Research

Coherent quantum evolution in many-body systems usually generates a large amount of entanglement. A key question in quantum dynamics is to understand how entanglement behaves. 

Using the tools of random quantum circuits, we systematically developed an membrane theory for entanglement, in which the statistical mechanics of a membrane-like object determines the entanglement at the coarse grained scales. 

Relevant papers: Entanglement Membrane in Chaotic Many-Body Systems, Phys. Rev. X 10, 031066, Emergent statistical mechanics of entanglement in random unitary circuits Phys. Rev. B 99, 174205 

The speed of light sets the limit of information propagation in our world. The notion of light cone sets a conical region in spacetime beyond which a local signal can not reach. 

For quantum simulation platforms in the laboratory, the speed of light is effectively infinite. Yet there is still an emergent light cone stemmed from the locality of the interaction. We study this light cone in the context of how quickly quantum chaos -- specifically the quantum butterfly effect spreads. We argued and computed in a solvable noisy model that the problem can be mapped into a classical biological dispersal problem. We further developed a reaction-diffusion type hydrodynamic equation to describe this process.

Relevant papers: Operator Lévy Flight: Light Cones in Chaotic Long-Range Interacting Systems Phys. Rev. Lett. 124, 180601, Hydrodynamic theory of scrambling in chaotic long-range interacting systems, Phys. Rev. B 107, 014201 

Quantum chaos has its intrinsic complex natures that defies both analytic and computational approaches. 

One of the exceptional case is the dual unitary point, at which the evolution in both space and time are unitary. Despite its extremely chaotic nature in general, many dynamical properties are exactly solvable. 

We proved that a maximal entanglement growth rate in a quantum circuit implies that the gates inside to have dual unitarity. The maximal entangling feature helps us to design and understand some constructions of quantum error correction codes. 

Relevant paper: Maximal entanglement velocity implies dual unitarity, Phys. Rev. B 106, L201104 

Recent studies show that unitary evolution interspersed by random measurements can create critical behaviors about entanglement. At a finite measurement rate, the long time steady state in numerics features conformal invariance that also appears at critical point in equilibrium. 

The transition at simplifying limits can be understood as the percolation transition of the effective spin models that host the membrane. However, the nature of the transitions, depending on the different measurement protocols and circuit setups are not completely settled and understood. 

We used random measurement to create boundary critical phases by bulk random measurements. The idea stems from the measurement-based quantum computing. The boundary criticality in the mapping to the statistical mechanical can be understood as a random bond Ising model at the lowest order approximation.

Relevant paper: Measurement-induced entanglement transition in a two-dimensional shallow circuit, Phys. Rev. B 106, 144311  

Large entanglement is a barrier to classically simulate quantum states, particularly to algorithms based on tensor network representation. However thermalization of subsystem might be an aid. 

Researchers working on tensor network approach have proposed and empirically tested the idea of the folding algorithm - that is to simulate the (reduced-) density rather than the quantum states to save computational resources. At least the eventual thermalized state appears to have low cost. 

We showed that for interacting quantum systems, there is still an inevitable volume law quantum entanglement that acts as a barrier to classically simulate the intermediate stage. We showed the volume law mechanism in quantum circuits and holographic field theories.

More recently, researchers argued that the temporal entanglement of an influence matrix, based on the idea of Feynman and Vernon, does not have this barrier. Our exact calculation and proofs (with mild assumptions) show that there is still a volume law or linear in time growth of temporal entanglement in chaotic quantum circuits. 

Relevant papers: Temporal Entanglement in Chaotic Quantum Circuits, arxiv: 2023.08502, Barrier from chaos: operator entanglement dynamics of the reduced density matrix. J. High Energ. Phys. 2019, 20 (2019) 

Quantum many-body dynamics is perplexing with enormous quantum degrees of freedom. It is sometimes beneficial to "de-quantize" and study the classical many-body dynamics. Without entanglement, numerical approaches are more feasible. And the (semi-)classical picture always proves to be insightful even for its quantum counterpart. 

We studied the classical limit of the Haldane-Shastry spin chain. The quantum Haldane-Shastry model has one over distance squared interaction and like its Calogero-Sutherland cousin, it is integrable. We proposed a hydrodynamic equation at the classical continuum limit. In crude terms, it is the "square root" of the Landau-Lifshitz equation. We solved its single soliton sector. We can use the soliton gas approach to study transport in integrable models. 

The equation was independently discovered slightly later and known as the half-wave maps equation among the mathematics community. It is later proved to be integrable and contain multi-soliton solutions through a pole dynamics much like the Calogero-Sutherland-Moser model. 

Relevant paper: Solitons in a continuous classical Haldane–Shastry spin chain, Physics Letters A Volume 379, Issues 43–44, 6 November 2015, Pages 2817-2825