Absence of Barren Plateaus in Finite Local-Depth Circuits with Long-Range Entanglement.

Ground state preparation is classically intractable for general Hamiltonians. On quantum devices, shallow parametrized circuits can be effectively trained to obtain short-range entangled states under the paradigm of variational quantum eigensolver, while deep circuits are generally untrainable due to the barren plateau phenomenon. In this Letter, we give a general lower bound on the variance of circuit gradients for arbitrary quantum circuits composed of local 2-designs. Based on our unified framework, we prove the absence of barren plateaus in training finite local-depth circuits (FLDC) for the ground states of local Hamiltonians. FLDCs are allowed to be deep in the conventional circuit depth to generate long-range entangled ground states, such as topologically ordered states, but their local depths are finite, i.e., there is only a finite number of gates acting on individual qubits. This characteristic sets FLDC apart from shallow circuits: FLDC in general cannot be classically simulated to estimate local observables efficiently by existing tensor network methods in two and higher dimensions. We validate our analytical results with extensive numerical simulations and demonstrate the effectiveness of variational training using the generalized toric code model.

Strong Pairing Originated from an Emergent Z_{2} Berry Phase in La_{3}Ni_{2}O_{7}.

The recent discovery of high-temperature superconductivity in La_{3}Ni_{2}O_{7} offers a fresh platform for exploring unconventional pairing mechanisms. Starting with the basic argument that the electrons in d_{z^{2}} orbitals nearly form local moments, we examine the effect of the Hubbard interaction U on the binding strength of Cooper pairs based on a single-orbital bilayer model with intralayer hopping t_{∥} and interlayer superexchange J_{⊥}. By extensive density matrix renormalization group calculations, we observe a remarkable enhancement in binding energy as much as 10-20 times larger with U/t_{∥} increasing from 0 to 12 at J_{⊥}/t_{∥}∼1. We demonstrate that such a substantial enhancement stems from a kinetic-energy-driven mechanism. Specifically, a Z_{2} Berry phase will emerge at large U due to the Hilbert space restriction (Mottness), which strongly suppresses the mobility of single particle propagation as compared to U=0. However, the kinetic energy of the electrons (holes) can be greatly restored by forming an interlayer spin-singlet pairing, which naturally results in a superconducting state even for relatively small J_{⊥}. An effective hard-core bosonic model is further proposed to estimate the superconducting transition temperature at the mean-field level.

Identification of magnetic interactions and high-field quantum spin liquid in α-RuCl3.

The frustrated magnet α-RuCl3 constitutes a fascinating quantum material platform that harbors the intriguing Kitaev physics. However, a consensus on its intricate spin interactions and field-induced quantum phases has not been reached yet. Here we exploit multiple state-of-the-art many-body methods and determine the microscopic spin model that quantitatively explains major observations in α-RuCl3, including the zigzag order, double-peak specific heat, magnetic anisotropy, and the characteristic M-star dynamical spin structure, etc. According to our model simulations, the in-plane field drives the system into the polarized phase at about 7 T and a thermal fractionalization occurs at finite temperature, reconciling observations in different experiments. Under out-of-plane fields, the zigzag order is suppressed at 35 T, above which, and below a polarization field of 100 T level, there emerges a field-induced quantum spin liquid. The fractional entropy and algebraic low-temperature specific heat unveil the nature of a gapless spin liquid, which can be explored in high-field measurements on α-RuCl3.