A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets

TL;DR

This paper introduces a class of exactly solvable two-dimensional quantum spin-1/2 Hamiltonians that embed one-dimensional spinless fermion liquids and Majorana excitations using bond-dependent couplings, offering new avenues for quantum engineering.

Contribution

It presents a novel solvable grid structure for 2D spin-1/2 systems that hosts spinless fermions and Majorana modes, distinct from Kitaev's model, with simpler conserved quantities.

Findings

Exact solvability via Jordan-Wigner transformation.

Embedding of 1D fermion liquids and Majorana excitations in 2D.

Potential for quantum architecture with controllable qubits.

Abstract

We write down a class of two-dimensional quantum spin-1/2 Hamiltonians whose eigenspectra are exactly solvable via the Jordan-Wigner transformation. The general structure corresponds to a suitable grid composed of XY or XX-Ising spin chains and ZZ-Ising spin chains and is generalizable to higher dimensions. They can host stacks of one-dimensional spinless fermion liquids with gapless excitations and power-law correlations coexisting with ordered spin moments (localized spinless fermions). Bond-dependent couplings thus can be an alternate mechanism than geometric frustration of SU(2)-symmetric couplings to obtain spinless fermionic excitations. Put in a different way, bond-dependent couplings allow for an embedding of one-dimensional spinless fermion (Tomonoga-Luttinger) liquids and solids and also Majorana excitations in higher dimensions. They can accommodate a simpler set of site-local conserved quantities apart from the more intricate, interlocked set of plaquette-local or bond-local conserved quantities in Kitaev's honeycomb model with Majorana excitations. The proposed grid structure may provide an architecture for quantum engineering with controllable qubits.