strong interaction, and its possible connection to the Standard Model and Grand Unified Theories.

Slide, Video I, II, III, IV
11:00-11:30
----- Break -----
11:30-12:15
Brian Swingle
Renormalization Group Constructions of Quantum Phases of Matter I
I will describe an RG inspired wavefunction construction (1407.8203) that is expected to apply to a wide class of quantum many-body systems. The construction proceeds by hierarchically building up the ground state wavefunction at larger system sizes from copies of the ground state at smaller sizes mixed with initially unentangled degrees of freedom. In the first lecture I will set the basic framework and outline some rigorous results showing that essentially all known gapped phases have such ground states. In the second lecture I will describe recent rigorous results for a wide class of gapless systems. I will also set out the current state of the art, including what we believe is true but cannot yet prove and the major open questions with this approach.

Slide, Video I, II
12:15-14:00
----- Lunch (not catered)-----
Chair: Yidun Wan
14:00-14:45
Brian Swingle
Renormalization Group Constructions of Quantum Phases of Matter II
I will describe an RG inspired wavefunction construction (1407.8203) that is expected to apply to a wide class of quantum many-body systems. The construction proceeds by hierarchically building up the ground state wavefunction at larger system sizes from copies of the ground state at smaller sizes mixed with initially unentangled degrees of freedom. In the first lecture I will set the basic framework and outline some rigorous results showing that essentially all known gapped phases have such ground states. In the second lecture I will describe recent rigorous results for a wide class of gapless systems. I will also set out the current state of the art, including what we believe is true but cannot yet prove and the major open questions with this approach.

Video I, II
14:45-15:00
----- Break -----
15:00-15:45
Xi Luo
Topology induced emergent dynamic gauge theory in an extended Kane-Mele-Hubbard model
We study a Kane-Mele model with extended Hubbard interactions. We show that in the long wavelength limit there are low-lying collective excitations which are described by an emergent dynamic massive Maxwell gauge theory. The emergence of this Proca theory is related to the nontrivial topology of the Fermion model. The mass gap of the photon, namely the spin gap, can be revealed by measuring the dynamic structure factor in Bragg scattering. By coupling to an extra species of fermion, the low energy effective theory turns out to be an emergent "quantum electrodynamics" in 2+1 dimensions with/without a Chern-Simons term. We predict that a non-quantized plateau Hall effect and quantum anomalous Hall effect responding to the "electric" field, i.e., the gradient of the spin density, can be observed either individually or combinatorially.

Slide, Video I, II
15:45-17:00
Yuting Hu
Levin-Wen model with symmetry
The role of symmetry in topological phases attracts much attention in condensed matter physics. The Levin-Wen model is an important exactly solvable model for a large class of non-chiral topological phases. Enriching the Levin-Wen model with symmetry provides a natural playground for studying symmetry protected and symmetry enriched topological phases. In this talk, I will show that (1) the input data can be extended from unitary fusion categories to unitary multi-fusion categories, leading to the enrichment of global symmetries; (2) the resulting symmetry enriched topological phases are characterized by graded quantum doubles.

Slide, Video I, II, III


1/6 Tue.
Time
Speaker
Title
Chair: Ling-Yan Hung

9:30-11:00

Brian Swingle
Renormalization Group Constructions of Quantum Phases of Matter III
I will describe an RG inspired wavefunction construction (1407.8203) that is expected to apply to a wide class of quantum many-body systems. The construction proceeds by hierarchically building up the ground state wavefunction at larger system sizes from copies of the ground state at smaller sizes mixed with initially unentangled degrees of freedom. In the first lecture I will set the basic framework and outline some rigorous results showing that essentially all known gapped phases have such ground states. In the second lecture I will describe recent rigorous results for a wide class of gapless systems. I will also set out the current state of the art, including what we believe is true but cannot yet prove and the major open questions with this approach.

Video I, II, III
11:00-11:30
----- Break -----

11:30-12:15

Yidun Wan
Topological Gauge Theory Model of Topological Phases in 3-Spaces
In this talk, I shall introduce our exactly solvable lattice Hamiltonian model of topological phases in 3+1 dimensions, based on a generic finite group G and a 4-cocycle ω over G. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the 3-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasi-excitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the S⁢L⁢(3,ℤ) generators as the modular S and T matrices of the ground states, which yield a set of topological quantum numbers classified by ω and quantities derived from ω. Our model fulfills a Hamiltonian extension of the 3+1-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group G.

Video I, II, III, IV
Chair: Jiunn-Wei Chen
14:20-16:00
Xiao-Gang Wen
A unification of matter and information -- a second quantum revolution
Physics, in particular, condensed matter physics, is a very old field. Many people are thinking that the exciting time of physics has passed. We enter the beginning of the end of physics. The only important things in physics are its engineering applications, such as optical fiber and blue LED.
However, I feel that we only see the end of the beginning. The exciting time is still ahead of us. In particular, now is a very exciting time in physics, like 1900 - 1930. We are seeing/making the second quantum revolution which unifies information, matter and geometry.
Here I will describe the previous four revolutions in physics: mechanical revolution, electromagnetic revolution, general relativity revolution, and quantum revolution, as well as the fifth -- the second quantum revolution. Each revolution unifies seemingly unrelated phenomena. Each revolution requires new mathematics to describe the new theory. Each revolution changes our world view.

MAP link

Slide,Video I, II, III
@ Chin-Pao Yang Lecture Hall (Rm. 104), Department of Physics/CCMS, NTU