The Bi Group works on the theory of quantum many-body systems — how the simple rules of quantum mechanics, applied to many interacting particles, give rise to distinct phases of matter and the transitions between them. We focus on phases and transitions that lie beyond the standard textbook framework, where the usual descriptions in terms of order parameters or independent electrons no longer apply. To understand them we draw on quantum field theory, topology, and the evolving notion of symmetry — using these tools to predict new phases, classify the forms they can take, and identify how to detect them. The five directions below span this program, from the topological and gapless phases of closed systems to the new forms of order that emerge in open, noisy quantum matter.
Mixed-state phases of quantum matter
Real quantum systems are never perfectly isolated. They are measured, jostled by noise, and entangled with their surroundings — and for most of physics this openness was treated as a nuisance, the decoherence that washes quantum behavior away. A central theme of our work is that the opposite can hold: open, noisy quantum systems can host genuinely new phases of matter, with forms of order, topology, and criticality that have no counterpart in the isolated, ground-state world. Capturing them forces us to rethink ideas as basic as symmetry itself — in a system described only statistically, by a mixed state, a symmetry can be obeyed in more than one distinct sense, and the tension between those senses gives rise to new phases and transitions. We are building the theory of this landscape: which mixed-state phases are possible, how they emerge under measurement and decoherence, and how to tell them apart. These questions are fundamental, and also timely — they describe exactly the noisy, controllable quantum systems now being built in laboratories and quantum computers.
Fidelity Strange Correlators for Average Symmetry-Protected Topological Phases
@article{zhang2025fidelity,title={Fidelity Strange Correlators for Average Symmetry-Protected Topological Phases},author={Zhang, Jian-Hao and Qi, Yang and Bi, Zhen},journal={Science Bulletin},volume={71},pages={688--691},year={2026}}
@article{luo2025topological,title={Topological Holography for Mixed-State Phases and Phase Transitions},author={Luo, R. and Wang, Y.-N. and Bi, Zhen},journal={PRX Quantum},volume={6},number={4},pages={040358},year={2025},publisher={American Physical Society},doi={10.1103/PRXQuantum.6.040358}}
@misc{srinivasan2025classification,title={Classification of Average Crystalline Topological Superconductors through a Generalized Real-Space Construction},author={Srinivasan, S. and Zhang, J.-H. and Qi, Y. and Bi, Zhen},year={2026},note={Accepted, Physical Review B}}
@article{sun2025holographic,title={Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems},author={Sun, S. and Zhang, J.-H. and Bi, Zhen and You, Y.},journal={PRX Quantum},volume={6},number={2},pages={020333},year={2025},publisher={American Physical Society},doi={10.1103/PRXQuantum.6.020333}}
@article{zhang2025strong,title={Strong-to-Weak Spontaneous Breaking of 1-Form Symmetry and Intrinsically Mixed Topological Order},author={Zhang, C. and Xu, Y. and Zhang, J.-H. and Xu, C. and Bi, Zhen and Luo, Z.-X.},journal={Physical Review B},volume={111},number={11},pages={115137},year={2025},publisher={American Physical Society},doi={10.1103/PhysRevB.111.115137}}
@article{lessa2025strong,title={Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States},author={Lessa, L. and Ma, R. and Zhang, J.-H. and Bi, Zhen and Cheng, M. and Wang, C.},journal={PRX Quantum},volume={6},number={1},pages={010344},year={2025},publisher={American Physical Society},doi={10.1103/PRXQuantum.6.010344}}
@article{guo2025locally,title={Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States},author={Guo, Y. and Zhang, J.-H. and Zhang, H.-R. and Yang, S. and Bi, Zhen},journal={Physical Review X},volume={15},number={2},pages={021060},year={2025},publisher={American Physical Society},doi={10.1103/PhysRevX.15.021060}}
@article{ma2025topological,title={Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic},author={Ma, R. and Zhang, J.-H. and Bi, Zhen and Cheng, M. and Wang, C.},journal={Physical Review X},volume={15},number={2},pages={021062},year={2025},publisher={American Physical Society},doi={10.1103/PhysRevX.15.021062}}
@article{guo2023triggering,title={Triggering Boundary Phase Transitions through Bulk Measurements in 2{D} Cluster States},author={Guo, Y. and Zhang, J. and Bi, Zhen and Yang, S.},journal={Physical Review Research},volume={5},pages={043069},year={2023},publisher={American Physical Society},doi={10.1103/PhysRevResearch.5.043069}}
@article{zhang2023fractonic,title={Fractonic Higher-Order Topological Phases in Open Quantum Systems},author={Zhang, J.-H. and Ding, K. and Yang, S. and Bi, Zhen},journal={Physical Review B},volume={108},pages={155123},year={2023},publisher={American Physical Society},doi={10.1103/PhysRevB.108.155123}}
@misc{lee2022decoding,title={Decoding Measurement-Prepared Quantum Phases and Transitions: From Ising Model to Gauge Theory, and Beyond},author={Lee, J. Y. and Ji, W. and Bi, Zhen and Fisher, M.},year={2022},}
@misc{li2026generalized,title={Generalized Symmetry-Protected Topological Phases in Mixed States from Gauging Dualities},author={Li, L. and Bi, Zhen and Cao, W.},year={2026},}
@misc{ding2026swssb,title={Strong-to-Weak Spontaneous Symmetry Breaking in a (2+1)D Transverse-Field Ising Model under Decoherence},author={Ding, Y.-M. and Guo, Y. and Bi, Zhen and Yan, Z.},year={2026},note={Submitted to Physical Review Letters}}
@misc{tian2026dissipative,title={Dissipative Preparation of Correlated Quantum States in Dipolar Rydberg Arrays},author={Tian, M. and Bi, Zhen and Iadecola, T. and Gadway, B.},year={2026},note={Submitted to Physical Review Letters}}
Quantum matter with generalized symmetry
Symmetry is the deepest organizing principle in physics: it fixes conservation laws, classifies particles, and determines the phases that matter can take. In recent years that principle has itself been dramatically expanded. A system’s symmetries, it turns out, need not act on it all at once — they can be confined to lower-dimensional slices of it, keep track of where objects sit or how their charge is distributed, or act on extended objects like loops rather than on points. These generalized symmetries vastly enlarge the space of phases that quantum matter can realize, while sharpening the constraints — anomalies and no-go theorems — that limit what any phase can do. Their most dramatic consequence is fracton order, a phase whose elementary excitations are frozen in place, or can move only along a line or a plane — behavior with no counterpart in conventional matter, and one that has built surprising bridges between condensed matter, quantum information, and quantum field theory. Our group maps this expanding landscape: we classify the new phases that generalized symmetries make possible and uncover their unexpected consequences, from novel topological states to exotic metals whose behavior is dictated not by ordinary charge, but by the conservation of dipoles.
@misc{anakru2024topological,title={Topological Phases and Phase Transitions with Dipolar Symmetry Breaking},author={Anakru, A. and Bi, Zhen},year={2024},}
@article{zhang2023fractonic,title={Fractonic Higher-Order Topological Phases in Open Quantum Systems},author={Zhang, J.-H. and Ding, K. and Yang, S. and Bi, Zhen},journal={Physical Review B},volume={108},pages={155123},year={2023},publisher={American Physical Society},doi={10.1103/PhysRevB.108.155123}}
@article{anakru2023nonfermi,title={Non-{F}ermi Liquids from Dipolar Symmetry Breaking},author={Anakru, A. and Bi, Zhen},journal={Physical Review B},volume={108},pages={165112},year={2023},publisher={American Physical Society},doi={10.1103/PhysRevB.108.165112}}
@article{zhang2023classification,title={Classification and Construction of Interacting Fractonic Higher-Order Topological Phases},author={Zhang, J.-H. and Cheng, M. and Bi, Zhen},journal={Physical Review B},volume={108},pages={045133},year={2023},publisher={American Physical Society},doi={10.1103/PhysRevB.108.045133}}
@article{maymann2022interaction,title={Interaction-Enabled Fractonic Higher-Order Topological Phases},author={May-Mann, J. and You, Y. and Hughes, T. L. and Bi, Zhen},journal={Physical Review B},volume={105},pages={245122},year={2022},publisher={American Physical Society},doi={10.1103/PhysRevB.105.245122}}
@article{you2020emergent,title={Emergent Fractons and Algebraic Quantum Liquid from Plaquette Melting Transitions},author={You, Y. and Bi, Zhen and Pretko, M.},journal={Physical Review Research},volume={2},pages={013162},year={2020},publisher={American Physical Society},doi={10.1103/PhysRevResearch.2.013162}}
@article{williamson2019fractonic,title={Fractonic Matter in Symmetry-Enriched {U}(1) Gauge Theory},author={Williamson, D. and Bi, Zhen and Cheng, M.},journal={Physical Review B},volume={100},pages={125150},year={2019},publisher={American Physical Society},doi={10.1103/PhysRevB.100.125150},}
@misc{li2026generalized,title={Generalized Symmetry-Protected Topological Phases in Mixed States from Gauging Dualities},author={Li, L. and Bi, Zhen and Cao, W.},year={2026},}
@misc{anakru2026matrix,title={Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond},author={Anakru, A. and Li, L. and Srinivasan, S. and Bi, Zhen},year={2026},note={Submitted to Physical Review Letters}}
Topological phases of matter and quantum field theory
Conventional phases of matter are defined by the order they display — a magnet points in a definite direction, a crystal arranges its atoms in a regular pattern. Topological phases are different. They can look essentially featureless in the bulk, yet remain distinct from ordinary matter, with the difference showing up only at their boundaries: an edge that is forced to conduct, or to behave in some other unusual way, and that no local change can remove. What protects this behavior is a concept borrowed from particle physics — an anomaly — which places topological phases at the interface of condensed matter and quantum field theory. Our group works to understand why such phases exist, to classify the forms they can take (particularly once strong interactions are included), and to construct the field theories that describe them. Using dualities — equivalences between theories that look quite different — we connect concrete lattice models and candidate materials to more formal structures in theoretical physics, work that underpins much of our research on the topics above.
@misc{bi2019lattice,title={Lattice Analysis of {SU}(2) with 1 Adjoint Dirac Flavor},author={Bi, Zhen and Grebe, A. and Kanwar, G. and Ledwith, P. and Murphy, D. and Wagman, M.},year={2019},note={Presentation at the 37th Annual International Symposium on Lattice Field Theory},}
@article{jian2019lattice,title={Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1{D}},author={Jian, C.-M. and Bi, Zhen and You, Y.-Z.},journal={Physical Review B},volume={100},pages={075109},year={2019},publisher={American Physical Society},doi={10.1103/PhysRevB.100.075109}}
@article{cheng2018classification,title={Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions},author={Cheng, M. and Bi, Zhen and You, Y.-Z. and Gu, Z.-C.},journal={Physical Review B},volume={97},pages={205109},year={2018},publisher={American Physical Society},doi={10.1103/PhysRevB.97.205109},}
@article{jian2018lieb,title={{L}ieb-{S}chultz-{M}attis Theorem and Its Generalizations from the Perspective of the Symmetry-Protected Topological Phase},author={Jian, C.-M. and Bi, Zhen and Xu, C.},journal={Physical Review B},volume={97},pages={054412},year={2018},publisher={American Physical Society},doi={10.1103/PhysRevB.97.054412}}
@article{bi2017bilayer,title={Bilayer Graphene as a Platform for Bosonic Symmetry Protected Topological States},author={Bi, Zhen and Zhang, R.-X. and You, Y.-Z. and Young, A. and Balents, L. and Liu, C.-X. and Xu, C.},journal={Physical Review Letters},volume={118},pages={126801},year={2017},publisher={American Physical Society},doi={10.1103/PhysRevLett.118.126801}}
@article{you2016quantum,title={Quantum Phase Transitions between Bosonic Symmetry-Protected Topological States without Sign Problem: Nonlinear Sigma Model with a Topological Term},author={You, Y.-Z. and Bi, Zhen and Mao, D. and Xu, C.},journal={Physical Review B},volume={93},pages={125101},year={2016},publisher={American Physical Society},doi={10.1103/PhysRevB.93.125101}}
@article{bi2015construction,title={Construction and Field Theory of Bosonic Symmetry Protected Topological States beyond Group Cohomology},author={Bi, Zhen and Xu, C.},journal={Physical Review B},volume={91},pages={184404},year={2015},publisher={American Physical Society},doi={10.1103/PhysRevB.91.184404}}
@article{bi2015classification,title={Classification and Description of Bosonic Symmetry Protected Topological Phases with Semiclassical Nonlinear Sigma Models},author={Bi, Zhen and Rasmussen, A. and Slagle, K. and Xu, C.},journal={Physical Review B},volume={91},pages={134404},year={2015},publisher={American Physical Society},doi={10.1103/PhysRevB.91.134404},}
@article{you2015bridging,title={Bridging Fermionic and Bosonic Short-Range Entangled States},author={You, Y.-Z. and Bi, Zhen and Rasmussen, A. and Cheng, M. and Xu, C.},journal={New Journal of Physics},volume={17},pages={075010},year={2015},doi={10.1088/1367-2630/17/7/075010}}
@misc{bi2015selfdual,title={Self-Dual Quantum Electrodynamics on the Boundary of 4d Bosonic Symmetry Protected Topological States},author={Bi, Zhen and Slagle, K. and Xu, C.},year={2015},}
@article{bi2014anyon,title={Anyon and Loop Braiding Statistics in Field Theories with a Topological $\Theta$-Term},author={Bi, Zhen and You, Y.-Z. and Xu, C.},journal={Physical Review B},volume={90},pages={081110},year={2014},publisher={American Physical Society},doi={10.1103/PhysRevB.90.081110},}
@article{you2014wavefunction,title={Wavefunction and Strange Correlator of Short-Range Entangled States},author={You, Y.-Z. and Bi, Zhen and Rasmussen, A. and Slagle, K. and Xu, C.},journal={Physical Review Letters},volume={112},pages={247202},year={2014},publisher={American Physical Society},doi={10.1103/PhysRevLett.112.247202}}
@article{bi2014line,title={Line Defects in Three-Dimensional Symmetry Protected Topological Phases},author={Bi, Zhen and Rasmussen, A. and Xu, C.},journal={Physical Review B},volume={89},pages={184424},year={2014},publisher={American Physical Society},doi={10.1103/PhysRevB.89.184424}}
@misc{chen2025intertwining,title={Intertwining Josephson and Vortex Topologies in Conventional Superconductors},author={Chen, Z. and Li, J. and Hu, L.-H. and Bi, Zhen and Zhang, R.-X.},year={2025},note={Submitted to Physical Review X}}
Correlated and topological phases in moiré materials
Stacking two atomically thin crystals with a small relative twist produces a moiré superlattice, a striking recent development in condensed-matter physics. In these structures the electrons move so slowly that their mutual interactions, usually a small correction, come to control the physics. This makes moiré materials a highly tunable setting for correlated and topological states — insulators, superconductors, ferroelectrics, and fractionalized states that ordinarily require strong magnetic fields can appear in a single device and be adjusted with an applied voltage. Our group works on the theory of these systems: we design the stacked and strained structures needed to realize a target electronic behavior, and we predict the correlated and topological phases that emerge inside them. A recurring theme is the interplay between the geometry and topology of the engineered bands and the interacting states they support, connecting the ideas of topology to materials that can be built and measured.
@misc{fedorko2025engineering,title={Engineering Moir{\'e} Kagome Superlattices in Twisted Transition Metal Dichalcogenides},author={Fedorko, A. and Liu, C.-X. and Bi, Zhen},year={2025},}
@article{xu2024maximally,title={Maximally Localized {W}annier Orbitals, Interaction Models and Fractional Quantum Anomalous {H}all Effect in Twisted Bilayer {MoTe$_2$}},author={Xu, C. and Li, J. and Xu, Y. and Bi, Zhen and Zhang, Y.},journal={Proceedings of the National Academy of Sciences},volume={121},number={8},pages={e2316749121},year={2024},doi={10.1073/pnas.2316749121}}
Excitonic Density Wave and Spin-Valley Superfluid in Bilayer Transition Metal Dichalcogenide
@article{bi2021excitonic,title={Excitonic Density Wave and Spin-Valley Superfluid in Bilayer Transition Metal Dichalcogenide},author={Bi, Zhen and Fu, Liang},journal={Nature Communications},volume={12},pages={642},year={2021}}
Z. Zheng, Q. Ma, Zhen Bi, S. Barrera, M. Liu, N. Mao, Y. Zhang, N. Kiper, K. Watanabe, T. Taniguchi, J. Kong, W. Tisdale, R. Ashoori, N. Gedik, L. Fu, S. Xu, and P. Jarillo-Herrero
@article{zheng2020unconventional,title={Unconventional Ferroelectricity in Moir{\'e} Heterostructures},author={Zheng, Z. and Ma, Q. and Bi, Zhen and de la Barrera, S. and Liu, M. and Mao, N. and Zhang, Y. and Kiper, N. and Watanabe, K. and Taniguchi, T. and Kong, J. and Tisdale, W. and Ashoori, R. and Gedik, N. and Fu, L. and Xu, S. and Jarillo-Herrero, P.},journal={Nature},volume={588},pages={71--76},year={2020},doi={10.1038/s41586-020-2970-9}}
@article{bi2019designing,title={Designing Flat Bands by Strain},author={Bi, Zhen and Yuan, N. and Fu, L.},journal={Physical Review B},volume={100},pages={035448},year={2019},publisher={American Physical Society},doi={10.1103/PhysRevB.100.035448},}
Topological Minibands and Interaction-Driven Quantum Anomalous Hall State in Topological-Insulator-Based Moiré Heterostructures
K. Yang, Z. Xu, Y. Feng, F. Schindler, Y. Xu, Zhen Bi, B. A. Bernevig, P. Tang, and C.-X. Liu
@article{yang2024topological,title={Topological Minibands and Interaction-Driven Quantum Anomalous Hall State in Topological-Insulator-Based Moir{\'e} Heterostructures},author={Yang, K. and Xu, Z. and Feng, Y. and Schindler, F. and Xu, Y. and Bi, Zhen and Bernevig, B. A. and Tang, P. and Liu, C.-X.},journal={Nature Communications},volume={15},pages={2670},year={2024}}
Unconventional quantum criticality and gapless phases
When matter changes from one phase to another — water freezing, or a metal becoming magnetic — the system becomes especially sensitive right at the transition, fluctuating across many length scales at once. For much of the twentieth century, a single framework due to Landau described these critical points. Some quantum transitions, however, fall outside it: matter can pass continuously between two very different ordered states through a critical point whose natural description involves not the original particles, but emergent gauge fields and fractionalized excitations that appear only there. Gapless matter can be unusual away from any transition as well — as in “strange metals,” where the electron no longer behaves as a well-defined particle, a long-standing puzzle in many quantum materials. Our group builds and analyzes the theories of these gapless states, extending them to higher dimensions and relating them through dualities, to understand what universal behavior is possible beyond the Landau paradigm.
@article{anakru2025emergent,title={Emergent Gauge Field in Composite-Fermion Metals: A Large-Scale Microscopic Study},author={Anakru, A. and Gattu, M. and Balram, A. C. and Wu, X.-C. and Kumar, P. and Bi, Zhen and Jain, J. K.},journal={Physical Review Letters},volume={135},number={24},pages={246503},year={2025},publisher={American Physical Society},doi={10.1103/PhysRevLett.135.246503}}
@article{bi2020landau,title={Landau Ordering Phase Transition beyond the Landau Paradigm},author={Bi, Zhen and Lake, E. and Senthil, T.},journal={Physical Review Research},volume={2},pages={023031},year={2020},publisher={American Physical Society},doi={10.1103/PhysRevResearch.2.023031}}
@article{goldman2020collusion,title={Collusion of Interactions and Disorder at the Superfluid-Insulator Transition: A Dirty 2{d} Quantum Critical Point},author={Goldman, H. and Thomson, A. and Nie, L. and Bi, Zhen},journal={Physical Review B},volume={101},pages={144506},year={2020},publisher={American Physical Society},doi={10.1103/PhysRevB.101.144506}}
@article{kozii2019superconductivity,title={Superconductivity Near a Ferroelectric Quantum Critical Point in Ultra-Low-Density Dirac Materials},author={Kozii, V. and Bi, Zhen and Ruhman, J.},journal={Physical Review X},volume={9},pages={031046},year={2019},publisher={American Physical Society},doi={10.1103/PhysRevX.9.031046}}
@article{bi2019adventure,title={An Adventure in Topological Phase Transitions in {3+1-D}: Non-Abelian Deconfined Quantum Criticalities and a Possible Duality},author={Bi, Zhen and Senthil, T.},journal={Physical Review X},volume={9},pages={021034},year={2019},publisher={American Physical Society},doi={10.1103/PhysRevX.9.021034}}
@article{jian2018deconfined,title={Deconfined Quantum Critical Point on the Triangular Lattice},author={Jian, C.-M. and Thomson, A. and Rasmussen, A. and Bi, Zhen and Xu, C.},journal={Physical Review B},volume={97},pages={195115},year={2018},publisher={American Physical Society},doi={10.1103/PhysRevB.97.195115}}
@article{jian2017thermal,title={A Model for Continuous Thermal Metal to Insulator Transition},author={Jian, C.-M. and Bi, Zhen and Xu, C.},journal={Physical Review B},volume={96},pages={115122},year={2017},publisher={American Physical Society},doi={10.1103/PhysRevB.96.115122}}
@article{bi2017instability,title={Instability of the Non-{F}ermi Liquid State of the {Sachdev-Ye-Kitaev} Model},author={Bi, Zhen and Jian, C.-M. and You, Y.-Z. and Pawlak, K. and Xu, C.},journal={Physical Review B},volume={95},pages={205105},year={2017},publisher={American Physical Society},doi={10.1103/PhysRevB.95.205105}}
@article{bi2016exotic,title={Exotic Quantum Critical Point on the Surface of the Three-Dimensional Topological Insulator},author={Bi, Zhen and You, Y.-Z. and Xu, C.},journal={Physical Review B},volume={94},pages={024433},year={2016},publisher={American Physical Society},doi={10.1103/PhysRevB.94.024433}}
@misc{bi2016stable,title={Stable Interacting (2+1)-d Conformal Field Theories at the Boundary of a Class of (3+1)-d Symmetry Protected Topological Phases},author={Bi, Zhen and Rasmussen, A. and BenTov, Y. and Xu, C.},year={2016},}
The complete list of publications — including collaborative and earlier work not grouped above — is on the publications page and Google Scholar.