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 introduce magic-augmented Clifford circuits -- architectures in which Clifford circuits are preceded and/or followed by constant-depth circuits of non-Clifford (``magic") gates -- as a resource-efficient way to realize approximate k-designs. We prove that shallow Clifford circuits, when augmented with constant-depth circuits of magic gates, can generate approximate unitary and state k-designs with bounded relative error. The total circuit depth for these constructions improves upon previous results for small k>=4. The required number of magic gates is further reduced when considering k-designs with bounded additive error. We show that shallow Clifford circuits followed by O(k^2) single-qubit magic gates can generate an additive-error state k-design. I will also provide classical statistical mechanics understanding of our results and discuss the no-go theorems on design generation.

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.