Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry

子系统化的环面码：基于反向量子自旋液体的拓扑子系统码框架

Toric code made subsystem: a framework for topological subsystem codes using anticommuting quantum spin liquids

提出基于反向量子自旋液体的拓扑子系统码框架，通过空间修改环面码破坏稳定子码性质，利用大量基态简并作为子系统自由度，实现拓扑子系统码。

Experimental Realization of Classical $\mathbb{Z}_2$ Spin Liquids in a Programmable Quantum Device

We build and probe a $\mathbb{Z}_2$ spin liquid in a programmable quantum device, the D-Wave DW-2000Q. Specifically, we observe the classical 8-vertex and 6-vertex (spin ice) states and transitions between them. To realize this state of matter, we design a Hamiltonian with combinatorial gauge symmetry using only pairwise-qubit interactions and a transverse field, i.e., interactions which are accessible in this quantum device. The combinatorial gauge symmetry remains exact along the full quantum annealing path, landing the system onto the classical 8-vertex model at the endpoint of the path. Th…

Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice

We investigate the extended Heisenberg model on the Kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor super-exchanges are considered, we find that a gapped spin liquid described by non-trivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, le…

Spin liquids from Majorana Zero Modes in a Cooper Box

We propose a path for constructing diverse interacting spin systems from topological nanowires in Cooper Boxes. The wires are grouped into a three-wire building block called an 'hexon', consisting of six Majorana zero modes. In the presence of a strong charging energy, the hexon becomes a Cooper box equivalent to two spin-$1/2$ degrees of freedom. By considering arrays of hexons and controlling the distances between the various wires, one can tune the Hamiltonian governing the low-energy spins, thus providing a route for controllably constructing interacting spin systems in one- and two-dimens…

Quasihole condensates in quantum Hall liquids

We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states, and to several classes of non-Abelian hierarchical states. Most previously proposed spin-polarized quantum Hall wave functions appear as special cases. In this paper we explain the physical motivations for the approach, and exemplify it by explicitly constructing the level-two quasihole condensate state at filling fraction 2/3, and the two level-three states at 5/13 and 5/7 which are built from combinatio…

Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model

The Sachdev-Ye-Kitaev (SYK) model incorporates rich physics, ranging from exotic non-Fermi liquid states without quasiparticle excitations, to holographic duality and quantum chaos. However, its experimental realization remains a daunting challenge due to various unnatural ingredients of the SYK Hamiltonian such as its strong randomness and fully nonlocal fermion interaction. At present, constructing such a nonlocal Hamiltonian and exploring its dynamics is best through digital quantum simulation, where state-of-the-art techniques can already handle a moderate number of qubits. Here we demonst…

Spin-lattice Coupling in U(1) Quantum Spin Liquids

Quantum spin liquids (QSLs) are exotic phases with intrinsic massive entanglements. Instead of microscopic spins, fractionalized particles and gauge fluctuations are emergent, revealing QSLs' exotic natures. Quantum spins with strong spin-orbit coupling on a pyrchlore lattice, for example Pr2Zr2O7, are suggested to host a U(1) QSL with emergent photons, gapless excitations without breaking any symmetries, as well as emergent monopoles. One of the key issues in QSLs is an interplay between emergent degrees of freedom of QSLs and conventional degrees of freedom, and we investigate the interplay …

Tensor network wavefunction of $S=1$ Kitaev spin liquids

Recently there has been a great interest in understanding quantum spin liquid phases with varying spin magnitude, partly due to possible material realizations. A number of recent numerical computations suggest that the ground state of the S=1 Kitaev model may be a quantum spin liquid in analogy to the renowned $S$=$1/2$ model. On the other hand, the nature of the ground state remains elusive since the $S$=$1$ model is not exactly solvable in contrast to the $S$=$1/2$ model. In this work, we construct a tensor network ground state wavefunction for the S=1 Kitaev model, which is explicitly writt…