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Bulletin of the American Physical Society

Chiral spin liquid emerging between competing magnetic order states in the spin-1/2 J1-J2-J3 kagome Heisenberg model

Shou-Shu Gong, Wei Kang Zhu, Leon Balents, Dong-Ning Sheng

Published Mar 5, 2015• 0 citations
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Phase diagram and chirality of the spin-1/2 J1-J2 Heisenberg model on the kagome lattice

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Bulletin of the American Physical Society•Mar 20, 2013•0 citations

Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice

Shou-Shu Gong, Wei Kang Zhu, Leon Balents +1 more

We study the quantum phase diagram of the spin-$1/2$ Heisenberg model on the kagome lattice with first-, second-, and third-neighbor interactions ${J}_{1},{J}_{2}$, and ${J}_{3}$ by means of density matrix renormalization group. For small ${J}_{2}$ and ${J}_{3}$, this model sustains a time-reversal invariant quantum spin-liquid phase. With increasing ${J}_{2}$ and ${J}_{3}$, we find in addition a $q=(0,0)$ N\'eel phase, a chiral spin-liquid phase, an apparent valence-bond crystal phase, and a complex noncoplanar magnetically ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. Both the chiral spin liquid and cuboc1 phase break time-reversal symmetry in the sense of spontaneous scalar spin chirality. We show that the chiralities in the chiral spin liquid and cuboc1 are distinct, and that these two states are separated by a strong first-order phase transition. The transitions from the chiral spin liquid to both the $q=(0,0)$ phase and to time-reversal symmetric spin liquid, however, are consistent with continuous quantum phase transitions.

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We study the interplay of competing interactions in spin-$\frac{1}{2}$ triangular Heisenberg model through tuning the first- (${J}_{1}$), second- (${J}_{2}$), and third-neighbor (${J}_{3}$) couplings. Based on a large-scale density-matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a gapless chiral spin-liquid (CSL) phase in the intermediate ${J}_{2}$ and ${J}_{3}$ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin-liquid state, the $U(1)$ staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the $U(1)$ Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero ${J}_{2}$ and ${J}_{3}$, which naturally explains the numerical results. This realizes an example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of interesting quantum phases emergent from competing interactions in triangular-lattice magnets.

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Frustration induced quantum spin liquids and topological properties

Tristan Lugan

Frustrated quantum magnets have received a lot of attention in the past decades for they are expected to host exotic magnetic states such as quantum spin liquids exhibiting fractionalized excitations and topological properties. One way to study these spin liquid phases is to perform a parton construction of the quantum Heisenberg Hamiltonian. This mean-field method has the valuable advantage of treating magnetically ordered states and spin-liquid states on an equal footing. In this thesis, we have employed such a method based on the Schwinger boson mean-field theory (SBMFT) to study two magnetically frustrated systems. After a brief introduction of the core concepts behind frustrated magnetic systems in chapter 1 we will introduce the Schwinger boson theory and the associated numerical tools in chapter 2. In chapter 3, we will present the full phase diagram of the J1-J2 Heisenberg model on the square-kagome lattice with a particurlarly interesting ground state in the form of a topological nematic spin liquid. We will then make connections with a recently synthesized compound exhibiting perfect square-kagome geometry. In the final chapter of this manuscript, we will turn to the J1-J2-J3 Heisenberg model on the kagome lattice in the case where J2=J3=J. Once again, a full phase diagram is obtained thanks to our SBMFT self-consistent procedure. It is composed of three distinct ground states: a chiral spin liquid for J<1/3, a chiral long-range order for J>1/2 and a symmetric spin liquid in between. Finally, we will make connections with previous quantum and classical works, especially by discussing the presence of half-moon patterns in the static structure factor of an excited state of the model for J>1/2. In conclusion, we have revealed both rich and complex phase diagrams presenting various exotic spin-liquid states on the two frustrated systems studied in this manuscript.

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Chiral and Critical Spin Liquids in Spin-1/2 Kagome Antiferromagnet

Dong-Ning Sheng, Wei Kang Zhu, Shou-Shu Gong

Bulletin of the American Physical Society•Mar 5, 2015•1 citation
We study the quantum phase diagram of the spin-1/21/21/2 Heisenberg model on the kagome lattice with first-, second-, and third-neighbor interactions J1,J2{J}_{1},{J}_{2}J1​,J2​, and J3{J}_{3}J3​ by means of density matrix renormalization group. For small J2{J}_{2}J2​ and J3{J}_{3}J3​, this model sustains a time-reversal invariant quantum spin-liquid phase. With increasing J2{J}_{2}J2​ and J3{J}_{3}J3​, we find in addition a q=(0,0)q=(0,0)q=(0,0) N\'eel phase, a chiral spin-liquid phase, an apparent valence-bond crystal phase, and a complex noncoplanar magnetically ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. Both the chiral spin liquid and cuboc1 phase break time-reversal symmetry in the sense of spontaneous scalar spin chirality. We show that the chiralities in the chiral spin liquid and cuboc1 are distinct, and that these two states are separated by a strong first-order phase transition. The transitions from the chiral spin liquid to both the q=(0,0)q=(0,0)q=(0,0) phase and to time-reversal symmetric spin liquid, however, are consistent with continuous quantum phase transitions.
We study the interplay of competing interactions in spin-12\frac{1}{2}21​ triangular Heisenberg model through tuning the first- (J1{J}_{1}J1​), second- (J2{J}_{2}J2​), and third-neighbor (J3{J}_{3}J3​) couplings. Based on a large-scale density-matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a gapless chiral spin-liquid (CSL) phase in the intermediate J2{J}_{2}J2​ and J3{J}_{3}J3​ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin-liquid state, the U(1)U(1)U(1) staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the U(1)U(1)U(1) Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero J2{J}_{2}J2​ and J3{J}_{3}J3​, which naturally explains the numerical results. This realizes an example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of interesting quantum phases emergent from competing interactions in triangular-lattice magnets.
Frustrated quantum magnets have received a lot of attention in the past decades for they are expected to host exotic magnetic states such as quantum spin liquids exhibiting fractionalized excitations and topological properties. One way to study these spin liquid phases is to perform a parton construction of the quantum Heisenberg Hamiltonian. This mean-field method has the valuable advantage of treating magnetically ordered states and spin-liquid states on an equal footing. In this thesis, we have employed such a method based on the Schwinger boson mean-field theory (SBMFT) to study two magnetically frustrated systems. After a brief introduction of the core concepts behind frustrated magnetic systems in chapter 1 we will introduce the Schwinger boson theory and the associated numerical tools in chapter 2. In chapter 3, we will present the full phase diagram of the J1-J2 Heisenberg model on the square-kagome lattice with a particurlarly interesting ground state in the form of a topological nematic spin liquid. We will then make connections with a recently synthesized compound exhibiting perfect square-kagome geometry. In the final chapter of this manuscript, we will turn to the J1-J2-J3 Heisenberg model on the kagome lattice in the case where J2=J3=J. Once again, a full phase diagram is obtained thanks to our SBMFT self-consistent procedure. It is composed of three distinct ground states: a chiral spin liquid for J<1/3, a chiral long-range order for J>1/2 and a symmetric spin liquid in between. Finally, we will make connections with previous quantum and classical works, especially by discussing the presence of half-moon patterns in the static structure factor of an excited state of the model for J>1/2. In conclusion, we have revealed both rich and complex phase diagrams presenting various exotic spin-liquid states on the two frustrated systems studied in this manuscript.