相关论文: Hopf algebras and solvable unitary circuits

We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…

It is proved that the entire multi-parameter (small-)quantum groups of symmetrizable Kac-Moody algebras can be realized as certain subquotients of the cotensor Hopf algebras. This is an axiomatic construction. Hopf 2-cocycle deformations…

Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate…

We propose a nonstandard approach to solving the apparent incompatibility between the coalgebra structure of some inhomogeneous quantum groups and their natural complex conjugation. In this work we sketch the general idea and develop the…

We discover a variety of exact quantum many-body scars in higher-spin kinetically constrained models, through the recently developed DMRG-S algorithm [Zhang et al., Phys. Rev. Lett. 131, 020402]. Specifically, for the higher-spin PXP model…

The exactly solvable quantum many-particle model with harmonic one- and two-particle interaction terms is extended to include time-dependency. We show that when the external trap potential and finite-range interparticle interaction have a…

The discovery of chaotic quantum circuits with (partially) solvable dynamics has played a key role in our understanding of non-equilibrium quantum matter and, at the same time, has helped the development of concrete platforms for quantum…

Quantum simulators have made a remarkable progress towards exploring the dynamics of many-body systems, many of which offer a formidable challenge to both theoretical and numerical methods. While state-of-the-art quantum simulators are in…

Driving a quantum system periodically in time can profoundly alter its long-time correlations and give rise to exotic quantum states of matter. The complexity of the combination of many-body correlations and dynamic manipulations has the…

A class of non-Dirac-hermitian many-particle quantum systems admitting entirely real spectra and unitary time-evolution is presented. These quantum models are isospectral with Dirac-hermitian systems and are exactly solvable. The general…

Since the Connes--Kreimer Hopf algebra was proposed, revisiting present quantum field theory has become meaningful and important from algebraic points. In this paper, the Hopf algebra in the cutting rules is constructed. Its coproduct…

We develop a theory of \emph{locally Frobenius algebras} which are colimits of certain directed systems of Frobenius algebras. A major goal is to obtain analogues of the work of Moore \& Peterson and Margolis on \emph{nearly Frobenius…

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional…

Product code construction is a powerful tool for constructing quantum stabilizer codes, which serve as a promising paradigm for realizing fault-tolerant quantum computation. Furthermore, the natural mapping between stabilizer codes and the…

In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of…

Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…

We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We…

We study the non-equilibrium dynamics of kicked Ising models in $1+1$ dimensions which have interactions alternating between odd and even bonds in time. These models can be understood as quantum circuits tiling space-time with the…

Symmetry is a central concept for classical and quantum field theory, usually, symmetry is described by a finite group or Lie group. In this work, we introduce the weak Hopf algebra extension of symmetry, which arises naturally in anyonic…

We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations…