Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session S28: Focus Session: Kagome Antiferromagnets I |
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Sponsoring Units: GMAG DMP Chair: Steven White, University of California, Irvine Room: 205 |
Thursday, March 5, 2015 8:00AM - 8:12AM |
S28.00001: Exotic behavior of the magnetization process of the S=1/2 kagome-lattice antiferromagnet at one-third hight of the saturation Toru Sakai, Hiroki Nakano The magnetization process of the S=1/2 Heisenberg antiferromagnet on the kagome lattice is studied by the exact numerical diagonalization [1]. We successfully obtain a new result of the magnetization process of a 42-site cluster in the entire range. Our analysis clarifies that the critical behavior around one-third of the height of the saturation is different from the typical behavior of the well-known magnetization plateau in two-dimensional systems. We also examine the effect of the $\sqrt{3}\times \sqrt{3}$-type distortion added to the kagome lattice. We find at one-third of the height of the saturation in the magnetization process that the undistorted kagome point is just the boundary between two phases that show their own properties that are different from each other. Our results suggest a relationship between the anomalous critical behavior at the undistorted point and the fact that the undistorted point is the boundary. A similar critical behavior of the magnetization process was also predicted in some other frustrated systems [2,3].\\[4pt] [1] H. Nakano and T. Sakai: J. Phys. Soc. Jpn. 83 (2014) 104710.\\[0pt] [2] H. Nakano, M. Isoda and T. Sakai: J. Phys. Soc. Jpn. 83 (2014) 053702.\\[0pt] [3] M. Isoda, H. Nakano and T. Sakai: J. Phys. Soc. Jpn. 83 (2014) 084710. [Preview Abstract] |
Thursday, March 5, 2015 8:12AM - 8:24AM |
S28.00002: Measuring symmetry fractionalization in topological orders: application to Z2 spin liquids on kagome lattice Yuan-Ming Lu, Michael Zaletel, Ashvin Vishwanath Mounting numerical evidence for a gapped $Z_2$ spin liquid in the kagome Heisenberg model urges us to develop methods to measure the global and space group symmetry properties of fractional excitations. We show that the universal symmetry characterization of fractional quasiparticles, the projective symmetry group (PSG), can be measured by a dimensional reduction scheme, which relates two-dimensional (2d) symmetric topological orders to 1d symmetry protected topological phases. This general framework allows us to unify $Z_2$ spin liquids in different slave-particle (parton) constructions on the kagome lattice. It is also directly applicable to numeric results obtained in 2d DMRG studies. [Preview Abstract] |
Thursday, March 5, 2015 8:24AM - 8:36AM |
S28.00003: Chiral and Critical Spin Liquids in Spin-1/2 Kagome Antiferromagnet DongNing Sheng, Wei Zhu, ShouShu Gong The spin liquids (SL) and their phase transitions have attracted much attentions. The extended kagome antiferromagnet emerges as the primary candidate for hosting both time reversal symmetry (TRS) preserving and TRS breaking SLs based on DMRG simulations. To uncover the nature of the novel transition between them, we study a minimum XY model with the nearest-neighbor (NN) ($J_{xy}$), the second and third neighbor couplings ($J_{2xy}=J_{3xy}=J'_{xy}$). We identify the chiral SL (CSL) with the turn on of a small perturbation $J'_{xy}\sim 0.06 J_{xy}$, which is characterized by topological Chern number and conformal edge spectrum as the $\nu=1/2$ fractional quantum Hall state. On the other hand, the NN XY model ($J'_{xy}=0$) is shown to be a critical SL, characterized by the gapless spin singlet and vanishing small spin triplet excitations. The phase transition from the CSL to the critical SL is driven by the collapsing of singlet gap. By following the evolution of entanglement spectrum, we find the transition takes place through the coupling of the edge states with opposite chiralities, which merge into the bulk and become gapless neutral excitations. The effect of the NN spin-$z$ coupling is also studied, which leads to a phase diagram with an extended regime for the gapless SL. [Preview Abstract] |
Thursday, March 5, 2015 8:36AM - 8:48AM |
S28.00004: Chiral spin liquid in the extended Heisenberg model on the Kagome lattice Wenjun Hu, Wei Zhu, Yi Zhang, Shoushu Gong, Federico Becca, Dongning Sheng We investigate the extended Heisenberg model on the Kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor super-exchanges are considered, we find that a gapped spin liquid described by non-trivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, lead us to identify this flux state as the chiral spin liquid with $C=1/2$ fractionalized Chern number. [Preview Abstract] |
Thursday, March 5, 2015 8:48AM - 9:00AM |
S28.00005: Chiral spin liquid emerging between competing magnetic order states in the spin-1/2 J1-J2-J3 kagome Heisenberg model Shoushu Gong, Wei Zhu, Leon Balents, Dongning Sheng We studied the extended spin-$1/2$ kagome model with the first neighbor ($J_1$), the second ($J_2$) and third neighbor ($J_3$) couplings using density matrix renormalization group. We established a quantum phase diagram for $0\leq J2\leq 0.25J_1$ and $0\leq J_3\leq J_1$, where we find a $q=(0,0)$ Neel phase, a chiral spin liquid (CSL), a cuboc1 phase that breaks both time-reversal and spin rotational symmetries, and a valence-bond solid at the neighbor of the Heisenberg model, where a possible $Z_2$ spin liquid has been previously identified. Interestingly, the classical cuboc1 phase could survive in the spin-$1/2$ system with strong quantum fluctuations, and the CSL emerges between the $q=(0,0)$ and the cuboc1 phases. We discover that the CSL has the short spin correlation pattern consistent with the cuboc1 phase, but the chiral order structure is totally different. The CSL might be understood as a result of the competitions between the $q=(0,0)$ and the cuboc1 phases in the presence of strong quantum fluctuations. We further studied the quantum phase transitions from the CSL to the magnetically ordered phases, and to the possible $Z_2$ spin liquid of the Heisenberg kagome model. Interestingly, the exotic continuous topological phase transition might be realized in the system. [Preview Abstract] |
Thursday, March 5, 2015 9:00AM - 9:12AM |
S28.00006: Quantum dimer model for the spin-1/2 kagome Z2 spin liquid Ioannis Rousochatzakis, Yuan Wan, Oleg Tchernyshyov, Frederic Mila We revisit the description of the low-energy singlet sector of the spin-1/2 Heisenberg antiferromagnet on kagome in terms of an effective quantum dimer model. With the help of exact diagonalizations of appropriate finite-size clusters, we show that the embedding of a given process in its kagome environment leads to dramatic modifications of the amplitudes of the elementary loop processes, an effect not accessible to the standard approach based on the truncation of the Hamiltonian to the nearest-neighbour valence-bond basis. The resulting parameters are consistent with a Z2 spin liquid rather than with a valence-bond crystal, in agreement with the last density matrix renormalization group results. [Preview Abstract] |
Thursday, March 5, 2015 9:12AM - 9:24AM |
S28.00007: Novel magnetic orderings in the kagome Kondo-lattice model Gia-Wei Chern, Kipton Barros, Jorn Venderbos, Cristian Batista We consider the Kondo-lattice model on the kagome lattice and study its weak-coupling instabilities at band filling fractions for which the Fermi surface has singularities. These singularites include Dirac points, quadratic Fermi points in contact with a flat band, and Van Hove saddle points. By combining a controlled analytical approach with large-scale numerical simulations, we demonstrate that the weak-coupling instabilities of the Kondo-lattice model lead to exotic magnetic orderings. In particular, some of these magnetic orderings produce a spontaneous quantum anomalous Hall state. [Preview Abstract] |
Thursday, March 5, 2015 9:24AM - 10:00AM |
S28.00008: Gapless and gapped spin liquids in frustrated spin-1/2 models Invited Speaker: Federico Becca We present our recent numerical calculations on the Heisenberg model on various two-dimensional lattices, showing that gapped and gapless spin liquids may be stabilized in highly-frustrated regimes. The magnetically disordered phases can be described by considering Abrikosov fermions coupled to gauge fields. This approach gives a flexible and transparent representation of a myriad of states, ranging from valence-bond solids to spin liquids with different properties, including chiral order. For the Kagome lattice, we find that a gapless U(1) spin liquid with Dirac cones is competitive with previously proposed gapped spin liquids [1,2] also when small second- ($J_2$) and third-neighbor ($J_3$) antiferromagnetic couplings are considered on top of the nearest-neighbor ($J_1$) super-exchange [3-5]. For the $J_1{-}J_2$ model on finite clusters, a gapped $Z_2$ spin liquid can be stabilized in presence of a finite $J_2$ super-exchange, with a substantial energy gain with respect to the gapless U(1) Dirac spin liquid. However, this energy gain vanishes in the thermodynamic limit [4]. The presence of $J_3$ favors a chiral spin liquid with non-trivial magnetic fluxes and $C=1/2$ fractionalized Chern number [5].\\[4pt] [1] S. Yan, D. Huse, and S. White, Science 332, 1173 (2011).\\[0pt] [2] S. Depenbrock, I.P. McCulloch, and U.Schollwock, Phys. Rev. Lett. 109, 067201 (2012).\\[0pt] [3] Y. Iqbal, D. Poilblanc, and F. Becca, Phys. Rev. B 89, 020407(R) (2014).\\[0pt] [4] Y. Iqbal, D. Poilblanc, and F. Becca, arXiv:1410.7359.\\[0pt] [5] W.-J. Hu, W. Zhu, Y. Zhang, S. Gong, F. Becca, and D.N. Sheng, arXiv:1411.1327. [Preview Abstract] |
Thursday, March 5, 2015 10:00AM - 10:12AM |
S28.00009: Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagom\'{e} Lattice Alexander Chernyshev, Michael Zhitomirsky By advancing the non-linear $1/S$ expansion and the real-space perturbation theory we investigated quantum order-by-disorder selection of the ground state of the nearest-neighbor $XXZ$ antiferromagnet on the kagom\'{e} lattice. The two methods unanimously favor ${\bf q}\!=\!0$ over $\sqrt{3}\times\!\sqrt{3}$ magnetic order in a wide range of the anisotropy parameter $0\leq \Delta\!\alt\!0.72$. We demonstrated that the order selection is generated by topologically non-trivial spin-flip processes, presented a strong evidence of the rare case of quantum and thermal fluctuations favoring different ground states, proposed a tentative $S\!-\!\Delta$ phase diagram of the model, and suggested further studies. [Preview Abstract] |
Thursday, March 5, 2015 10:12AM - 10:24AM |
S28.00010: Detecting crystal symmtry fractionalizations in Z$_2$ spin liquids on kagom\'e lattice -- insights from quantum dimer models Yang Qi, Liang Fu In topological quantum spin liquid states, the crystal symmetry operations often act on fractionalized spinon excitations in a fractionalized way. These features are important for identifying the symmetry enriched topological orders of the spin liquid states. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the symmetry representations of the ground state wave function. We demonstrate our method on different exactly solvable quantum dimer models on the kagom\'e lattice, and show that it can also be applied to generic dimer and spin models. Particularly our method can be used to distinguish several proposed candidates of Z$_2$ spin liquid states on the kagom\'e lattice. [Preview Abstract] |
Thursday, March 5, 2015 10:24AM - 10:36AM |
S28.00011: Chern-Simons theory for Heisenberg spins on the Kagome Lattice Krishna Kumar, Kai Sun, Eduardo Fradkin We study the problem of Heisenberg spins on the frustrated Kagome lattice using a 2D Jordan-Wigner transformation that maps the spins (hard-core bosons) onto a system of (interacting) fermions coupled to a Chern-Simons gauge field. This mapping requires us to define a discretized version of the Chern-Simons term on the lattice. Using a recently developed result on how to define Chern-Simons theories on a class of planar lattices, we can consistently study spin models beyond the mean-field level and include the effects of fluctuations, which are generally strong in frustrated systems. Here, we apply these results to study magnetization plateau type states on the Kagome lattice in the regime of XY anisotropy. We find that the 1/3 and 2/3 magnetization plateaus are chiral spin liquid states equivalent to a primary Laughlin fractional quantum Hall state of bosons with (spin) Hall conductivity $\frac{1}{2} \frac{1}{4\pi}$ and semionic excitations. The $\frac{5}{9}$ plateau is a chiral spin liquid equivalent to the first Jain descendant. We also consider the spin-1/2 Heisenberg model on the Kagome lattice with a chirality-breaking term on the triangular plaquettes. This situation also leads to a primary Laughlin bosonic fractional quantum Hall type state with filling fraction $1/2$. [Preview Abstract] |
Thursday, March 5, 2015 10:36AM - 10:48AM |
S28.00012: A discretized Chern-Simons gauge theory on arbitrary graphs and the hydrodynamic theory of fraction Chern insulators Kai Sun, Krishna Kumar, Eduardo Fradkin In this talk, we study how to discretize the Chern-Simons gauge theory on generic planar lattices/graphs, with or without translational symmetries, embedded on arbitrary 2D closed orientable manifolds. We show that as long as a one-to-one correspondence between vertices and faces can be defined on the graph such that each face is paired up with a neighboring vertex (and vice versa), a discretized Chern-Simons theory can be constructed. We further verify that all the essential properties of the Chern-Simons gauge theory are preserved in the discretized setup. In addition, we find that the existence of such a one-to-one correspondence is not only a sufficient condition for discretizing a Chern-Simons gauge theory, but also a necessary one, if we want the discretized theory to be nonsingular and to preserve some key properties of this topological field theory. A specific example will then be provided, in which we discretize the Chern-Simons gauge theory on a tetrahedron. In addition, as one application of our discoveries, we present a hydrodynamic theory for (discrete) fractional Chern insulators. [Preview Abstract] |
Thursday, March 5, 2015 10:48AM - 11:00AM |
S28.00013: No-go constraints on topological order in symmetric Mott Insulators Michael Zaletel, Ashvin Vishwanath The search for anyonic excitations in Mott insulators (quantum magnets with an odd number of $S=1/2$ spins per unit cell) has an ally in the Hastings-Oshikawa-Lieb-Schultz-Mattis theorem, which guarantees that a symmetric, gapped Mott insulator must be topologically ordered. However, this theorem is silent on which topological orders are permitted. We point out a new class of symmetry induced constraints on the topological order of a Mott insulator. For example, we show that double semion topological order cannot be realized in a symmetric Mott insulator. An application of our result is to the Kagome lattice quantum antiferromagnet where recent numerical calculations of entanglement entropy indicate a ground state compatible with either toric code or double semion topological order. Our result rules out the latter possibility. [Preview Abstract] |
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