XiaoLiang Qi
Associate Professor of Physics, Stanford University Address: Room 312, McCullough Bldg. 476 Lomita Mall Stanford, CA 943054045
Phone: (650)7245259 Email: xlqi(at)stanford.edu
Recent Updates In the past year I have started to develop a new approach to holographic duality, which I named "exact holographic mapping". The goal of this approach is to construct the dual gravity theory and understand quantum spacetime geometry starting from the nongravity side of the duality. This approach is based on two simple principles: 1) The definition of "points" in a quantum manybody system is determined by locality of the physics. 2) Quantum entanglement determines distance between points. This proposal is discussed in http://arxiv.org/abs/1309.6282. Here is a lecture I gave on this topic: http://pirsa.org/14030107/
 I wrote a Perspective "Symmetry Meets Topology" on Science, which is a simple introduction for the article "SymmetryProtected Topological Orders in Interacting Bosonic Systems" by X. Chen, Z.C. Gu, Z.X. Liu, X.G. Wen, Science 338, 1604 (2012).
 Invited talk at Perimeter Institute, Synthetic nonAbelian anyons and beyond.
 Invited talk on APS March meeting 2012:
Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators
 One direction I am recently very interested in is the holographic duality, also known as AdS/CFT correspondence. Here is a talk I gave on the KITP workshop last Nov. An attempt to understand the holographic duality through a functional formalism
 I gave a "blackboard lunch" talk at KITP on topological states of matter, with the title of "To See A Knot In A Grain Of Sand  The Story Of Topological States"
 I am at KITP, UCSB this fall (Sep to Dec), coorganizing the workshop on topological insulators and superconductors.
 I recently organized a tutorial session on Topological insulators on the 2011 APS March meeting. The speakers are Joel Moore, M. Zahid Hasan, Marcel Franz, Yulin Chen and myself.
Selected Publications Topological Nematic States and NonAbelian Lattice Dislocations, Maissam Barkeshli and XiaoLiang Qi , Phys. Rev. X 2, 031013 (2012)
 Topological insulators and superconductors, XiaoLiang Qi and ShouCheng Zhang, Rev. Mod. Phys. 83, 1057–1110 (2011).
 General Relationship between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States, XiaoLiang Qi, Hosho Katsura and Andreas W. W. Ludwig, Phys. Rev. Lett. 108, 196402 (2012).
 Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators, XiaoLiang Qi, Phys. Rev. Lett. 107, 126803 (2011).
 Entanglement Entropy and Entanglement Spectrum of the Kitaev Model, Hong Yao and XiaoLiang Qi, Phys. Rev. Lett. 105, 080501 (2010)
 The quantum spin Hall effect and topological insulators XiaoLiang Qi and ShouCheng Zhang Physics Today 63, 3338 (2010)
 Inducing a Magnetic Monopole with Topological Surface States, XiaoLiang Qi, Rundong Li, Jiadong Zang and ShouCheng Zhang Science 323, 1184 (2009)
 Topological Insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with single Dirac cone on the surface Haijun Zhang, ChaoXing Liu, XiaoLiang Qi, Xi Dai, Zhong Fang, ShouCheng Zhang Nature Physics 5, 438 (2009)
 Topological Field Theory of TimeReversal Invariant Insulators, XiaoLiang Qi, Taylor L. Hughes, and ShouCheng Zhang Phys. Rev. B 78, 195424 (2008)
 Fractional charge and quantized current in the quantum spin Hall state, XiaoLiang Qi, Taylor L. Hughes, ShouCheng Zhang Nat. Phys. 4, 273  276 (2008)
 SpinCharge Separation in the Quantum Spin Hall State, XiaoLiang Qi and ShouCheng Zhang Phys. Rev. Lett. 101, 086802 (2008)

Career History 19992003, Bachelor, Tsinghua University
 20032007, Ph.D., Institute for Advanced Study, Tsinghua University
 20072009, Research Associate, SLAC, Stanford University
 20092010, Postdoctoral researcher, Microsoft Station Q, UCSB
 20092014, Assistant Professor of Physics, Stanford University
 Since 2014, Associate Professor of Physics, Stanford University
Research Interest At this moment I
am mainly interested in three related fields in condensed matter physicstopological phenomena, quantum entanglement and holographic duality.
Topological phenomena are the phenomena which are
determined by some topological structure in the physical system, which are thus
usually universal and robust against perturbations. For example, two famous topological
phenomena are the flux quantization in superconductors and Hall conductance
quantization in the Quantum Hall states. Recent discovery of topological
insulators and topological superconductors in different symmetry classes bring
the opportunity to study a large family of new topological phenomena. For
example the threedimensional topological insulator provides a condensed matter
realization of the important theoretical concepts in high energy physics such
as ”\thetavacuum” and “axion”. The interplay of topological insulators and
superconductors with conventional phases of matter such as ferromagnets and
superconductors lead to richer topological phenomena. For an intuitive
introduction to topological insulators, see Qi and Zhang, Physics Today Jan 2010.
Quantum entanglement is the unique feature of
quantum mechanics, which is essential for quantum information and quantum
computation. The understanding of quantum entanglement provides a new probe to
the physical properties of the manybody systems compared to the conventional
response properties such as conductivity, spin susceptibility, etc. On the
other hand, more systematical understanding of quantum entanglement in
manybody systems may also lead to breakthrough in building a quantum computer.
It is far more difficult to study entanglement properties in manybody systems
compared to fewbody systems. There are a lot of open questions for which the
answer is not known or only known for specific systems. For example, what is
the general relation between entanglement properties and other physical
observables in a given system? What is the relation between quantum
entanglement and topological states of matter? Besides the known description of
entanglement such as von Neumann entropy, what other measure can be defined to
provide more refined characterization of entanglement? I am pursuing these
directions. For a recent work I did along this line, click here.
Holographic duality uncovers an intrinsic relationship
between
dimensional gravitational theories and
dimensional nongravitational theories such as
CFT’s. This duality is often referred to as AdS/CFT correspondence when
the ddimensional nongravitational theory is a conformal field theory
(CFT). Each field
in the bulk gravity theory corresponds to a
local operator
in the boundary theory, in the sense that all correlation
functions in the large N limit are determined by the
classical action of the bulk theory as a functional of the boundary conditions. The extra dimension in the (d +
1) dimensional gravity theory can be interpreted as corresponding to energy
scale in the CFT. In a suitable coordinate choice, the scaling dimension of an
operator
is determined by the mass of the corresponding
bulk field. I am interested in understanding holography starting from the boundary quantum field theory (a condensed matter system) rather than the string theory. I am interested in developing a new framework called
“functional holographic duality” which takes a generic boundary theory as the
starting point and exactly constructs the dual bulk theory. I gave a talk at KITP about this subject.
