Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session X24: Spin Frustrated Systems: Novel TheoriesFocus
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Sponsoring Units: GMAG DMP Chair: Stephen Winter, Goethe University Room: LACC 403A |
Friday, March 9, 2018 8:00AM - 8:12AM |
X24.00001: A general approach to Lieb-Schultz-Mattis type results in quantum spin systems Dominic Else, Ryan Thorngren The Lieb-Schultz-Mattis (LSM) theorem states that a spin system with translation and spin rotation symmetry and half-integer spin per unit cell does not admit a trivial gapped symmetric ground state. That is, the ground state must be gapless, spontaneously break a symmetry, or be a non-trivial spin liquid. Thus, such systems are natural spin-liquid candidates. We have conjectured (and proven in certain cases) a much more general criterion that determines when an LSM-type theorem holds in a spin system. The general statement is intimately connected to recent work on the general classification of symmetry-protected topological (SPT) phases with spatial symmetries. The criterion is applicable to the experimentally relevant cases of systems with strong spin-orbit coupling, or in the presence of magnetic field. |
Friday, March 9, 2018 8:12AM - 8:24AM |
X24.00002: Classification of magnetic frustration from topology Krishanu Roychowdhury, Michael Lawler Studies of frustrated magnets have mostly concentrated on analyzing their response to perturbations leaving open the fundamental question of why they are frustrated. In a recent work we demonstrated that topological mechanics can be used as an efficient tool to answer this question when frustration is encoded in a “rigidity matrix”, a non-Hermitian matrix found in all frustrated magnets whose ground states are determined by Moessner-Chalker-Maxwell counting. Here we classify all topological invariants associated with these rigidity matrices by generalizing methods used in the construction of the 10-fold way from Hermitian to non-Hermitian matrices resulting in a 3-fold way classification for each counting index ν= D - K where D are the number of degrees of freedom and K the number of constraints. We illustrate the classification by demonstrating the existence of a new vortex-like invariant for real rigidity matrices using random matrices and models of kagome Heisenberg antiferromagnets. Surprisingly in the latter we discover topological properties of kagome coplanar states. So by classifiying all rigidity matrices, we answer the question of the origin of frustration in the form of accidental degeneracy in a wide class of frustrated magnets by linking it to topological invariants. |
Friday, March 9, 2018 8:24AM - 8:36AM |
X24.00003: Novel Phases and Chiral Interactions in Spin-1 Magnets Ciarán Hickey Recent theoretical work has uncovered a rich and diverse array of physics in spin-1/2 systems with scalar 3-spin chiral interactions, including non-coplanar magnetic phases and Abelian chiral spin liquids. Spin-1 magnets offer even more exciting possibilities, with the capacity for a more complex order parameter structure and the possibility of realising non-Abelian chiral spin liquids, as predicted by studies of exact parent Hamiltonians. We will discuss the effects of scalar chiral interactions on spin-1 Heisenberg-biquadratic models in two dimensions, elucidating the new phases and exotic physics that emerges. |
Friday, March 9, 2018 8:36AM - 8:48AM |
X24.00004: Topological Phase Transition in a Frustrated Magnet Using a Superconducting Quantum Processor Isil Ozfidan We demonstrate a large-scale quantum simulation of a geometrically frustrated square-octagonal lattice using a programmable quantum processor of up to 1800 superconducting flux qubits. Our experiments provide evidence of a topological Kosterlitz-Thouless phase transition separating a paramagnet from a critical phase. Essential to the Kosterlitz-Thouless critical behaviour, we observe the emergence of a two-component order parameter with a continuous symmetry that originates from the interplay between frustration, thermal effects, and quantum fluctuations. We compare our results with quantum Monte Carlo simulations. These results and techniques may help pave the way towards future large-scale quantum simulations based upon superconducting flux qubits for problems that are impractical to simulate classically. |
Friday, March 9, 2018 8:48AM - 9:00AM |
X24.00005: Antiferromagnetic Magnons from Fractionalized Excitations Rui Wang, Baigeng Wang, Tigran Sedrakyan We develop an approach to describe antiferromagnetic magnons on a bipartite lattice supporting |
Friday, March 9, 2018 9:00AM - 9:12AM |
X24.00006: Universal Magnetic Fragmentation in Frustrated Magnets Alexei Andreanov, Paul McClarty, Michel J Gingras Fragmentation of degrees of freedom appearing in some many-body systems shows rich physics and gives rise to interesting concepts. Magnetic fragmentation has been recently predicted theoretically and observed in experiments in certain frustrated magnets. Theoretically fragmentation requires fine-tuned models in most cases. We demonstrate based on several frustrated models, that fragmentation is much more universal. Monte-Carlo simulations and spin-wave calculations show that once a model featuring a Coulomb phase is perturbed and an ordered phase emerges, one still observes simultaneously the Bragg peaks associated to the ordered phase and the pinch point patterns in the structure factor. |
Friday, March 9, 2018 9:12AM - 9:24AM |
X24.00007: Feedforward Neural Networks for Quantum Frustrated Magnets Dmitrii Kochkov, Bryan Clark Representation of an arbitrary quantum mechanical wave-function requires an exponential amount of memory. A key question in the field, then, is to understand whether there are interesting classes of wave-functions which can be compactly represented. In this talk, we explore this question in the context of feedforward neural networks. We numerically study the expressivity of the feedforward artificial neural networks as variational ansatz for ground states of frustrated magnetic systems, investigating the scaling of the number of variational parameters with the system size as well as the effect of different network architectures. |
Friday, March 9, 2018 9:24AM - 9:36AM |
X24.00008: Representing Gutzwiller-Projected Variational Wavefunctions as Matrix Product States Amir M-Aghaei, Bela Bauer, Kirill Shtengel, Ryan Mishmash Gapless free fermion states are notoriously challenging to represent with tensor network state methods. In a recent breakthrough, Fishman and White [PRB 92, 075132 (2015)] described an algorithm for efficiently representing the ground states of fermionic quadratic Hamiltonians in one spatial dimension as matrix product states (MPSs). We investigate generalizations of this method to construct efficient MPS representations of Gutzwiller-projected model variational wavefunctions for various quantum spin liquid states in 1D and quasi-1D. We benchmark our approach on a single half-filled band of spin-1/2 fermionic spinons---Gutzwiller projection of this state is known to be a quantitatively accurate description of the ground state of the 1D nearest-neighbor Heisenberg antiferromagnet. We then march toward 2D by considering quasi-1D incarnations of U(1) spin liquids on both the triangular and kagome lattices. We will compare the numerical effort of these calculations to that required for traditional variational Monte Carlo techniques, as well as comment on the feasibility of our approach for constructing good initial states for ground-state DMRG simulations of model Hamiltonians. |
Friday, March 9, 2018 9:36AM - 9:48AM |
X24.00009: AKLT-like states on the kagome lattice using tensor-network methods Tzu-Chieh Wei, Ching-Yu Huang, Nicholas Pomata Following our previous work in arχiv:1711-00036 on deformations of the spin-2 AKLT state on the square lattice, we study analogous states on the kagome lattice. In addition to modifying the AKLT construction as before by inserting an on-site deformation that breaks the construction's SU(2) symmetry down to O(2), we alter the "bond states," considering not only the original singlet state but also triplet states oriented parallel or perpendicular to the symmetry axis of the deformation. Although these cases are equivalent when the state is constructed on a bipartite lattice, they are not when, as here, lattice frustration is present. This leaves us with three different phase diagrams, which we obtain using tensor-network methods. The first two appear at first to be completely featureless, and require further study to understand their physics. In the third, we find two different ferromagnetic phases: one polarized along the axis of the deformation, and one polarized along the axis of the bond state. |
Friday, March 9, 2018 9:48AM - 10:00AM |
X24.00010: Interaction Induced Special Temperatures in Magnets and Gases Patrik Henelius, Laura Bovo, Mikael Twengström, Michel J Gingras, Steven Bramwell The magnetic bulk susceptibility can be used to classify magnets as ferromagnets (chi T/C >1) or antiferromagnets (chi T/C <1). In this study we identify a new class of ``inverting'' magnets that exhibit a maximum in chi T/C as a function of temperature. In strong analogy with van der Waals theory of classical gases we identify the peak temperature with a magnetic Joule temperature, where the system is quasi-ideal, dU/dM=0, and the onset of antiferromagnetic correlations. In addition, we find a magnetic Boyle temperature, where chi T/C=1, and the incipient ferromagnet turns to an antiferromagnet at low temperature. We provide a phenomenological model of the susceptibility which reveals the mechanism that induces the special temperatures and elevates the effects of minute frustrated exchange interactions to surprisingly high temperature. By explicitly decomposing the dipolar Hamiltonian we demonstrate that these special temperatures and eventual antiferromagnetic ordering are caused by the quadrupolar corrections to a monopolar (dumbbell) Hamiltonian. Our study establishes chi T/C as a direct measure of interaction parameters which are otherwise difficult to access experimentally, and we find that the spin ice materials Dy/Ho2Ti2O7 and the spinel GeCo2O4 belong to this group. |
Friday, March 9, 2018 10:00AM - 10:12AM |
X24.00011: Building Symmetry Fractionalizations from a Bipartite Lattice Construction Jong Yeon Lee, Ari Turner, Ashvin Vishwanath We introduce a construction of symmetry-enriched topological phases on bipartite lattices in which two Z2 spin liquids (SL) defined on the individual sublattices are combined. We demonstrate for a honeycomb lattice with spin-1/2 per site, where we can approach two different kinds of Z2 SLs by condensing different anyon bound states. The first kind reproduces the known Z2 SLs on the honeycomb lattice and makes explicit the fact that one can obtain a featureless ground state on the honeycomb lattice with spin-1/2 per site. The second kind gives a Z2 SL with spinless excitations, which cannot be readily constructed from parton based approaches. We discuss generalizations to other bipartite lattices including a nonsymmorphic lattice and a lattice with magnetic translation symmetry. |
Friday, March 9, 2018 10:12AM - 10:24AM |
X24.00012: Quantum phases of SU(N) spins on a BCC lattice Nisheeta Desai, Jonathan Demidio, Ribhu Kaul We study the SU(N) generalization of the Heisenberg antiferromagnet on the BCC lattice. Our numerical studies of the model show that magnetic order present for N=2 is destroyed for N>15 and valence bond solid order is observed for N>16. The nature of the phase transition between the two phases is investigated paying attention to the possibility of an intervening U(1) spin liquid phase. |
Friday, March 9, 2018 10:24AM - 10:36AM |
X24.00013: Magnetic excitations in hyperhoneycomb Kitaev system Natalia Perkins, Samuel Ducatman, Ioannis Rousochatzakis We argue that the incommensurate magnetic order experimentally observed |
Friday, March 9, 2018 10:36AM - 10:48AM |
X24.00014: A Simple Anisotropic Three-dimensional Quantum Spin Liquid with Fracton Topological Order Olga Petrova, Nicolas Regnault Fracton phases are one of the latest developments in three-dimensional topological order. Characterized by the presence of immobile pointlike excitations, named fractons, these phases exhibit subextensive topological degeneracy. We present an anisotropic three-dimensional cubic lattice spin model, that exhibits fracton topological order. In addition to the topological degeneracy that is exponential in the system's length, our model displays ground state degeneracy, that can be lifted locally. The latter is exponential in the system's surface area. The fractons can be combined into composite excitations that move either in a straight line along the anisotropic direction, or freely in the plane perpendicular to it. While our model draws inspiration from the toric code, we demonstrate that it cannot be adiabatically connected to a layered toric code construction. Additionally, we investigate the effects of imposing open boundary conditions on our system. |
Friday, March 9, 2018 10:48AM - 11:00AM |
X24.00015: Hexatic and Liquid Antiferromagnets in Two Dimensions Itamar Shamai, Daniel Podolsky We study melting in two-dimensional antiferromagnetic systems. We focus on the case of a six-state clock model on a triangular lattice, as motivated by structural transitions of ions confined in two dimensions. We map this problem to a Coulomb gas and derive renormalization group equations, which we solve to obtain a rich phase diagram. Most interestingly, we find that in the limit of strong magnetic interactions, antiferromagnetic order survives even when the system is in its hexatic and liquid phases. |
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