Detection and characterization of symmetry-broken long-range orders in the spin-1/2 triangular Heisenberg model

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Author(s)
Saadatmand, SN
McCulloch, IP
Griffith University Author(s)
Year published
2017
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Show full item recordAbstract
We present new numerical tools to analyze symmetry-broken phases in the context of
SU(2)-symmetric translation-invariant matrix product states (MPS) and density-matrix renormalization-group (DMRG) methods for infinite cylinders, and determine the phase diagram of the geometrically frustrated triangular Heisenberg model with nearest- and next-nearest-neighbor (NN and NNN) interactions. The appearance of Nambu-Goldstone modes in the excitation spectrum is characterized by “tower of states” levels in the momentum-resolved entanglement spectrum. Symmetry-breaking phase transitions are detected by a combination of the correlation ...
View more >We present new numerical tools to analyze symmetry-broken phases in the context of SU(2)-symmetric translation-invariant matrix product states (MPS) and density-matrix renormalization-group (DMRG) methods for infinite cylinders, and determine the phase diagram of the geometrically frustrated triangular Heisenberg model with nearest- and next-nearest-neighbor (NN and NNN) interactions. The appearance of Nambu-Goldstone modes in the excitation spectrum is characterized by “tower of states” levels in the momentum-resolved entanglement spectrum. Symmetry-breaking phase transitions are detected by a combination of the correlation lengths and second and fourth cumulants of the magnetic order parameters (which we call the Binder ratio), even though symmetry implies that the order parameter itself is strictly zero. Using this approach, we have identified a 120° order, a columnar order, and an algebraic spin liquid (specific to width-6 systems), alongside the previously studied topological spin liquid phase. For the latter, we also demonstrate robustness against chiral perturbations.
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View more >We present new numerical tools to analyze symmetry-broken phases in the context of SU(2)-symmetric translation-invariant matrix product states (MPS) and density-matrix renormalization-group (DMRG) methods for infinite cylinders, and determine the phase diagram of the geometrically frustrated triangular Heisenberg model with nearest- and next-nearest-neighbor (NN and NNN) interactions. The appearance of Nambu-Goldstone modes in the excitation spectrum is characterized by “tower of states” levels in the momentum-resolved entanglement spectrum. Symmetry-breaking phase transitions are detected by a combination of the correlation lengths and second and fourth cumulants of the magnetic order parameters (which we call the Binder ratio), even though symmetry implies that the order parameter itself is strictly zero. Using this approach, we have identified a 120° order, a columnar order, and an algebraic spin liquid (specific to width-6 systems), alongside the previously studied topological spin liquid phase. For the latter, we also demonstrate robustness against chiral perturbations.
View less >
Journal Title
Physical Review B: Covering Condensed Matter and Materials Physics
Volume
96
Issue
7
Copyright Statement
© 2017 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
Subject
Quantum physics not elsewhere classified