What is recorded here?
Hastings extended the Lieb–Schultz–Mattis argument to higher-dimensional local quantum spin systems by combining separated twists with locality estimates. For the specified lattice families with a half-odd-integer spin per transverse column, a unique ground state has an excitation gap bounded by a constant times log(L)/L. Nachtergaele and Sims later gave a detailed rigorous proof with explicit geometric, interaction and symmetry hypotheses. The result restricts the possible low-energy structure of these many-body systems.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The bound concerns particular finite-size sequences with even periodic length and the required odd transverse spin parity; it is not a theorem for every width, boundary condition or long-range interaction. The later proof assumes its F1/F2 and LSM1–6 conditions, including U(1) symmetry, zero total spin component of the ground state and a real-basis condition used to control twist derivatives. A vanishing first gap can reflect near-degenerate ground states and does not by itself prove a continuous gapless spectrum, magnetic order or a particular spin-liquid phase.
Read the original work
- Lieb-Schultz-Mattis in higher dimensions (arXiv cond-mat/0305505v6)
- A Multi-Dimensional Lieb-Schultz-Mattis Theorem (arXiv math-ph/0608046v2)
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People and systems
M. B. Hastings; Bruno Nachtergaele; Robert Sims
These are the listed authors of the cited contribution sources. Paper authorship does not quantify individual effort. An incomplete list is explicitly marked; same names are not automatically merged.
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English catalogue narrative
Higher-dimensional spin constraints rule out a unique ground state with a size-independent gap
Hastings extended the Lieb–Schultz–Mattis argument to higher-dimensional local quantum spin systems by combining separated twists with locality estimates. For the specified lattice families with a half-odd-integer spin per transverse column, a unique ground state has an excitation gap bounded by a constant times log(L)/L. Nachtergaele and Sims later gave a detailed rigorous proof with explicit geometric, interaction and symmetry hypotheses. The result restricts the possible low-energy structure of these many-body systems.
Scientific scope
The bound concerns particular finite-size sequences with even periodic length and the required odd transverse spin parity; it is not a theorem for every width, boundary condition or long-range interaction. The later proof assumes its F1/F2 and LSM1–6 conditions, including U(1) symmetry, zero total spin component of the ground state and a real-basis condition used to control twist derivatives. A vanishing first gap can reflect near-degenerate ground states and does not by itself prove a continuous gapless spectrum, magnetic order or a particular spin-liquid phase.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
M. B. Hastings; Bruno Nachtergaele; Robert Sims
These are the listed authors of the cited contribution sources. Paper authorship does not quantify individual effort. An incomplete list is explicitly marked; same names are not automatically merged.