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In this paper we propose a special type of a tree tensor network that has the geometry of a comb—a one-dimensional (1D) backbone with finite 1D teeth projecting out from it. This tensor network is designed to provide an effective description of higher-dimensional objects with special limited interactions or, alternatively, one-dimensional systems composed of complicated zero-dimensional objects. We provide details on the best numerical procedures for the proposed network, including an algorithm for variational optimization of the wave function as a comb tensor network and the transformation of the comb into a matrix product state. We compare the complexity of using a comb versus alternative matrix product state representations using density matrix renormalization group algorithms. As an application, we study a spin-1 Heisenberg model system which has a comb geometry. In the case where the ends of the teeth are terminated by spin-1/2 spins, we find that Haldane edge states of the teeth along the backbone form a critical spin-1/2 chain, whose properties can be tuned by the coupling constant along the backbone. By adding next-nearest-neighbor interactions along the backbone, the comb can be brought into a gapped phase with a long-range dimerization along the backbone. The critical and dimerized phases are separated by a Kosterlitz-Thouless phase transition, the presence of which we confirm numerically. Finally, we show that when the teeth contain an odd number of spins and are not terminated by spin-1/2's, a special type of comb edge states emerge.
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Characterizing pump line phase offset of a single-soliton Kerr comb by dual comb interferometry
- Award ID(s):
- 1809784
- PAR ID:
- 10087901
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optics Letters
- Volume:
- 44
- Issue:
- 6
- ISSN:
- 0146-9592; OPLEDP
- Page Range / eLocation ID:
- Article No. 1460
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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