Research 

A primary goal of my research is to explore the new mixed-state quantum phases of matter from a quantum information-theoretic perspective. In particular, emergent many-body phenomena that are intrinsically mixed lacking analogs in isolated quantum systems are being actively investigated.

Strong-to-weak Spontaneous Symmetry Breaking

Global symmetry is an important organizing principle in modern physics. Symmetry in mixed quantum states can manifest in two distinct forms: strong symmetry, where each individual pure state in the quantum ensemble is symmetric with the same charge, and weak symmetry, which applies only to the entire ensemble. 

Recently, we discovered a new phase of quantum matter in open quantum systems dubbed strong-to-weak spontaneous symmetry breaking (SW-SSB). SW-SSB has been neglected by conventional linear response theory due to the short-ranged two-point correlation function. To characterize SW-SSB, we introduce an information-theoretic quantity named fidelity correlator as the local order parameter, and another information-theoretic quantity named fidelity susceptibility to characterize the dynamical response to external perturbations.

Mixed-State/Average Symmetry-Protected Topological Phases

Symmetry-protected topological (SPT) states have been intensively studied as a universal phase of quantum matter, as well as applications to measurement-based quantum computation and quantum teleportation. We systematically construct and classify the average SPT (ASPT) phases in systems subject to local noise or disorder.

Surprisingly, we uncover a plethora of ASPT phases without pure-state analog, namely intrinsic average SPT phases. Systematic classification of ASPT phases has been obtained from homological algebra, tensor network techniques, and holographic duality. 

Another main direction of my research program is to explore the quantum error correction codes subject to local noises. In fact, the robustness of QECCs under external noises, namely the decodability of QECCs, plays a central role in the research of quantum error correction.

Mixed-State Topological Order

We introduced a new understanding of the decodability of quantum error-correction codes through the strong-to-weak spontaneous breaking of higher-form symmetry. A wide variety of QECCs can be comprehended as spontaneous symmetry breaking (SSB) of some loop-like higher-form symmetry, and the degenerate subspace of this SSB can store logical quantum information. We show that the decodability transition of QECCs is the transition between SSB and SW-SSB of higher-form symmetry: in the SSB phase, the logical information is decodable; in the SW-SSB phase, the logical information corrupts to classical information and no longer decodable. 

Quantum Low-Density Parity-Check Codes

Classical LDPC codes have been widely used as powerful classical error-correction algorithms in our lives such as Wi-Fi Routers. Thus a systematic generalization to quantum LDPC (qLDPC) codes would be invaluable for quantum technology because of low computational overhead and robustness against local noises.

In particular, one of my research directions is to understand if qLDPC codes can be treated as stable phases of quantum matter, as well as their exotic properties such as elementary excitations and their braiding statistics. This direction would be beneficial for realizing qLDPC codes in quantum simulators or real quantum materials, as well as the understanding of the universal properties of qLDPC codes.

Topological phases of quantum matter have become a fascinating subject of condensed matter physics during the past few decades. In particular, the patterns of long-range entanglement provide us with a systematic way of understanding intrinsic topological order. Furthermore, the interplay between symmetry and topology has played a central role in recent years. In particular, the symmetry-protected topological (SPT) phases greatly expand our knowledge of phases of quantum matter beyond the Landau symmetry-breaking paradigm.

Crystalline Symmetry-Protected Topological Phases

Topological phases of matter are generally realized in quantum materials with some crystalline symmetry. We systematically established the general paradigm of crystalline SPT phases in two- and three-dimensional interacting fermion systems by real-space construction of topological crystal. The real-space construction also implies the boundary anomaly of crystalline SPT states, which makes our paradigm experimentally relevant.  

Subsystem Symmetry-Protected Topological Phases

Coming from a rather orthogonal direction, a new type of symmetry, namely subsystem symmetry, is discovered along the exploration of so-called fracton topological phases. Compared to ordinary global symmetry, subsystem symmetries are more closely intertwined with the underlying foliation structure of space and only act on a rigid submanifold/leaf of the whole system. We systematically constructed and classified the subsystem SPT phases in arbitrary dimensional interacting systems.