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Heisenberg antiferromagnet on the Husimi lattice
Strongly Correlated Electrons · Submitted 29 Oct 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The nature of the ground state varies strongly with the spin quantum number, $S$.
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The abstract, sentence by sentence
We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on Projected Entangled Simplex States (PESS). The nature of the ground state varies strongly with the spin quantum number, $S$. For $S = 1/2$, it is an algebraic (gapless) quantum spin liquid. For $S = 1$, it is a gapped, non-magnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For $S = 2$, it is a simplex-solid state with a spin gap and no symmetry-breaking; both integer-spin simplex-solid states are characterized by specific degeneracies in the entanglement spectrum. For $S = 3/2$, and indeed for all spin values $S \ge 5/2$, the ground states have $120$-degree antiferromagnetic order. In a finite magnetic field, we find that, irrespective of the value of $S$, there is always a plateau in the magnetization at $m = 1/3$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on Projected Entangled Simplex States (PESS). | contribution 0.69 | 0.97 | 0.04 | asserted 0.98 |
| s1 | The nature of the ground state varies strongly with the spin quantum number, $S$. | result 1.00 | 0.81 | 0.11 | asserted 1.00 |
| s2 | For $S = 1/2$, it is an algebraic (gapless) quantum spin liquid. | result 1.00 | 0.89 | 0.10 | asserted 1.00 |
| s3 | For $S = 1$, it is a gapped, non-magnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). | result 1.00 | 0.91 | 0.10 | asserted 1.00 |
| s4 | For $S = 2$, it is a simplex-solid state with a spin gap and no symmetry-breaking; both integer-spin simplex-solid states are characterized by specific degeneracies in the entanglement spectrum. | result 1.00 | 0.92 | 0.12 | asserted 1.00 |
| s5 | For $S = 3/2$, and indeed for all spin values $S \ge 5/2$, the ground states have $120$-degree antiferromagnetic order. | result 1.00 | 0.89 | 0.19 | asserted 1.00 |
| s6 | In a finite magnetic field, we find that, irrespective of the value of $S$, there is always a plateau in the magnetization at $m = 1/3$. | result 1.00 | 0.95 | 0.16 | asserted 1.00 |
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The paper
Original abstract
We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on Projected Entangled Simplex States (PESS). The nature of the ground state varies strongly with the spin quantum number, $S$. For $S = 1/2$, it is an algebraic (gapless) quantum spin liquid. For $S = 1$, it is a gapped, non-magnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For $S = 2$, it is a simplex-solid state with a spin gap and no symmetry-breaking; both integer-spin simplex-solid states are characterized by specific degeneracies in the entanglement spectrum. For $S = 3/2$, and indeed for all spin values $S \ge 5/2$, the ground states have $120$-degree antiferromagnetic order. In a finite magnetic field, we find that, irrespective of the value of $S$, there is always a plateau in the magnetization at $m = 1/3$.
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1 arXiv paper cite this in 1 sentence
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Cites as background 2 papers
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Various proposals have been put forward for the spin-1 case, including the hexagonal singlet solid state [ref] , the resonating AKLT loop state [ref] , and the trimerized simplex-solid state [ref] , among which the last has the best variational energy [ref] .
Symmetry fractional quantization in two dimensions · Introduction · 0.84
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PESS are also an extension of PEPS [ref] , sharing a number of the advantages of the PEPS formulation, including the ability to satisfy the boundary area law of entanglement entropy and to represent any state if the bond dimension is sufficiently large.
Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions · Simplex-Solid States · 0.81
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