A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911130701529088 |
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| author | Pujari, Sumiran |
| author_facet | Pujari, Sumiran |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets Pujari, Sumiran Strongly Correlated Electrons Quantum Physics 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. |
| title | A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2406.17034 |