Commensurability, Excitation Gap, and Topology in Quantum Many-Particle Systems on a Periodic Lattice
Top Cited Papers
- 14 February 2000
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 84 (7) , 1535-1538
- https://doi.org/10.1103/physrevlett.84.1535
Abstract
In combination with Laughlin's treatment of the quantized Hall conductivity, the Lieb-Schultz-Mattis argument is extended to quantum many-particle systems (including quantum spin systems) with a conserved particle number on a periodic lattice in arbitrary dimensions. Regardless of dimensionality, interaction strength, and particle statistics (Bose or Fermi), a finite excitation gap is possible only when the particle number per unit cell of the ground state is an integer.Keywords
All Related Versions
This publication has 26 references indexed in Scilit:
- Two soluble models of an antiferromagnetic chainPublished by Elsevier ,2004
- The renormalization group and the ϵ expansionPublished by Elsevier ,2002
- Nonperturbative Approach to Luttinger's Theorem in One DimensionPhysical Review Letters, 1997
- Magnetization Plateaus in Spin Chains: “Haldane Gap” for Half-Integer SpinsPhysical Review Letters, 1997
- Magnetic Properties of the Spin-1/2 Ferromagnetic-Ferromagnetic-Antiferromagnetic Trimerized Heisenberg ChainJournal of the Physics Society Japan, 1994
- A two-dimensional isotropic quantum antiferromagnet with unique disordered ground stateJournal of Statistical Physics, 1988
- Valence bond ground states in isotropic quantum antiferromagnetsCommunications in Mathematical Physics, 1988
- Rigorous results on valence-bond ground states in antiferromagnetsPhysical Review Letters, 1987
- Field theories with « Superconductor » solutionsIl Nuovo Cimento (1869-1876), 1961
- Axial Vector Current Conservation in Weak InteractionsPhysical Review Letters, 1960