Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet

Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-$1/2$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in spin-$3/2$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian CSL emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in spin-$3/2$ system suggests a new route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.Comment: LA-UR-22-3320

Stochastic representation for solutions of a system of coupled HJB-Isaacs equations with integral-partial operators

In this paper, we focus on the stochastic representation of a system of coupled Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs (HJBI), for short) equations which is in fact a system of coupled Isaacs' type integral-partial differential equation. For this, we introduce an associated zero-sum stochastic differential game, where the state process is described by a classical stochastic differential equation (SDE, for short) with jumps, and the cost functional of recursive type is defined by a new type of backward stochastic differential equation (BSDE, for short) with two Poisson random measures, whose wellposedness and a prior estimate as well as the comparison theorem are investigated for the first time. One of the Poisson random measures appearing in the SDE and the BSDE stems from the integral term of the HJBI equations; the other random measure in BSDE is introduced to link the coupling factor of the HJBI equations. We show through an extension of the dynamic programming principle that the lower value function of this game problem is the viscosity solution of the system of our coupled HJBI equations. The uniqueness of the viscosity solution is also obtained in a space of continuous functions satisfying certain growth condition. In addition, also the upper value function of the game is shown to be the solution of the associated system of coupled Issacs' type of integral-partial differential equations. As a byproduct, we obtain the existence of the value for the game problem under the well-known Isaacs' condition.Comment: 37 page

Dual Effects of the US-China Trade War and COVID-19 on United States Imports: Transfer of China's industrial chain?

The trade tension between the U.S. and China since 2018 has caused a steady decoupling of the world's two largest economies. The pandemic outbreak in 2020 complicated this process and had numerous unanticipated repercussions. This paper investigates how U.S. importers reacted to the trade war and worldwide lockdowns due to the COVID-19 pandemic. We examine the effects of the two incidents on U.S. imports separately and collectively, with various economic scopes. Our findings uncover intricate trading dynamics among the U.S., China, and Southeast Asia, through which businesses relocated portions of their global supply chain away from China to avoid high tariffs. Our analysis indicates that increased tariffs cause the U.S. to import less from China. Meanwhile, Southeast Asian exporters have integrated more into value chains centered on Chinese suppliers by participating more in assembling and completing products. However, the worldwide lockdowns over pandemic have reversed this trend as, over this period, the U.S. effectively imported more goods directly from China and indirectly through Southeast Asian exporters that imported from China.Comment: 30 pages, 6 figure