Quantum Matter

Fermi surfaces have a number of fascinating properties, including a continuum of gapless excitations, a landscape of possible collective modes, universal super-area law entanglement, and relevant deformations that can produce non-Fermi liquid quantum critical metals. Their extreme gaplessness makes them difficult to tame with the conventional tools of QFT. Bosonization provides a potential nonperturbative approach by describing Fermi surface dynamics through a collective field living on a part of phase space. However, while such a field is sensible semiclassically, the challenge of treating it quantum mechanically has prevented bosonization from providing as powerful a tool as in one dimension. I will show that general Fermi surfaces can be exactly described by a particular large N limit of a U(N)_1 WZW model, with a tower of irrelevant corrections. This matrix-valued description encodes the noncommutative nature of phase space, and its (solvable) strongly coupled dynamics resolves the naive overcounting of degrees of freedom in the collective field without the need to cut the Fermi surface into patches. 

The study of entanglement in the ground states of locally interacting many-body quantum systems has provided connections between spectral properties and the computational resources required for tensor-network calculations. Generic quantum states have volume-law entanglement, but ground states are typically observed to satisfy an area law, with corrections in gapless systems. I will introduce a new framework that provides rigorous upper bounds on entanglement entropies of states with fixed energy. These results constrain (i) ground-state entanglement in both gapped and gapless systems in general spatial dimensions, (ii) the crossover from area-law to volume-law entanglement as the system energy is increased and (iii) the computational resources necessary for calculations of zero-temperature response functions.

Entanglement provides a powerful framework for characterizing quantum phases. The reduced density matrix (RDM) of a local region is known to encode non-trivial information about the phase of matter, as demonstrated by topological entanglement entropy and the Li-Haldane conjecture. We argue that this RDM harbors a much richer structure, which is revealed by examining the genuine multipartite entanglement (GME) shared among different partitions of the subregion. This talk introduces a comprehensive toolkit based on bipartite and multipartite entanglement witnesses to rigorously study how entanglement is distributed in quantum matter. Using these tools, we will explore a range of quantum phases such as the quantum Ising model, quantum spin liquids as well as measurement-induced phase transitions. In the end, we will move beyond GME and present a more collective form of entanglement, Genuine Network Multiparty entanglement (GNME), recently developed in the field of quantum information and foundations, and see how it serves as a sharper tool for detecting and characterizing novel phases of matter.

Entanglement bootstrap (EB) is a framework that aims to explain all the universal properties of quantum phases of matter from entanglement conditions. In this seminar, I will talk about our efforts in building such an EB framework for 2+1D chiral gapped phases. Many interesting properties that do not exist in non-chiral gapped states, such as robust gapless boundary and sharp corner contributions in entanglement entropies, can be derived in this framework. To capture the algebraic relations among local entanglement Hamiltonians, we defined a quantum-information-theoretic primitive called instantaneous modular flow. We then derived several instantaneous modular-flow equations that generalize the well-known formulas of topological entanglement entropy and chiral central charge. If time permits, I will also discuss a few applications of EB in conformal field theories in both 1+1D and 2+1D with fuzzy sphere.

In this talk, I will discuss the projects I have done in my Ph.D. https://scholar.google.com/citations?user=SiMLZi8AAAAJ&hl=en. My research lies at the intersection of quantum many-body physics and quantum information, aiming to unravel the intrinsic complexity of many-body dynamics using both analytical methods and quantum informational approaches. In the first direction, we develop several analytical frameworks, including solvable quantum circuit dynamics, tensor-network states, and non-equilibrium field-theoretic calculations, to study both non-equilibrium physics and open-system dynamics. In particular, we proposed the concept of mixed state deep thermalization, a new paradigm that extends conventional thermalization to the ensemble of conditional mixed states. In the second direction, we investigate the quantum complexity of non-Markovian open many-body systems, establishing Lieb–Robinson bounds and determining the optimal digital-simulation resources required to simulate such dynamics.

I will talk about the 1D quantum breakdown model in boson and spin systems, which has an exponential U(1) symmetry with charge decaying exponentially in space. We show that the ground state of the model exhibits a phase transition from a symmetric paramagnetic phase to a quantum breakdown condensate phase that spontaneously breaks the exponential U(1) symmetry. Unconventionally, the condensate phase does not have gapless Goldstone modes, making the spontaneous symmetry breaking stable at zero temperature in 1D. The condensate phase also has an exponentially large ground state degeneracy, which resembles a quantum glass but requires no disorder. This challenges the existing classification schemes of quantum phases of matter.

Preparation of thermal and ground states of many-body systems is a central challenge for quantum processors, needed e.g. as the starting point for many quantum physics experiments or for quantum chemistry applications. In this talk, I will discuss recent work on efficient state preparation using engineered system-bath physics. First, I will overview results from the Google experiment [Science 383 6689 2024], where a version of the dissipative algorithm was used to prepare low-energy states of quantum magnetic systems. I will then explain how to modify the algorithm to accurately prepare thermal and ground states [arXiv:2506.21318 & PRX Quantum 6, 010361 2025]: the resulting algorithm is suitable for near-term quantum devices, and exhibits partial robustness to noise owing to the dissipative nature. We demonstrate its efficiency numerically for ground states of 1d chain and ladder systems, and thermal states of the 2D quantum Ising model, providing perturbative arguments for its more general validity.

Although many-body localization (MBL) is most widely studied for systems with random potentials, various interesting phenomena occur naturally in quasiperiodic potentials. In particular, there is the lack of low-disorder rare regions which may destabilize MBL, the existence of a regime which is non-ergodic but with extended states, and a regime where all single-particle orbitals are critical. In this talk, I will give a theoretical picture of these phenomena (and some generalizations) based on the structure of the quasiperiodic potentials. First, I will show that regularly spaced deep wells in the potential create a separation of particle and information spreading timescales, leading to the non-ergodic extended behavior. Secondly, I will demonstrate that local mirror symmetries in the potential give rise to a hierarchy of resonances in the presence of interaction, leading to many-body critical states. Finally, I will discuss how such resonances may lead to rare-region effects in quasiperiodic systems, even though there is no low-disorder region in such systems.