Xiao-Chuan Wu

University of Chicago

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Cenke Xu

University of California, Santa Barbara

Chao‐Ming Jian

Cornell University

Yichen Xu

Central South University

Yichen Xu

University of California, Santa Barbara

Ran Cheng

University of California, Riverside

Zhu-Xi Luo

Harvard University

Bingzhi Zhang

University of Southern California

Yi‐Zhuang You

University of California, San Diego

Hao Geng

Tianjin University of Traditional Chinese Medicine

Mi Pang

Xi'an University of Technology

Cooperative Institutions

University of California, Santa Barbara

Rice University

Oak Ridge National Laboratory

Tsinghua University

Harvard University

Massachusetts Institute of Technology

Kavli Institute for Particle Astrophysics and Cosmology

University of California, Berkeley

Chinese Academy of Sciences

University of Tennessee at Knoxville

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Interacting valley Chern insulator and its topological imprint on moiré superconductors

Physical review. B./Physical review. B (2019)

Xiao-Chuan Wu Yichen Xu Chao‐Ming Jian Cenke Xu

One salient feature of systems with Moir\'{e} superlattice is that, Chern number of "minibands" originating from each valley of the original graphene Brillouin zone becomes a well-defined quantized number because the miniband from each valley can be isolated from the rest of the spectrum due to the Moir\'{e} potential. Then a Moir\'{e} system with a well-defined valley Chern number can become a nonchiral topological insulator with $U(1) \times Z_3 $ symmetry and a $\mathbb{Z}$ classification at the free fermion level. Here we demonstrate that the strongly interacting nature of the Moir\'{e} system reduces the classification of the valley Chern insulator from $\mathbb{Z}$ to $\mathbb{Z}_3$, and it is topologically equivalent to a bosonic symmetry protected topological state made of local boson operators. We also demonstrate that, even if the system becomes a superconductor when doped away from the valley Chern insulator, the valley Chern insulator still leaves a topological imprint as the localized Majorana fermion zero mode in certain geometric configuration.

Topological insulator

Brillouin zone

10.1103/physrevb.100.155138

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Non-Landau quantum phase transitions and nearly-marginal non-Fermi liquid

Journal of Statistical Mechanics Theory and Experiment (2020)

Yichen Xu Hao Geng Xiao-Chuan Wu Chao‐Ming Jian Cenke Xu

Non-Fermi liquid and unconventional quantum critical points (QCP) with strong fractionalization are two exceptional phenomena beyond the classic condensed matter doctrines, both of which could occur in strongly interacting quantum many-body systems. This work demonstrates that using a controlled method one can construct a non-Fermi liquid within a considerable energy window based on the unique physics of unconventional QCPs. We will focus on the 'nearly-marginal non-Fermi liquid', defined as a state whose fermion self-energy scales as Σf(iω) ∼ i sgn(ω)|ω|α with α close to 1 in a considerable energy window. The nearly-marginal non-fermi liquid is obtained by coupling an electron fermi surface to unconventional QCPs that are beyond the Landau's paradigm. This mechanism relies on the observation that the anomalous dimension η of the order parameter of these unconventional QCPs can be close to 1, which is significantly larger than conventional Landau phase transitions, for example the Wilson–Fisher fixed points. The fact that η ∼ 1 justifies a perturbative renormalization group calculation proposed earlier. Various candidate QCPs that meet this desired condition are proposed.

Fermi energy

10.1088/1742-5468/ab99a0

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Exact wave functions for the edge state of a disk-shaped two dimensional topological insulator

arXiv (Cornell University) (2013)

Mi Pang Xiao-Chuan Wu

We report the exact wave functions for the eigen state of a disk-shaped two dimensional topological insulator. The property of the edge state whose energy lies inside the bulk gap is studied. It is found that the edge state energy is affected by the radius of the disk. For a fixed angular momentum index, there is a critical disk radius below which there exists no edge state. The value of this critical radius increases as the angular momentum index increases. In the limit of large disk radius, the energy of the edge state approaches a limiting value determined by the system parameters and independent of the angular momentum index. The derivation from this limiting value is inversely proportional to the radius with a coefficient proportional to the angular momentum index. In the general case, the energy differences between two edge states with adjacent angular momentum indexes are not equal. The exact and analytical wave functions also facilitates the investigation of electronic state in other structures of the two dimensional topological insulator.

Topological insulator

Topological index

Critical radius

10.48550/arxiv.1309.5559

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Report on scipost_202006_00045v1

Chao‐Ming Jian Yichen Xu Xiao-Chuan Wu Cenke Xu

One dimensional (1d) interacting systems with local Hamiltonians can be studied with various well-developed analytical methods.Recently novel 1d physics was found numerically in systems with either spatially nonlocal interactions, or at the 1d boundary of 2d quantum critical points, and the critical fluctuation in the bulk also yields effective nonlocal interactions at the boundary.This work studies the edge states at the 1d boundary of 2d strongly interacting symmetry protected topological (SPT) states, when the bulk is driven to a disorder-order phase transition.We will take the 2d Affleck-Kennedy-Lieb-Tasaki (AKLT) state as an example, which is a SPT state protected by the SO(3) spin symmetry and spatial translation.We found that the original (1 + 1)d boundary conformal field theory of the AKLT state is unstable due to coupling to the boundary avatar of the bulk quantum critical fluctuations.When the bulk is fixed at the quantum critical point, we find that by tuning one parameter at the boundary, there is a generic direct transition between the long range antiferromagnetic Néel order and the valence bond solid (VBS) order.This transition is very similar to the Néel-VBS transition recently found in numerical simulation of a spin-1/2 chain with nonlocal spatial interactions.Connections between our analytical studies and recent numerical results concerning the edge states of the 2d AKLT-like state at a bulk quantum phase transition will also be discussed.

10.21468/scipost.report.1834

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Topological edge and interface states at bulk disorder-to-order quantum critical points

Bulletin of the American Physical Society (2021)

Yichen Xu Xiao-Chuan Wu Chao‐Ming Jian Cenke Xu

We study the interplay between two nontrivial boundary effects: (1) the two-dimensional ($2d$) edge states of three-dimensional ($3d$) strongly interacting bosonic symmetry-protected topological states, and (2) the boundary fluctuations of $3d$ bulk disorder-to-order phase transitions. We then generalize our study to $2d$ gapless states localized at an interface embedded in a $3d$ bulk, when the bulk undergoes a quantum phase transition. Our study is based on generic long-wavelength descriptions of these systems and controlled analytic calculations. Our results are summarized as follows: (i) The edge state of a prototype bosonic symmetry-protected state can be driven to a new fixed point by coupling to the boundary fluctuations of a bulk quantum phase transition; (ii) the states localized at a $2d$ interface of a $3d\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N)$ quantum antiferromagnet may be driven to a new fixed point by coupling to the bulk quantum critical modes. Properties of the new fixed points identified are also studied.

Gapless playback

Critical point (mathematics)

Quantum phases

Phase boundary

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Candidate theory for the strange metal phase at a finite-energy window

Physical review. B./Physical review. B (2018)

Xiao-Chuan Wu Xiaohong Chen Chao‐Ming Jian Yi‐Zhuang You Cenke Xu

We propose a lattice model for strongly interacting electrons with the potential to explain the main phenomenology of the strange metal phase in the cuprate high temperature superconductors. Our model is motivated by the recently developed "tetrahedron" rank-3 tensor model that mimics much of the physics of the better-known Sachdev-Ye-Kitaev (SYK) model. Our electron model has the following advantageous properties: (1) it only needs one orbital per site on the square lattice; (2) it does not require any quenched random interaction; (3) it has local interactions and respects all the symmetries of the system; (4) the soluble limit of this model has a longitudinal DC resistivity that scales linearly with temperature within a finite temperature window; (5) again the soluble limit of this model has a fermion pairing instability in the infrared, which can lead to either superconductivity or a "pseudogap" phase. The linear$-T$ longitudinal resistivity and the pairing instability originate from the generic scaling feature of the SYK model and the tetrahedron tensor model.

Pseudogap

Square lattice

Tetrahedron

10.1103/physrevb.98.165117

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Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry

Bulletin of the American Physical Society (2021)

Chao‐Ming Jian Yichen Xu Xiao-Chuan Wu Cenke Xu

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Topological edge and interface states at bulk disorder-to-order quantum critical points

Physical review. B./Physical review. B (2020)

Yichen Xu Xiao-Chuan Wu Chao‐Ming Jian Cenke Xu

We study the interplay between two nontrivial boundary effects: (1) the two dimensional ($2d$) edge states of three dimensional ($3d$) strongly interacting bosonic symmetry protected topological states, and (2) the boundary fluctuations of $3d$ bulk disorder-to-order phase transitions. We then generalize our study to $2d$ gapless states localized at an interface embedded in a $3d$ bulk, when the bulk undergoes a quantum phase transition. Our study is based on generic long wavelength descriptions of these systems and controlled analytic calculations. Our results are summarized as follows: ($i.$) The edge state of a prototype bosonic symmetry protected states can be driven to a new fixed point by coupling to the boundary fluctuations of a bulk quantum phase transition; ($ii.$) the states localized at a $2d$ interface of a $3d$ SU(N) quantum antiferromagnet may be driven to a new fixed point by coupling to the bulk quantum critical modes. Properties of the new fixed points identified are also studied.

Quantum phases

Gapless playback

Critical point (mathematics)

Phase boundary

10.1103/physrevb.101.184419

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Citations (15)

A candidate Theory for the ''Strange Metal'' phase based on the Sachdev-Ye-Kitaev physics

Bulletin of the American Physical Society (2019)

Xiao-Chuan Wu Xiaohong Chen Chao‐Ming Jian Yi‐Zhuang You Cenke Xu

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