2015 IASTU Informal Summer Program on Frontiers in Condensed Matter Physics

Venue: Conference Hall 322, Science Building, Tsinghua

Title: From orbital selective Mott transition to Hund's metal in multi-band Hubbard model

4:00pm-5:00pm, Tuesday, June 16, 2015

Xi Dai  ( Institute of Physics, CAS )

Abstract: In this talk, I will review the main progress in multi-band Hubbard model in recent years. Including the orbital degree of freedom in Hubbard model will generate several new features, such as the coexistence of the itinerant and local moment features for the electrons, which are impossible for the single band systems. I will also explain in detail that the interplay between the orbital and spin fluctuation will lead to non-Fermi liquid behavior in these systems in a quite wide temperature range.

Title: A discretized Chern-Simons gauge theory on arbitrary graphs

2:30pm-3:30pm, Wednesday, June 17, 2015

Kai Sun  ( University of Michigan )

Abstract: In this talk, I will show how to discretize the Chern-Simons gauge theory on generic planar lattices/graphs (with or without translational symmetries) embedded in arbitrary 2D closed orientable manifolds. We find that, as long as a one-to-one correspondence between vertices and faces can be defined on the graph such that each face is paired up with a neighboring vertex (and vice versa), a discretized Chern-Simons theory can be constructed consistently. We further verify that all the essential properties of the Chern-Simons gauge theory are preserved in the discretized setup. In addition, we find that the existence of such a one-to-one correspondence is not only a sufficient condition for discretizing a Chern-Simons gauge theory but, for the discretized theory to be nonsingular and to preserve some key properties of the topological field theory, this correspondence is also a necessary one. A specific example will then be provided, in which we discretize the Chern-Simons gauge theory on a tetrahedron.

Title: Topological Phases of Bosonic Matter and Topological Quantum Field Theory

4:00pm-5:00pm, Tuesday, June 23, 2015

Peng Ye (Perimeter Institute for Theoretical Physics)

Abstract: It is known that fractional quantum Hall effect is a star physics platform for the application of Chern-Simons theory that is a typical type of topological quantum field theory (TQFT). In this talk, I would like to explore more TQFT examples from the perspective of generalization of non-local Aharonov-Bohm effect. I will introduce (a) twisted bosonic superconductors; (b) bosonic integer quantum Hall effect; (c) TQFT of bosonic topological insulators where a "cosmological constant term" emerges; (d) towards complete TQFT description of Abelian SPT (symmetry-protected topological phases) in three dimensions. The talk is technique-free and in a plain language.

Title: Measuring symmetry fractionalization in quantum spin liquids and beyond

4:00pm-5:00pm, Wednesday, June 24, 2015

Yuan-Ming Lu ( The Ohio State University )

Abstract: Quantum spin liquids are symmetric ground states of frustrated magnets, featured by fractional excitations called "spinons". Similar to fractional quantum Hall effects where quasiparticles carry fractional charge, spinons and other fractional excitations in a quantum spin liquid can also carry fractional quantum numbers of global and crystal symmetries. This phenomena is coined "symmetry fractionalization".

Motivated by mounting numerical evidence for spin liquid ground states in various two-dimensional frustrated spin models, here we develop systematic methods to measure the global and crystal symmetry quantum numbers of fractional excitations. We show that the symmetry fractionalization patterns in a quantum spin liquid can be measured by a dimensional reduction regime, which relates the two-dimensional symmetric topological orders to one-dimensional symmetry protected topological phases. This general framework is directly applicable to numeric results obtained in 2d DMRG studies, and can be generalized to other gapped topological orders in two dimensions.

Title: Weyl semi-metal phase in non-centrosymmetric metal pnictide family

4:00pm-5:00pm, Friday, June 26, 2015

Yulin Chen ( Oxford / Tsinghua )

Abstract: The discovery of quantum materials with non-trivial topological electronic structures has recently ignited intensive interest in physics and materials science. Topological Weyl semimetals (TWSs) represent a new state that that not only possesses Weyl fermions in the bulk and unique Fermi-arcs generated by topological surface states, but also exhibits appealing physical properties such as extremely large magnetoresistance and ultra-high carrier mobility.

In this talk, I will show our angle-resolved photoemission spectroscopy (ARPES) measurement on a recently proposed materials (represented by TaAs), we directly observed the band structures with characteristic Fermi-arcs. In addition, by systematically investigating different compounds from the same material family, we observed the Fermiology evolution with spin-orbit coupling (SOC) strength. The discovery of this family of TWSs provides a rich material base for exploring many exotic physical phenomena and novel future applications.

Title: Geometry of Reduced Density Matrices

2:30pm-3:30pm, Friday, July 10, 2015

Bei Zeng (University of Guelph)

Abstract: This talk discusses the concepts of the local Hamiltonian problem, the quantum marginal problem, and the relationship to the geometry of the reduced density matrices. We then discuss how this geometry is related to quantum phase and phase transitions.

Title: Spin-helical surface Dirac fermions in topological insulators: quantum transport and potential applications

4:00pm-5:00pm,   Friday, July 10, 2015

Yong P. Chen ( Purdue Univ )

Abstract: I will discuss our recent experimental measurements of characteristic transport phenomena of topological surface state spin-helical Dirac fermions in topological insulators, such as the “half-integer” quantum Hall effect, current-induced helical spin polarization, and “half-integer” Aharonov-Bohm effect.  Such spin-helical surface Dirac fermions may find promising applications in spintronics and quantum information devices. 

Title: Universal Incoherent Metallic Transport

2:00pm, Thursday, July 23, 2015

Sean Hartnoll (Stanford University)

Abstract: I will discuss various aspects of transport in strongly correlated metals. The current theoretical situation is that while many different families of materials (cuprates, pncitides, heavy fermions, organs, ruthenates, etc.) seem to exhibit similar behavior, such as T-linear resistivity, a compelling explanation is lacking. I will argue that strongly correlated transport needs to be thought about in a very different way than the conventional Boltzmann equation quasiparticle picture. I will give a sort of “classification” of strongly correlated transport and discuss how universal bounds may be able to explain the similarity in behavior across so many materials.

Title: From 3He Superfluid A Phase to Weyl Semimetals

4:30pm, Friday, July 24, 2015

Shun-Qing Shen (Department of Physics, The University of Hong Kong )

Abstract: Liquid 3He becomes superfluid at low temperatures, and has two different phases, A phase and B phase. Since 3He atoms are neutral, there is no Meissner effect, but atoms form pairing like the Copper pairs of electrons in superconductors. Atoms also avoid the singlet pairing, as in metals, and tend to pair in the form of spin triplet. The 3He A phase is an equal spin pairing state with gapless excitations. Weyl semimetals are three-dimensional topological states of matter, in a sense that they host paired monopole and anti-monopole of Berry curvature in momentum space, leading to the chiral anomaly. The chiral anomaly has long been believed to give a positive magnetoconductivity in strong and parallel fields.

In this talk, I start with the 3He A phase, and show the connection between the phase and Weyl semimetals. Weyl semimetals and Weyl superconductors/superfluids can be described by the same mathematical model as the 3He A phase.

Title: Topological nonsymmorphic crystalline superconductors

10:30am, Monday, July 27, 2015

Chao-Xing Liu  (Pennsylvania State University)

Abstract: Topological superconductors possess a superconducting gap in the bulk and gapless zero energy modes, known as “Majorana zero modes”, at the boundary of a finite system. In a crystal, when crystalline symmetry is taken into account, more classes of topological superconductors can exist and are protected by crystalline symmetry. These types of topological superconductors are known as "topological crystalline superconductors". In this talk, I will introduce a new class of topological crystalline superconductors, which are protected by nonsymmorphic crystalline symmetry, the glide symmetry, and thus dubbed “topological nonsymmorphic crystalline superconductors”. For a space group, glide symmetry means a symmetry operation that is a combination of mirror symmetry and non-primitive translation. Compared to mirror symmetry, additional phase factor can be introduced to the eigen wave function of a non-symmorphic crystal due to the non-primitive translation. We will show that this fact will lead to the classification of topological nonsymmorphic crystalline superconductors different from that of topological mirror superconductors. We construct an explicit Bogoliubov-de Gennes type of model for this topological superconducting phase in the D class of Altland-Zirnbauer classification and show explicitly that Majorana zero modes in this model are protected by glide symmetry.

Title: Dirac string gas approach to the spontaneous spin textures in dipolar spinor condensates

3:30pm, Monday, July 27, 2015

Biao Lian  (Stanford University )

Abstract: We study the spontaneous spin textures induced by magnetic dipole-dipole interaction in ferromagnetic spinor condensates under various trap geometries. At the mean-field level, we show the system is dual to a Dirac string gas with a negative string tension in which the ground state spin texture can be easily determined. We find that three-dimensional condensates prefer a meron-like vortex texture, quasi-one-dimensional condensates prefer the axially polarized flare texture, while condensates in quasi-two-dimensions exhibit either a meron texture or an in-plane polarized texture.

Title: The mutual information as the diagnostic of classical and topological order and the topological uncertainty principle

3:30pm, Wednesday, July 29, 2015

Chao-Ming Jian  (Stanford University)

Abstract: In the Landau paradigm, classical orders are characterized by local order parameters. It is one of the most prevailing framework for understanding classical orders in different phases of matter. Yet the use local order parameters leads to a certain limitation of this paradigm. In the detection of the orders in a given phase, some knowledge of the specific form of the order parameters, which could sometime be hard to obtain, is often require a priori. Also, this paradigm fails to capture the topological order which are not described local order parameters. In this talk, we propose to use the mutual information, as an alternative to local order parameters, as a generalized probe that describes both classical and topological orders in the same language. We will illustrate the behavior of the mutual information in both classically and topologically ordered systems in various of spacetime dimensions. We will propose the topological uncertainty principle of the mutual information which serves as the unique features of topological orders in general dimensions.

Title: Characterizing eigenstate thermalization via measures in the Fock space of operators

2:30pm, Friday, July 31, 2015

Blackboard talk by Xiao-Liang Qi   (Stanford University)

Abstract: The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap between quantum mechanical and statistical mechanical descriptions of isolated quantum systems. Here, we define unbiased measures for how well the ETH works in various regimes, by mapping general interacting quantum systems on regular lattices onto a single particle living on a high-dimensional graph. By numerically analyzing deviations from ETH behavior in the non-integrable Ising model, we propose a quantity that we call the weight to democratically characterize the average deviations for all operators residing on a given number of sites, irrespective of their spatial structure. It appears to have a simple scaling form, that we conjecture to hold true for all non-integrable systems. A closely related quantity, that we term the distinguishability, tells us how well two states can be distinguished if only site operators are measured. Along the way, we discover that complicated operators on average are worse than simple ones at distinguishing between neighboring eigenstates, contrary to the naive intuition created by the usual statements of the ETH that few-body (many-body) operators acquire the same (different) expectation values in nearby eigenstates at finite energy density. Finally, we sketch heuristic arguments that the ETH originates from the limited ability of simple operators to distinguish between quantum states of a system, especially when the states are subject to constraints such as roughly fixed energy with respect to a local Hamiltonian.

Reference: Pavan Hosur and Xiao-Liang Qi, http://arxiv.org/abs/1507.04003

Title: 1. The honeycomb lattice with multi-orbital structure: strong correlation and topological states with large gap 2. Epitaxial growth and STM observation of multi-layer silicene

10:00am, Monday, August 3, 2015

Speaker: 1. Prof. Congjun Wu, University of California, San Diego, USA  2.Dr. Yi Du and Dr. Zhi Li, Australian Institute for Innovative Materials, Wollongong, Australia


1.Different from graphene which is orbitally inactive, the $p_x/p_y$-orbital bands in the 2D honeycomb lattice are orbitally active, which apply to both optical lattices and several classes of solid state systems including organic materials, fluoridated tin film, BiX/SbX(X=H, F, Cl, Br). The interplay between the orbital structure and spin-orbit coupling gives rise to the 2D quantum spin Hall state and quantum anomalous Hall state with large topological gaps. The gap magnitudes are equal to the spin-orbit coupling strength at the atomic level, and thus are much larger than those based on the s-p band inversion. The energy spectra and eigen-wavefunctions are solved analytically based on the Clifford algebra, which greatly facilitates the topological analysis. Flat bands also naturally arise and the consequential non-perturbative physics includes Wigner crystallization and ferromagnetism. In the Mott-insulating state, orbital exchange is highly frustrated described by a quantum 120$^\circ$ model which is similar to but different from the Kitaev model. An f-wave Cooper pairing arises if the band is filled with spinless fermions exhibiting boundary zero energy Andreev modes. Although the pairing mechanism is conventional, the unconventional pairing symmetry is driven by the non-trivial band structure.

2.It is controversial whether multi-layer silicene could exist with retaining 2D honeycomb features, considering the strong interlayer interaction and the competition between sp2 and sp3 hybridization.  In this talk, we report √3×√3  multilayer silicene epitaxially grown on Ag (111) surface.  The scanning tunneling microscopy (STM) topography indicates a low-buckled structure different from bulk silicon. In addition, we managed to mechanically peel off the top Si layer, and observed the same √3×√3 structure of the underlying layers.  These studies suggest a quasi-layered structure. The interlayer interaction provides an important yet rarely explored degree of freedom for tuning the electronic structure. We demonstrate that a rotation between stacked silicene layers can create van Hove singularities within a large range of twisting angle.  More surprisingly, electrons with certain energy are found to spontaneously form a kagome lattice. We will also mention possible features of flat bands and nontrivial edge states we recently noticed in this system.


1.Congjun Wu received his Ph.D. in physics from Stanford University in 2005, and did his postdoctoral research at the Kavli Institute for Theoretical Physics, University of California, Santa Barbara, from 2005 to 2007. He became an assistant professor in the Department of Physics at the University of California, San Diego (UCSD) in 2007, and an associate professor at UCSD in 2011. His research interests include quantum magnetism, superconductivity, orbital physics, and topological states in condensed-matter and cold-atom systems.

2.Yi Du was awarded his Ph.D. in Materials Science and Engineering from University of Wollongong (UOW) in 2011, and became the Vice-Chancellor’s Postdoctoral Research Fellow at the Australian Institute for Innovative Materials (AIIM), UOW from 2012 to 2013. He currently works as a research fellow in Institute of Superconducting and Electronic Materials (ISEM), AIIM, UOW.

Zhi Li received his Ph.D. in condensed matter physics from Institute of Physics (IOP), Chinese Academy of Sciences (CAS) in 2014. He is currently a postdoctoral fellow at ISEM, AIIM, UOW.

Yi and Zhi’s group is mainly working on topological and superconducting two-dimensional materials by using molecular beam epitaxy (MBE) and scanning tunneling microscopy (STM) techniques.

 Selected References

1. Gu-Feng Zhang, Yi Li, Congjun Wu, ,The honeycomb lattice with multi-orbital structure: topological and quantum anomalous Hall insulators with large gaps ,Phys. Rev. B 90, 075114 (2014) .

Wei-cheng Lee, Congjun Wu, and S. Das Sarma, "$F$-wave pairing of cold atoms in optical lattices", Phys. Rev. A 82, 053611 (2010).

Congjun Wu, "Orbital analogue of quantum anomalous Hall effect in $p$-band systems", Phys. Rev. Lett. 101, 186807 (2008).

Congjun Wu, "Orbital orderings and frustrations of p-band systems in optical lattices", Phys. Rev. Lett. 100, 200406 (2008).

Congjun Wu, Doron Bergman, Leon Balents, and S. Das Sarma, "Flat bands and Wigner crystallization in the honeycomb optical lattice", Phys. Rev. Lett. 99, 70401 (2008).

2. J. Zhuang, X. Xu, Y. Du, K. Wu, L. Chen, W. Hao, J. Wang, W. K. Yeoh, X. L. Wang, and S. X. Dou, “Investigation of Electron-Phonon Coupling in Epitaxial Silicene by In-situ Raman Spectroscopy”,  Phys. Rev. B 91, 161409(R) (2015)

Yi Du, Jincheng Zhuang, Hongsheng Liu, Xun Xu, Stefan Eilers, Kehui Wu, Peng Cheng, Jijun Zhao, Xiaodong Pi, Khay Wai See, Germanas Peleckis, Xiaolin Wang, and Shi Xue Dou, “Tuning the Band Gap in Silicene by Oxidation”, ACS Nano 8, 10019 (2014)

Xun Xu, Jincheng Zhuang, Yi Du, Haifeng Feng, Nian Zhang, Chen Liu, Tao Lei, Jiaou Wang*, Michelle Spencer, Tetsuya Morishita, Xiaolin Wang and Shi Xue Dou, “Effect of Oxygen Adsorption on the Surface State of Epitaxial Silicene on Ag(111)”, Sci. Rep. 4, 7543 (2014)

Zhi Li, Haifeng Feng, Jincheng Zhuang, Na Pu, Li Wang, Xun Xu, Weichang Hao, Yi Du, “Metal-silicene interaction studied by scanning tunneling microscopy”, J. Phys.: Condens. Matter (2015, accepted).

Title: Topological Cooper pairing from magnetic dipolar interactions and in doped Weyl semi-metal

3:00pm, Tuesday, August 18, 2015

Yi Li  ( Princeton University )


Part I:  Ultra-cold dipolar fermions have become a major research focus of cold atom physics. The progress of laser cooling of the rare earth fermions 161Dy and 163Dy has opened up a whole new opportunity to study novel itinerant fermion systems characterized by magnetic dipolar interactions, which are qualitatively different from solid-state electron systems. Magnetic dipole moments are intrinsically quantum operators proportional to the hyperfine-spin. In unpolarized systems, magnetic dipolar interactions are isotropic but exhibit the spin-orbit coupled nature, which brings important consequences to the many-body physics. As a starting point, we use spin-1/2 fermions as a prototype model which preserves the spin-orbit coupled feature of the magnetic dipolar interaction.

Magnetic dipolar interaction leads to a robust mechanism for the p-wave spin triplet pairing, which is different from the usual spin fluctuation mechanism in 3He. Furthermore, a novel pairing symmetry appears, which, to our knowledge, has not been studied in condensed matter systems before. The spin and orbital angular momenta of Cooper pairs are coupled to form total angular momentum J = 1. This J-triplet pairing phase is different from both the spin-orbit coupled 3He-B phase whose J=0 and the spin-orbit decoupled 3He-A phase. It possesses nodal Bogoliubov quasi-particles which exhibit either time-reversal invariant Dirac type spectra or the time-reversal symmetry breaking Weyl type spectra.


1) YL, C. Wu, Scientific Report 2, 392 (2012);

2) YL, C. Wu, Phys. Rev. B 85, 205126 (2012);

3) YL, C. Wu, J. Phys. Cond. Matt. 26, 493203 (2014);

Part II: I will discuss how the topology of Fermi surfaces may fundamentally change the Cooper pairing nodal structure as well as the pairing symmetry. Fermi surfaces with non-trivial topology widely exist, for example, in doped Weyl metals. For pairing between two Fermi surfaces carrying opposite Chern numbers ±q, the pairing phases cannot be globally well-defined over the Fermi surface, which exhibit non-trivial Berry phase structure characterized by the monopole charge q. Consequently, it exhibits novel Cooper pairing with non-zero total vorticity over the Fermi surface. In the presence of rotational symmetry, the Cooper pairing symmetry cannot be classified by ordinary spherical harmonic functions but by monopole harmonic functions defined on the Fermi surface.


1) YL, APS 2015 March Meeting Talk;

2) YL, F.D.M. Haldane, to be submitted.

Title: Axion field theory approach for classification of topological superconductors

3:00pm, Wednesday, August 19, 2015

Ying-Fei Gu   ( Stanford University )

Abstract: Time-reversal invariant topological superconductors (TRI TSC) are gapped superconductors with topologically robust gapless modes on the boundary. In the work by X. L. Qi et al, [PRB, 87, 134519(2013)], a topological field theory description was proposed for 3+1-dimensional TRI TSC, which contains an axionic coupling between superconducting phase and electromagnetic field. In my talk, I will describe an argument based on topological response in axion field theory for the classification problem of TRI TSC in general 4k(k-integer) space-time dimensions, e.g., in 3+1 dimension, this argument indicates a Z16 classification.

Title: Non-perturbative Results for Itinerant Ferromagnetism in Multi-orbital Systems

3:00pm, Friday, August 21, 2015

Yi Li  ( Princeton University )

Abstract: Although ferromagnetism (FM) was discovered more than 2000 years ago, it remains one of the major challenges of contemporary condensed matter physics. Different from superconductors of which the BCS theory usually provides a controllable weak-coupling description, itinerant FM is intrinsically a strong-correlation phenomenon and needs non-perturbative study. On the other hand, most FM materials are orbitally active with prominent Hund’s coupling. However, Hund’s rule is local physics, which can only polarize electrons on the same site, and it is a longstanding problem under what conditions Hund’s coupling can lead to the global FM coherence.

In this talk, I will present non-perturbative studies on a class of 2D and 3D multi-orbital Hubbard models in which Hund’s coupling plays the essential role, including exact theorems proving itinerant FM ground states and high precision quantum Monte-Carlo (QMC) simulations on thermodynamic properties. These exact results set up stable phases of itinerant FM in a large region of electron densities. Hence, they serve as a reference point for further explorations and can be applied to a wide class of systems ranging from the transition-metal-oxide hetero-structure of the LaAlO3/SrTiO3 interface, and to the p-orbital band systems of ultra-cold fermions in optical lattices. Their connection to the 3D FM material in the SrRuO3 will also be discussed. The results provide helpful guidance for the searching of novel 2D and 3D itinerant FM materials.

Furthermore, the magnetic phase transition is another long-standing problem in itinerant FM due to the lack of non-perturbative treatment on the strong magnetic fluctuations with electron itineracy. QMC simulations are ideal non-perturbative numeric methods. However, they usually suffer from the notorious sign problem for fermions. In this talk, our itinerant FM systems will be shown free of the sign problem. The QMC results of thermodynamic properties will be presented.


1) YL, E. H. Lieb, C. Wu, Phys. Rev. Lett. 112, 217201 (2014).

2) YL, Phys. Rev. B 91, 115112 (2015).

3) S. Xu, YL, C. Wu, Phys. Rev. X 5, 021032 (2015).

Title: Symmetry Fractionalization in 2D and 3D Topological Phases

4:00pm, Monday, August 24, 2015 & 4:00pm, Wednesday, August 26, 2015

Xie Chen   (California Institute of Technology)

Abstract: In 2D topological phases with symmetry, the fractional excitations in the system can transform under symmetry in a fractional way, e.g. by carrying fractional symmetry charges. With different types of topological order and different symmetries, what symmetry fractionalization (SF) patterns are possible in general? This question becomes particularly interesting with recent experimental progress towards realizing spin liquids and we try to answer this question in this talk. First, we discuss a simple consistency condition that all SF patterns have to satisfy. Surprisingly, some seemingly consistent SF patterns are actually anomalous, i.e. they cannot be realized in purely 2D systems. To exclude these cases, we discuss two anomaly detection methods: the flux fusion method, which is physically intuitive but applies only to special cases, and the gauging obstruction method, which is mathematically complete and straight-forward to apply. We give specific examples of anomalous SF patterns to be detected by these methods and discuss the interesting possibility of realizing them on the surface of 3D systems.

After obtaining a pretty complete understanding in 2D, we move on to address the same question in 3D. A new feature of 3D topological phases is the existence of loop excitations and we discuss first how to properly describe symmetry fractionalization on loops. Using a dimension reduction procedure, we show that loop excitations exist as the boundary between two 2D symmetry enriched topological phases and it is the difference in these phases that characterize the symmetry action. Moreover, similar to the 2D case, we find that some seemingly possible symmetry fractionalization patterns are actually anomalous and cannot be realized in 3D. To detect such anomalies, we generalize the flux fusion method and apply it to 3D. To illustrate these ideas, we use the 3D Z2 gauge theory with Z2 symmetry as an example and completely list the corresponding SET phases. In particular, we find four non-anomalous SETs and one anomalous SET which we show to be realizable as the surface of a 4D system.

Title: A classification of bosonic/fermionic topological order with/without symmetry

2:00pm-4:00pm, Thursday, August 27, 2015

Xiao-Gang Wen   (MIT/ PI/ Tsinghua)

Abstract: We show that 2+1D fermionic topological orders without symmetry and 2+1D fermionic/bosonic topological orders with symmetry G are classified by braided fusion category (BFC) over symmetric tensor category (STC); where the STC describes a fermion product state without symmetry or a fermion/boson product state with symmetry G. We developed a simplified theory of BFC over STC based on the fusion coefficients Nijk  and spins si. In this talk, I will explain this kind of theory in simple terms.