Nature of the randomness-induced quantum spin liquids in two dimensions

Abstract

The nature of the randomness-induced quantum spin liquid state, the random-singlet state, is investigated in two dimensions (2D) by means of the exact-diagonalization and the Hams-de Raedt methods for several frustrated lattices, e.g., the triangular, the kagome and the J_1-J_2 square lattices. Properties of the ground state, the low-energy excitations and the finite-temperature thermodynamic quantities are investigated. The ground state and the low-lying excited states consist of nearly isolated singlet-dimers, clusters of resonating singlet-dimers, and orphan spins. Low-energy excitations are either singlet-to-triplet excitations, diffusion of orphan spins accompanied by the recombination of nearby singlet-dimers, creation or destruction of resonating singlet-dimers clusters. The latter two excitations give enhanced dynamical `liquid-like' features to the 2D random-singlet state. Comparison is made with the random-singlet state in a 1D chain without frustration, the similarity and the difference between in 1D and in 2D being highlighted. Frustration in a wide sense, not only the geometrical one but also including the one arising from the competition between distinct types of interactions, play an essential role in stabilizing this frustrated random singlet state. Recent experimental situations on both organic and inorganic materials are reviewed and discussed.

arXiv commentFig.8 modified (finite-field data added); three references added (Refs.19,77,80); paragraphs added with discussion and and explanation expanded, especially in the last section

References in corpus (65)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Entanglement of a Pair of Quantum Bits
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Spin-lattice coupling in frustrated antiferromagnets
• Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
• Rare-earth triangular lattice spin liquid: a single-crystal study of YbMgGaO${}_4$
• Evidence for a spinon Fermi surface in a triangular lattice quantum spin liquid candidate
• Evidence for a Gapped Spin-Liquid Ground State in a Kagome Heisenberg Antiferromagnet
• Entangled Rings
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• Infinite-randomness quantum Ising critical fixed points
• 17O NMR study of the intrinsic magnetic susceptibility and spin dynamics of the quantum kagome antiferromagnet ZnCu3(OH)6Cl2
• $\mu$SR evidence for the U(1) quantum spin liquid ground state in the triangular antiferromagnet YbMgGaO${}_4$
• Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
• Crystalline Electric Field Randomness in the Triangular Lattice Spin-Liquid YbMgGaO${}_4$
• Quantum Kagome antiferromagnet ZnCu3(OH)6Cl2
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• The magnetic groundstate of an experimental $S=1/2$ kagomé antiferromagnet
• A new high-temperature quantum spin liquid with polaron spins
• Spin-glass ground state in a triangular-lattice compound YbZnGaO${}_4$
• Anomalous dielectric response in the dimer Mott insulator $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$
• High pressure sequence of Ba_3NiSb_2O_9 structural phases: new $S=1$ quantum spin-liquids based on Ni^{2+}
• Possible valence-bond condensation in the frustrated cluster magnet LiZn2Mo3O8
• Absence of magnetic thermal conductivity in the quantum spin liquid candidate YbMgGaO4
• Emergence of inhomogeneous moments from spin liquid in the triangular-lattice Mott insulator $\kappa$-(ET)${}_2$Cu${}_2$(CN)${}_3$
• Scaling and data collapse from local moments in frustrated disordered quantum spin systems
• Quantum spin-liquid behavior in the spin-1/2 random Heisenberg antiferromagnet on the triangular lattice
• Dynamic Scaling in the Susceptibility of the Spin-1\2 Kagome Lattice Antiferromagnet Herbertsmithite
• Spin-liquid-like state in a spin-1/2 square-lattice antiferromagnet perovskite induced by $d^{10}$-$d^0$ cation mixing
• Lattice effects and entropy release at the low-temperature phase transition in the spin-liquid candidate $\kappa$-(BEDT-TTF)${}_2$Cu${}_2$(CN)${}_3$
• Static and dynamical spin correlations of the S=1/2 random-bond antiferromagnetic Heisenberg model on the triangular and the kagome lattices
• Gapless excitations in the ground state of 1T-TaS${}_2$
• The low-temperature highly correlated quantum phase in the charge-density-wave 1T-TaS_2 compound
• Random Quantum Spin Chains: A Real-Space Renormalization Group Study
• Pressure-Tuned Exchange Coupling of a Quantum Spin Liquid in the Molecular Triangular Lattice $\kappa$-(ET)${}_2$Ag${}_2$(CN)${}_3$
• Valence Bond Glass Phase in the Diluted Kagome Antiferromagnets
• Molecular Quantum Magnetism in LiZn2Mo3O8
• The Low-Energy Fixed Points of Random Quantum Spin Chains
• Novel Pauli-paramagnetic quantum phase in a Mott insulator
• Dynamics and transport in random quantum systems governed by strong-randomness fixed points
• Quantum spin-liquid behavior in the spin-1/2 random-bond Heisenberg antiferromagnet on the kagome lattice
• Nearest-neighbor resonating valence bonds in YbMgGaO4
• Hierarchy of exchange interactions in the triangular-lattice spin-liquid YbMgGaO${}_4$
• Low-energy fixed points of random Heisenberg models
• From Spin Glass to Quantum Spin Liquid Ground States in Molybdate Pyrochlores
• Collective excitation of electric dipole on molecular dimer in organic dimer-Mott insulator
• Heat transport study of the spin liquid candidate 1T-TaS2
• Local magnetism and spin correlations in the geometrically frustrated cluster magnet LiZn${}_2$Mo${}_3$O${}_8$
• Tuning the $S=1/2$ square-lattice antiferromagnet Sr${}_2$Cu(Te${}_{1-x}$W${}_x$)O${}_6$ from Néel order to quantum disorder to columnar order
• Randomness-induced quantum spin liquid behavior in the $s=\frac{1}{2}$ random $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice
• Dynamics and Transport in Random Antiferromagnetic Spin Chains
• Randomness-induced quantum spin liquid behavior in the s=1/2 random J1-J2 Heisenberg antiferromagnet on the honeycomb lattice
• Randomness-induced quantum spin liquid behavior in the $s=$1/2 bond-random Heisenberg antiferromagnet on the pyrochlore lattice
• The Valence Bond Glass phase
• Randomness induced spin-liquid-like phase in the spin-$1/2$ $J_1-J_2$ triangular Heisenberg model
• Microscopic phase separation in triangular-lattice quantum spin magnet kappa-(BEDT-TTF)2Cu2(CN)3 probed by muon spin relaxation
• Valence-Bond-Glass State with Singlet Gap in the Spin-1/2 Square-Lattice Random $J_1$-$J_2$ Heisenberg Antiferromagnet Sr${}_2$CuTe${}_{1-x}$W${}_x$O${}_6$
• Instabilities of Spin-Liquid States in a Quantum Kagome Antiferromagnet
• $\mu$SR Insight into the Impurity Problem in Quantum Kagome Antiferromagnets
• A new high pressure form of Ba3NiSb2O9
• First-principles study of hydrogen-bonded molecular conductor $\kappa$-H${}_3$(Cat-EDT-TTF/ST)${}_2$
• Fragmented Electronic Spins with Quantum Fluctuations in Organic Mott Insulators near Quantum Spin Liquid

Cited by in corpus (39)

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• Dimer Crystallization Induced by Elemental Substitution in the Honeycomb Lattice of Ru1-xOsxCl3
• Non-magnetic ion site disorder effects on the quantum magnetism of a spin-1/2 equilateral triangular lattice antiferromagnet
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• The Future of the Correlated Electron Problem
• Scaling and data collapse of two-dimensional random singlet state in magnetic field
• Local spin dynamics in geometrically frustrated Mo pyrochlore antiferromagnet Lu${}_2$Mo${}_2$O${}_{5-y}$N${}_2$
• Is Herbertsmithite far from an ideal antiferromagnet? Ab-initio answer including in-plane Dzyaloshinskii-Moriya interactions and coupling with extra-plane impurities
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• Gapless behavior in a two-leg spin ladder with bond randomness
• Magnetic interactions of 4$f$ electrons in the topological insulator chalcogenide Bi${}_2$Se${}_3$
• Witnessing Disorder in Quantum Magnets
• Local probe investigation of the spin dynamics in the kagome and inter-layers of orthorhombic barlowite Cu${}_4$(OD)${}_6$FBr: ${}^{79}$Br and ${}^{63}$Cu NQR study
• Entanglement-based tensor-network strong-disorder renormalization group