Professor Peng Ye

Research

My research lies in quantum many-body theory, especially at the interface of quantum field theory and quantum information. I am broadly interested in the universal structure of strongly correlated quantum matter, with particular focus on higher-dimensional topological phases of matter, fractonic superfluidity, fracton-related lattice models, subsystem symmetries, and entanglement in fermionic systems. Across these topics, a central theme of my work is to connect continuum field-theoretic descriptions with microscopic lattice constructions, and to use this connection to understand new phases of matter, their excitations, and their entanglement structures.

Field theory and lattice models of higher-dimensional topological phases of matter

One major direction of my current research concerns the field-theoretic structure of topological order in three and higher spatial dimensions. In these systems, the relevant excitations are not limited to point-like quasiparticles, but can also include extended objects such as loops and membranes. Their fusion, shrinking, and braiding processes are correspondingly richer than in two-dimensional topological order, and require theoretical frameworks beyond the standard Chern–Simons paradigm. My work in this area develops topological field-theory (TQFT) descriptions of such phases and studies universal structures including non-Abelian fusion rules, shrinking rules, and associated pentagon and hexagon consistency equations in terms of diagrammatic representations. An important aspect of this program is to clarify how these continuum descriptions encode universal infrared physics and how they connect to explicit microscopic realizations in lattice models.

Fractonic superfluids and higher-moment conservation laws

A second main direction of my research is fractonic superfluidity and, more broadly, quantum many-body systems with higher-moment conservation laws. These generalized conservation laws can substantially modify familiar notions in many-body physics, including spontaneous symmetry breaking, off-diagonal long-range order, Goldstone modes, and finite-temperature phase transitions. My work develops continuum and perturbative field-theoretic approaches to these systems and explores how mobility constraints and higher-moment symmetries give rise to unconventional collective behavior, including generalized Hohenberg-Mermin-Wagner theorems, hierarchical Kosterlitz–Thouless-type transitions. This direction is motivated both by fracton physics, conceptual questions in field theory and by connections to cold-atom and related many-body settings.

Fracton phases, subsystem structure, and quantum-information perspectives

I also work on correlated topological phases from a quantum-information perspective, especially fracton topological order and subsystem-symmetry-protected phases. This includes the construction of exactly solvable models in arbitrary dimensions, the development of quantum-circuit frameworks, and the use of higher-order cellular automata as a systematic tool for generating nontrivial subsystem symmetry structures. Related to this, I am interested in diagnostic tools for many-body order, including multi-point strange correlators, which can be used to probe classes of topological and subsystem-structured states that are difficult to characterize by more conventional means. These problems sit naturally at the intersection of condensed matter theory, quantum information, and computational structures in many-body systems.

Entanglement in fermion systems

Another continuing line of research concerns entanglement in fermion systems. Here I study universal aspects of entanglement entropy and entanglement spectra, especially in settings with nontrivial geometry (e.g., fractal lattice and hyperbolic lattice) and in non-Hermitian systems. A recurring goal is to understand how geometry, fermionic statistics, and spectral structure are reflected in entanglement observables, and how these observables can reveal robust many-body features beyond standard band-theoretic descriptions. This work connects quantum information ideas with analytical tools in many-body theory and mathematical physics.

Broader perspective

Across these directions, I am interested in problems where field theory, lattice models, topology, symmetry, and entanglement meet. My research combines continuum field-theoretical methods, exactly solvable constructions, and quantum-information-inspired diagnostics to study the structure of quantum phases and phase transitions in quantum many-body systems.

Publications

The bracketed identifiers preceding each publication indicate the arXiv posting order, where [25a] refers to the first paper posted on arXiv in 2025, followed by [25b], [25c], etc.

68 [26b] To be arXived..
67 [26a] Zhi-Feng Zhang, Yizhou Huang, Qing-Rui Wang, and PY, arXiv:2601.01523. Title: Non-invertible symmetries and mixed anomalies from conserved current construction in (3+1)D twisted $BF$ topological quantum field theories. 标题：基于守恒流构造研究(3+1)维BF拓扑场论的不可逆对称性以及混合量子反常[TO][CFTT][GSYM][QANO]
66 [25g] Yizhou Huang, Zhi-Feng Zhang, Qing-Rui Wang, and PY, arXiv:2512.21148. Title: Bridging microscopic constructions and continuum topological field theory of three-dimensional non-Abelian topological order. 标题：三维非阿贝尔拓扑序的微观构造与连续拓扑场论之间的桥梁[TO][CFTT][LATT][STBL]
65 [25f] Wei-Liang Gao, Jie-Yu Zhang, Zheng-Xin Liu, and PY, Chin. Phys. Lett. (2026, accepted, in press). arXiv:2512.06691. Title: Spurious strange correlators in symmetry-protected topological phases. 标题：对称性保护拓扑相中的伪奇异关联函数[SPT]
64 [25e] Bo-Xi Li and PY, Phys. Rev. B 113, 125141 (2026). arXiv:2511.09301. Title: Infinite-component $BF$ field theory: Nexus of fracton order, Toeplitz braiding, and non-Hermitian amplification. 标题：无限分量 $BF$ 场论：分形子拓扑序、Toeplitz 编织与非厄米放大的交汇点 [FRTO][CFTT][NHP]
63 [25d] Meng-Yuan Li and PY, arXiv:2510.15766. Title: Subdimensional entanglement entropy: from virtual response to mixed-state holography. 标题：亚维纠缠熵：从虚响应到混态全息[ENEN][MIXT][LATT][FRTO][STBL]
62 [25c] Yao Zhou and PY, arXiv:2510.15370. Title: Entanglement complexification transition driven by a single non-Hermitian impurity. 标题：由单个非厄米杂质驱动的纠缠复复杂化转变[ENEN][NHP]
61 [25b] Jie-Yu Zhang and PY. arXiv:2508.13961. Title: Programmable anyon mobility through higher order cellular automata. 标题：基于高阶元胞自动机实现任意子迁移能力的可编程控制[CEAU][TO][LATT][STBL]
60 [25a] Yu-Tao Hu, Meng-Yuan Li, and PY. Phys. Rev. B 112, 165139 (2025). arXiv:2503.05374. Title: Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes. 标题：通过"种子-纠缠机富化"的序列量子线路制备编码态：在"四位数"拓扑纠错码中的应用[STBL][LATT][TO]
59 [24f] Han-Xie Wang, Shuai A. Chen, and PY, Phys. Rev. Research 7, 033118 (2025). arXiv:2412.10280. Title: Fractonic superfluids. III. Hybridizing higher moments. 标题：分形子超流体 III：高阶矩的杂化[FRAS]
58 [24e] Li-Mei Chen, Yao Zhou, Shuai A. Chen, and PY, Chin. Phys. Lett. 41, 127302 (2024). arXiv:2408.11652. Title: Quantum entanglement and non-Hermiticity in free fermion systems. 标题：自由费米子系统中的量子纠缠与非厄米性[ENEN][NHP]
57 [24d] Xiang-You Huang, Yao Zhou, and PY, Phys. Rev. Research 7, 023098 (2025). arXiv:2408.01706. Title: Entanglement scaling behaviors of free fermions on hyperbolic lattices. 标题：双曲格子上的自由费米子系统的纠缠标度行为[ENEN]
56 [24c] Bo-Xi Li, Yao Zhou, and PY, Phys. Rev. B 110, 205108 (2024) arXiv:2406.02482. Title: Three-dimensional fracton topological orders with boundary Toeplitz braiding. 标题：具有边界Toeplitz编织的三维分形拓扑序[FRTO][TO][LATT][CFTT]
55 [24b] Yizhou Huang, Zhi-Feng Zhang, and PY, JHEP 06 (2025) 238. arXiv:2405.19077. Title: Diagrammatics, Pentagon Equations, and Hexagon Equations of Topological Orders with Loop- and Membrane-like Excitations. 标题：具有环状和膜状激发的拓扑序的图示表示理论、五边形方程和六边形方程[TO][CFTT]
54 [24a] Jie-Yu Zhang, Meng-Yuan Li, and PY, PRX Quantum 5, 030342 (2024). arXiv:2401.00505. Title: Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators. 标题：高阶元胞自动机生成的对称性保护拓扑相及通过多点奇异关联函数的检测[SPT][CEAU][SUBS]
53 [23g] Zhi-Kang Lin, Yao Zhou, Bin Jiang, Bing-Quan Wu, Li-Mei Chen, Xiao-Yu Liu, Li-Wei Wang, PY, and Jian-Hua Jiang, Nature Communications 15, 1601 (2024). arXiv:2312.08632. Title: Measuring entanglement entropy and its topological signature for phononic systems. 标题：基于声学系统探测纠缠熵及其拓扑特征[ENEN]
52 [23f] Liang-Hong Mo, Yao Zhou, Jia-Rui Sun, and PY, arXiv:2311.01997. Title: Hyperfine Structure of Quantum Entanglement. 标题：量子纠缠的超精细结构[ENEN]
51 [23e] Yao Zhou and PY, Phys. Rev. Research 6, 043145 (2024) arXiv:2311.01199. Title: Entanglement fractalization. 标题：纠缠分形化[ENEN]
50 [23d] Zhi-Feng Zhang, Qing-Rui Wang, and PY, Phys. Rev. Research 5, 043111 (2023). arXiv:2307.09983. Title: Continuum field theory of 3D topological orders with emergent fermions and braiding statistics. 标题：具有演生费米子和编织统计的三维拓扑序的连续场论[TO][CFTT]
49 [23c] Yizhou Huang, Zhi-Feng Zhang, and PY, JHEP 11 (2023) 210. arXiv:2306.14611. Title: Fusion rules and shrinking rules of topological orders in five dimensions. 标题：五维拓扑序的融合规则与收缩规则[TO][CFTT]
48 [23b] Shuai A. Chen and PY, arXiv:2305.00941. Title: Exploring spontaneous symmetry breaking through fractonic superfluids. [A topical review article] 标题：通过分形子超流体探索自发对称性破缺[FRAS]
47 [23a] Li-Mei Chen, Tyler D. Ellison, Meng Cheng, PY, and Ji-Yao Chen, Phys. Rev. B 109, 155161 (2024). arXiv:2302.05060. Title: Chiral spin liquid in a ℤ3 Kitaiv model. 标题：ℤ₃ Kitaev模型中的手性自旋液体[TO][LATT]
46 [22i] Meng-Yuan Li and PY, Phys. Rev. B 107, 115169 (2023). arXiv:2211.14136. Title: Hierarchy of Entanglement Renormalization and Long-Range Entangled States. 标题：纠缠重整化的层次结构与长程纠缠态[ENEN][FRTO][STBL]
45 [22h] Chengkang Zhou, Meng-Yuan Li, Zheng Yan, PY, and Zi Yang Meng, Phys. Rev. B 106, 214428 (2022). arXiv:2209.12917. Title: Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators. 标题：通过奇异关联函数检测子系统对称性保护的拓扑相[SPT][SUBS]
44 [22g] Yue-Yu Zou, Yao Zhou, Li-Mei Chen, and PY, Frontiers of Physics 19, 23201 (2024). arXiv:2208.14944. Title: Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors. 标题：通过广义Petermann因子探测非厄米系统中的体与边缘例外点[NHP]
43 [22f] Zhi-Feng Zhang, Qing-Rui Wang, and PY, Phys. Rev. B 107, 165117 (2023). arXiv:2208.09228. Title: Non-Abelian Fusion, Shrinking and Quantum Dimensions of Abelian Gauge Fluxes. 标题：非阿贝尔融合、收缩与阿贝尔规范磁通的量子维度[TO][CFTT]
42 [22e] Yao Zhou and PY, Phys. Rev. B 107, 085108 (2023). arXiv:2205.01654. Title: Entanglement Signature of Hinge Arcs, Fermi Arcs, and Crystalline Symmetry Protection in Higher-Order Weyl Semimetals. [Supplemental Material download link] 标题：高阶Weyl半金属的Hinge弧、费米弧及晶体对称性保护的纠缠特征[ENEN][SMET]
41 [22d] Chengkang Zhou, Meng-Yuan Li, Zheng Yan, PY, and Zi Yang Meng, Phys. Rev. Research 4, 033111 (2022). arXiv:2203.13274. Title: Evolution of Dynamical Signature in the X-cube Fracton Topological Order. 标题：X-cube分形拓扑序中动力学特征的演化[FRTO][LATT][STBL]
40 [22c] Jian-Keng Yuan, Shuai A. Chen, and PY, Chin. Phys. Lett. 39, 057101 (2022) (Editors' Suggestion) arXiv:2203.06984. Title: Quantum Hydrodynamics of Fractonic Superfluids with Lineon Condensate: from Navier-Stokes-like Equations to Landau-like Criterion. 标题：具有线子凝聚的分形子超流体的量子流体动力学：从Navier-Stokes-like方程到Landau-like判据[FRAS]
39 [22b] Guo-Yi Zhu, Ji-Yao Chen, PY, and Simon Trebst, Phys. Rev. Lett. 130, 216704 (2023). arXiv:2203.00015. Title: Topological fracton quantum phase transitions by tuning exact tensor network states. 标题：通过调节精确张量网络态实现拓扑分形量子相变[FRTO][LATT]
38 [22a] Jian-Keng Yuan, Shuai A. Chen, and PY, Phys. Rev. B 107, 205134 (2023). arXiv:2201.08597. Title: Higher Rank Symmetry Defects: Defect Bound States and Hierarchical Proliferation. 标题：高阶对称性缺陷：缺陷束缚态与层级增殖[FRAS]
37 [21d] Li-Mei Chen, Yao Zhou, Shuai A. Chen, and PY, Phys. Rev. B (Letter section) 105, L121115 (2022). arXiv:2112.13411. Title: Quantum Entanglement of Non-Hermitian Quasicrystals. 标题：非厄米准晶的量子纠缠[ENEN][NHP]
36 [21c] Zhi-Feng Zhang and PY, JHEP 04 (2022) 138. arXiv:2104.07067. Title: Topological Orders, Braiding Statistics, and Mixture of Two Types of Twisted BF Theories in Five Dimensions. 标题：五维拓扑序、编织统计及两类扭曲BF理论的混合[TO][CFTT]
35 [21b] Meng-Yuan Li and PY, Phys. Rev. B 104, 235127 (2021). arXiv:2104.05735. Title: Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models. 标题：空间扩展激发的Fracton物理 II：精确可解模型的多项式基态简并度[FRTO][LATT][STBL]
34 [21a] Hongchao Li and PY, Phys. Rev. Research 3, 043176 (2021). arXiv:2104.03237. Title: Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation. 标题：高阶对称性与高阶矩守恒演生的重整化群分析[FRAS]
33 [20d] Zhi-Feng Zhang and PY, Phys. Rev. Research 3, 023132 (2021). arXiv:2012.13761. Title: Compatible Braidings with Hopf links, Multi-loop and Borromean Rings in (3+1)-dimensional Spacetime. 标题：(3+1)维时空中与Hopf链环、多环及Borromean环兼容的编织[TO][CFTT]
32 [20c] Shuai A. Chen, Jian-Keng Yuan, and PY, Phys. Rev. Research 3, 013226 (2021). arXiv:2010.03261. Title: Fractonic superfluids. II. Condensing subdimensional particles. 标题：分形子超流体 II：亚维粒子凝聚[FRAS]
31 [20b] Li-Mei Chen, Shuai A. Chen, and PY, SciPost Phys. 11, 003 (2021). arXiv:2009.00546. Title: Entanglement, non-Hermiticity and duality. 标题：纠缠、非厄米性与对偶性[ENEN][NHP][DUAL]
30 [20a] PY, Acta Physica Sinica 69, 077102 (2020). (Invited Review in Chinese; Editors' Suggestion). Title: Gauge theory of strongly-correlated symmetric topological Phases. 标题：具有全局对称性的强关联拓扑物态的规范场论[SPT][CFTT][CFTT]
29 [19b] Jian-Keng Yuan, Shuai A. Chen, and PY, Phys. Rev. Research 2, 023267 (2020). arXiv:1911.02876. Title: Fractonic superfluids. 标题：分形子超流体[FRAS]
28 [19a] Meng-Yuan Li and PY, Phys. Rev. B 101, 245134 (2020). arXiv:1909.02814. Title: Fracton physics of spatially extended excitations. 标题：空间扩展激发的分形子物理[FRTO][LATT][STBL]
27 [18b] Bo Han, Huajia Wang, and PY, Phys. Rev. B 99, 205120 (2019). arXiv:1807.10844. Title: Generalized Wen-Zee terms. 标题：广义Wen-Zee项[SPT][TO][CFTT]
26 [18a] Shang-Qiang Ning, Zheng-Xin Liu, and PY, Phys. Rev. B 105, 205137 (2022). arXiv:1801.01638v3. Title: Fractionalizing Global Symmetry on Looplike Topological Excitations. 标题：环状拓扑激发上全局对称性的分数化[SET][TO][CFTT]
25 [17d] Chao-Xing Liu, PY, and Xiao-Liang Qi, Phys. Rev. B 96, 247302 (2017). Title: Reply to "Comment on 'Chiral gauge field and axial anomaly in a Weyl semimetal'". 标题：对"关于'Weyl半金属中的手性规范场与轴反常'的评论"的回复[SMET][QANO]
24 [17c] Xueda Wen, Huan He, Apoorv Tiwari, Yunqin Zheng, and PY, Phys. Rev. B 97, 085147 (2018). arXiv:1710.11168. Title: Entanglement entropy for (3+1)-dimensional topological orders with excitations. 标题：(3+1)维拓扑序激发态的纠缠熵[TO][ENEN]
23 [17b] AtMa P.O. Chan, PY, and Shinsei Ryu, Phys. Rev. Lett. 121, 061601 (2018). arXiv:1703.01926. Title: Braiding with Borromean Rings in (3+1)-Dimensional Spacetime. 标题：(3+1)维时空的Borromean环的编织[TO][CFTT]
22 [17a] PY, Meng Cheng, and Eduardo Fradkin, Phys. Rev. B 96, 085125 (2017). arXiv:1701.05559. Title: Fractional S-duality, classification of fractional topological insulators, and surface topological order. 标题：分数S-对偶性、分数拓扑绝缘体的分类与表面拓扑序[TO][DUAL][QH][CFTT]
21 [16e] Matthew F. Lapa, Chao-Ming Jian, PY, and Taylor L. Hughes, Phys. Rev. B 95, 035149 (2017). arXiv:1611.03504. Title: Topological electromagnetic responses of bosonic quantum Hall, topological insulator, and chiral semi-metal phases in all dimensions. 标题：所有维度中玻色子量子霍尔、拓扑绝缘体与手性半金属相的拓扑电磁响应[QH][SPT][CFTT]
20 [16d] PY, Phys. Rev. B 97, 125127 (2018). arXiv:1610.08645. Title: Three-dimensional anomalous twisted gauge theories with global symmetry: Implications for quantum spin liquids. 标题：具有全局对称性的三维反常扭曲规范理论：对量子自旋液体的启示[QANO][SET][CFTT]
19 [16c] Shang-Qiang Ning, Zheng-Xin Liu, and PY, Phys. Rev. B 94, 245120 (2016). arXiv:1609.00985. Title: Symmetry enrichment in three-dimensional topological phases. 标题：三维拓扑相中的对称性富化[SET][TO][CFTT]
18 [16b] Yuxuan Wang and PY, Phys. Rev. B 94, 075115 (2016). arXiv:1604.05311. Title: Topological density-wave states in a particle-hole symmetric Weyl metal. 标题：粒子-空穴对称Weyl金属中的拓扑密度波态[SMET]
17 [16a] PY, Taylor L. Hughes, Joseph Maciejko, and Eduardo Fradkin, Phys. Rev. B 94, 115104 (2016). arXiv:1603.02696. Title: Composite particle theory of three-dimensional gapped fermionic phases: Fractional topological insulators and charge-loop excitation symmetry. 标题：三维有能隙费米子相的复合粒子理论：分数拓扑绝缘体与荷-环激发对称性[TO][SET][CFTT]
16 [15a] PY and Zheng-Cheng Gu, Phys. Rev. B 93, 205157 (2016). arXiv:1508.05689. Title: Topological quantum field theory of three-dimensional bosonic Abelian-symmetry-protected topological phases. 标题：三维玻色子阿贝尔对称性保护拓扑相的拓扑量子场论[SPT][CFTT]
15 [14d] Ching Hua Lee and PY, Phys. Rev. B 91, 085119 (2015). arXiv:1410.8670. Title: Free-fermion entanglement spectrum through Wannier interpolation. 标题：通过Wannier插值研究自由费米子纠缠谱[ENEN]
14 [14c] PY and Zheng-Cheng Gu, Phys. Rev. X 5, 021029 (2015). arXiv:1410.2594. Media. Title: Vortex-line condensation in three dimensions: A physical mechanism of bosonic topological insulators. 标题：三维中的涡旋线凝聚：玻色子拓扑绝缘体的物理机制[SPT][QH][CFTT]
13 [14b] Zheng-Xin Liu, Jia-Wei Mei, PY, and Xiao-Gang Wen, Phys. Rev. B 90, 235146 (2014). arXiv:1408.1676. Title: U(1)×U(1) symmetry protected topological order in Gutzwiller wave functions. 标题：Gutzwiller波函数中U(1)×U(1)对称性保护的拓扑序[SPT][CFTT]
12 [14a] Ching Hua Lee, PY, and Xiao-Liang Qi, J. Stat. Mech. P10023 (2014). arXiv:1403.1039. Title: Position-momentum duality in the entanglement spectrum of free fermions. 标题：自由费米子纠缠谱中的位置-动量对偶性[ENEN][DUAL]
11 [13d] Yao Ma, PY, and Zheng-Yu Weng, New J. Phys. 16, 083039 (2014). arXiv:1311.3395. Title: Low-temperature pseudogap phenomenon: Precursor of high-Tc Superconductivity. 标题：低温赝能隙现象：高温超导电性的前兆[SC]
10 [13c] Qing-Rui Wang and PY, Phys. Rev. B 90, 045106 (2014). arXiv:1310.6496. Title: Sign structure and generalized Marshall theorem for the spin-S t-J chain. 标题：自旋S t-J链的符号结构与广义Marshall定理[TJ]
9 [13b] PY and Juven Wang, Phys. Rev. B 88, 235109 (2013). arXiv:1306.3695. Title: Symmetry-protected topological phases with charge and spin symmetries: Response theory and dynamical gauge theory in two and three dimensions. 标题：具有电荷与自旋对称性的对称性保护拓扑相：二维与三维的响应理论与动力学规范理论[SPT][CFTT]
8 [13a] PY and Xiao-Gang Wen, Phys. Rev. B 89, 045127 (2014). arXiv:1303.3572v3. Title: Constructing symmetric topological phases of bosons in three dimensions via fermionic projective construction and dyon condensation. 标题：通过费米子投影构造与dyon凝聚构建三维玻色子的对称拓扑相[SPT][CFTT]
7 [12c] PY and Xiao-Gang Wen, Phys. Rev. B 87, 195128 (2013). arXiv:1212.2121. Title: Projective construction of two-dimensional symmetry-protected topological phases with U(1), SO(3), or SU(2) symmetries. 标题：具有U(1)、SO(3)或SU(2)对称性的二维对称性保护拓扑相的投影构造[SPT][CFTT]
6 [12b] PY and Qing-Rui Wang, Nucl. Phys. B 874, 386 (2013). arXiv:1206.0258. Title: Monopoles, confinement and charge localization in the t-J model with dilute holes. 标题：稀薄空穴t-J模型中的单极子、禁闭与电荷局域化[TJ]
5 [12a] Chao-Xing Liu, PY, and Xiao-Liang Qi, Phys. Rev. B 87, 235306 (2013). arXiv:1204.6551 [ESI Highly Cited Paper] [Erratum]. Title: Chiral gauge field and axial anomaly in a Weyl-semi-metal. 标题：Weyl半金属中的手性规范场与轴反常[SMET][QANO]
4 [11b] PY, Long Zhang, and Zheng-Yu Weng, Phys. Rev. B 85, 205142 (2012). arXiv:1110.0125. Title: Superconductivity in mutual Chern-Simons gauge theory. 标题：交互Chern-Simons规范理论中的超导性[SC][CFTT]
3 [11a] PY, Chu-Shun Tian, Xiao-Liang Qi, and Zheng-Yu Weng, Nucl. Phys. B 854, 815 (2012). arXiv:1106.1223. Title: Electron fractionalization and unconventional order parameters of the t-J model. 标题：t-J模型的电子分数化与非常规序参量[TJ]
2 [10a] PY, Chu-Shun Tian, Xiao-Liang Qi, and Zheng-Yu Weng, Phys. Rev. Lett. 106, 147002 (2011). arXiv:1007.2507. Title: Confinement-deconfinement interplay in quantum phases of doped Mott insulators. 标题：掺杂Mott绝缘体量子相中的禁闭-去禁闭 interplay[TJ][SC]
1 [07a] PY, Xiao-Lu Yu, Yi Guan, and Xiang-Qian Luo, Mod. Phys. Lett. A 22, 547 (2007). Title: Overlap fermions in the strong coupling limit. 标题：强耦合极限下的重叠费米子[LATT]

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