Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session M43: Strong Electronic Correlations in Topological Materials IILive
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Sponsoring Units: DCMP Chair: Madhab Neupane, Univ of Central Florida |
Wednesday, March 17, 2021 11:30AM - 11:42AM Live |
M43.00001: Phonon Hall viscosity from spinon interactions Yanting Teng, Yunchao Zhang, Rhine Samajdar, Mathias Scheurer, Subir Sachdev Quantum spin liquids, exotic states of frustrated quantum magnets that are characterized by fractionalized spinon excitations, host a multitude of remarkable phenomena. While there have been many proposals to realize these states in actual materials, spin liquids are not directly sensitive to conventional experimental local probes and their unambiguous experimental observation has remained elusive. Here, we study the coupling of spinon excitations to phonons in a model that captures the magnetic-field-driven transition from the square-lattice Néel state to a state where Néel order coexists with a chiral spin liquid. We show how the broken time-reversal symmetry in the spin degrees of freedom can induce a non-dissipative phonon Hall viscosity. Our results suggest that the Hall viscosity can capture signatures of an underlying spin-liquid phase. As the Hall viscosity leads to a phonon thermal Hall effect, this study also offers some insight into recent experiments detecting anomalous thermal transport in the pseudogap phase of the cuprate superconductors. |
Wednesday, March 17, 2021 11:42AM - 11:54AM Live |
M43.00002: Non-Abelian chiral spin liquid in the frustrated spin-1 quantum antiferromagnet on the square lattice Yixuan Huang, Wei Zhu, Hong-Chen Jiang, Donna Sheng We investigate the ground state properties of the spin-1 antiferromagnetic Heisenberg J1-J2 model supplemented by time-reversal symmetry breaking chiral interaction on the square lattice using density-matrix renormalization group. Based on studies of numerous long cylinders with circumferences of up to 10 lattice spacings, we obtain strong evidence for a novel quantum spin liquid state in the ground state phase diagram. Remarkably, we find that this spin liquid is consistent with the non-Abelian Moore-Read chiral spin liquid, which is evidenced by both entanglement spectra and related flux threading experiments. Our results provide a concrete example of realizing the non-Abelian spin liquid in a general higher spin system, which is beyond previous attempts in spin-1/2 systems. |
Wednesday, March 17, 2021 11:54AM - 12:06PM Live |
M43.00003: Multipole Insulators and Higher-Form symmetries Oleg Dubinkin, Alexander D Rasmussen, Taylor L Hughes We present a suitable refinement of the notion of an insulator by investigating a class of systems that conserve both the total charge and the total dipole moment. In particular, we consider microscopic models for systems that conserve dipole moments exactly and show that one can divide charge insulators into two new classes: (i) a dipole metal, which is a charge-insulating system that supports dipole-moment currents, or (ii) a dipole insulator which is a charge-insulating system that does not allow dipole currents and thus, conserves an overall quadrupole moment. I this work we discuss a more formal description of dipole-conserving systems and show that a conservation of the overall dipole moment can be naturally attributed to a global 1-form electric U(1) symmetry, which is in direct analogy to how the electric charge conservation is guaranteed by the global U(1) phase-rotation symmetry for electrically charged particles. This new approach allows us to construct a topological response action which is especially useful for characterizing Higher-Order Topological phases carrying quantized quadrupole moments. |
Wednesday, March 17, 2021 12:06PM - 12:18PM Live |
M43.00004: Computing the Classification of Fermionic Symmetry-Protected Topological States Yunqing Ouyang, Qing-Rui Wang, Zhengcheng Gu, Yang Qi The bosonic symmetry protected topological (SPT) states are classified by the cohomology groups of the symmetry group. However, for interacting fermionic systems, the classification is much more complicated. It was untill very recent that a breakthrough was maded on the classification and construction of fermionic SPT states based on the concept of equivalence class under finite-depth symmetric fermionic local transformations. However, though layers of data for classification and construction can be obtained theoretically, the formalism based on the bar resolution of symmetry groups (also known as the inhomogeneous cochains) makes it impossible for realistic computation due to high computational costs. To solve these problems, we first design reduced resolutions for general groups by group extension, then we apply the chain maps between the bar resolution and reduced resolution to solve the obstruction function to get the unobstructed layers of data. Meanwhile, to simplify the computation, we apply the technique of spectral sequence. Finally, we give a classification of fermionic SPTs protected by 2D wallpaper-group symmetries. |
Wednesday, March 17, 2021 12:18PM - 12:30PM Live |
M43.00005: Hubbard parent model for Haldane-AKLT S=1 spin chains Goncalo Catarina, Ricardo Ortiz Cano, Joaquín Fernández-Rossier S=1 spin models, such as the Haldane and the AKLT, present topological order with gapped bulk excitations and fractional S=1/2 edge states. Here we address the question of how this class of models, generically described with the bilinear biquadratic (BLBQ) spin Hamiltonian, can be obtained as the strong coupling limit of a Hubbard model at half filling. We propose a lattice built with dimers of uncompensated bipartite blocks, that balance each other to give a compensated lattice. In the strong coupling limit of the Hubbard model, the blocks have S=1 and antiferromagneti coupling. At U=0 the model defines a topological insulator with edge states. Using DMRG calculations we map the evolution of the model as we ramp up U. In the large U limit, the model has the same energy levels and correlation functions that a BLBQ S=1 model, which features fractional edge S=1/2 excitations. The crossover between the U=0 non-interacting topological model and the strong coupling limit occurs without the closing of a gap, which indicates that they are topologically equivalent. Our work shows a way to engineer S=1 spin chains with S=1/2 fermions, that could be implemented with quantum dot arrays, cold atoms and planar aromatic hydrocarbons. |
Wednesday, March 17, 2021 12:30PM - 12:42PM Live |
M43.00006: New perspective on the Laughlin state from classical constrain Trung Ha Quang, Bo Yang We present a new framework of understanding the fractional quantum Hall (FQH) state at filling factor ν = n+1/3 in terms of the quasihole excitation of a different FQH state – the Gaffnian. The subspace of the Gaffnian quasiholes capture the physics at the higher Landau levels significantly better than the Laughlin state. Interestingly, this implies the fractionalisation of the Laughlin quasiholes into e/6 charges. The interactions between these charges are mediated by the Laughlin neutral excitations, which in the lowest Landau level is attractive, similar to the asymptotic freedom of quarks. However, on higher LLs, it is possible to separate these e/6 charges. This separation is linked to the softening of the quadrupole excitation that is believed to be responsible for the nematic FQH phase. The charge-e/6 quasiholes also mediate a phase transition within the same topological phase which has clear experimental signatures. We describes this phase transition in details and propose conditions for the e/6 fractional charge to be observed in experiment. Our analysis presents an application of the recently proposed local exclusion constrain (LEC) formalism, which generalizes the Jack polynomial formalism in classifying different FQH states. |
Wednesday, March 17, 2021 12:42PM - 12:54PM Live |
M43.00007: An exactly solvable model for fractional quantum Hall effect Sreejith Ganesh Jaya, Abhishek Anand, Jainendra Jain We present a model Hamiltonian for spinless electrons in a magnetic field with strong short-range interaction that lends itself to exact solutions for all low-energy states at arbitrary filling factor less than 1/2p. The model produces incompressible states at filling fractions n/(2pn + 1), where n and p are integers - precisely the filling fractions where fractional quantum Hall effect occurs. We present numerical evidence showing that the fractional quantum Hall ground states of this model are adiabatically connected, and thus topologically equivalent to the Coulomb ground states in the lowest Landau level. |
Wednesday, March 17, 2021 12:54PM - 1:06PM Live |
M43.00008: Superconductivity, pseudogap, and phase separation in topological flat bands Johannes Hofmann, Erez Berg, Debanjan Chowdhury Superconductivity (SC) is a macroscopic quantum phenomenon that requires electron pairs to delocalize over large distances. A long-standing question is whether SC can exist even if the electrons' kinetic energy is completely quenched, as is the case in a flat band. This is fundamentally a non-perturbative problem since the interaction energy scale is the only relevant energy scale, and hence it requires going beyond the traditional perturbative BCS theory of SC. We study a 2D model of an isolated narrow band at partial filling with local attractive interactions, using quantum Monte Carlo calculations. We focus on topologically non-trivial flat bands where the single-particle wavefunctions that span these bands cannot be completely spatially localized. Our calculations unambiguously show that the ground state is a superconductor; strikingly, the critical temperature scales nearly linearly with the interaction strength. Above the SC transition temperature, we find a broad pseudogap regime that exhibits strong pairing fluctuations and a tendency towards electronic phase separation. Weak nearest neighbor attraction suppresses SC entirely and drives the system to phase separate. We discuss the possible relevance of SC in this unusual regime to the physics of flat band moire materials. |
Wednesday, March 17, 2021 1:06PM - 1:18PM Live |
M43.00009: Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states Ajit Coimbatore Balram, Maissam Barkeshli, Mark Rudner The fractional quantum Hall (FQH) effect encompasses a wide range of quantum many-body phases which are characterized by exotic topological orders. Among these, the Read-Rezayi (RR) states harbor parafermionic excitations, whose non-Abelian braiding properties could potentially be used to carry out fault-tolerant quantum computation. Recent intriguing numerical results indicate that the 12/5 FQH state realized in GaAs could be described by the particle-hole conjugate of an RR state. However, numerically constructing the RR states for large systems, which is necessary for their characterization and for the demonstration of the exotic properties of their excitations, is computationally prohibitive. In this work, we use the parton framework to construct states that lie in the same phases as the particle-hole conjugates of the RR states. A nice feature of our parton states is that their wave functions can be evaluated for very large system sizes, thus, paving the way for the numerical investigation of parafermions. |
Wednesday, March 17, 2021 1:18PM - 1:30PM Live |
M43.00010: Topological phases induced by interactions and spin-orbit coupling in decorated honeycomb lattices Manuel Fernandez Lopez, Jaime Merino The decorated honeycomb lattice (DHL) is a playground to study non-interacting topological states of matter such as the quantum spin Hall (QSH) insulator due to its peculiar band structure containing flat bands, Dirac and quadratic band touching points. In the search of novel interacting topological states we have analyzed the interplay of spin-orbit coupling (SOC) and on-site Coulomb interaction based on a Kane-Mele-Hubbard model on the DHL. For weak Coulomb repulsion a transition from a QSH insulator to a non-trivial semimetal with a non-quantized spin Hall conductivity occurs as SOC is increased. In the strong interacting limit, SOC induces a transition from a resonance valence bond (RVB) spin liquid state to a magnetic insulator consisting of antiferromagnetically ordered S=3/2 localized moments on the honeycomb lattice. Our results are discussed in the context of organometallic compounds realizing the DHL. |
Wednesday, March 17, 2021 1:30PM - 1:42PM Live |
M43.00011: Chiral hinge modes in a dipole conserving lattice model Julian May-Mann, Taylor L Hughes Recently, a "dipolar Chern Simons" response theory has been proposed to describe the topological responses of higher order topological insulators in 3D. Remarkably, this response theory also captures the essential features of certain classes of fractons. Here, we present a 3D interacting lattice model that realizes the dipolar Chern-Simons response theory, and hosts topologically protected chiral hinge modes. Interestingly, in the self-consistent mean field limit, this model maps onto a known non-interacting higher order topological insulator. We also relate the interacting 3D model to a 2D model with quantized quadrupole moment using dimensional reduction. |
Wednesday, March 17, 2021 1:42PM - 1:54PM Live |
M43.00012: Universal SPT invariants using swap operators Shriya Pai, Michael A Hermele We introduce and describe many-body topological invariants/order parameters for SPT phases that involve acting with symmetry operators and a swap operator. To do so, we use the universal notion of distinguishing between different phases of matter: phases are equivalence classes defined in the thermodynamic limit by (i) adiabatic continuity, and (ii) adding trivial degrees of freedom. In the process, we also formulate gauge-invariant versions of these order parameters. Since our arguments for the universality of such many-body invariants do not depend on the spatial dimension we are working in, this discussion can help serve as a basis for generalizations to higher spatial dimensions. We will also show how to picture the invariant by putting the system on a spacetime manifold and by thinking in terms of TQFT partition functions. |
Wednesday, March 17, 2021 1:54PM - 2:06PM Live |
M43.00013: Unbounded Hydrodynamics in Nodal-Line Semimetals Sang Wook Kim, Geo Jose, Bruno Uchoa The ratio between the shear viscosity and the entropy η/s is considered a universal measure of the strength of interactions in quantum systems. In relativistic systems, this quantity was conjectured to have a universal lower bound (hbar/(4π kB)), which indicates a very strongly correlated quantum fluid. By solving the quantum kinetic theory for a nodal-line semimetal in the hydrodynamic regime, we show that η/s ∝T is unbounded, scaling towards zero with decreasing temperature T in the perturbative limit. We find that the hydrodynamic scattering time between collisions τ ~ hbar/(α2 ν kF), with (ν kF) the energy scale set by the radius of the ring and α the fine structure constant. We suggest that the lower bound criteria should be modified to account for unscreened relativistic systems with a Fermi surface. |
Wednesday, March 17, 2021 2:06PM - 2:18PM Live |
M43.00014: Microscopic theory for the nematic fractional quantum Hall effect Bo Yang We analyse properties of the nematic fractional quantum Hall effect (FQHN) in the thermodynamic limit, and present necessary microscopic conditions for the FQHN to be robust. Analytical expressions of the degenerate ground state manifold and gapless nematic modes are given in compact forms with the input interaction and the ground state structure factors. We relate the long wavelength limit of the neutral excitations (serving as the FQHN ground state from spontaneous symmetry breaking) to the guiding center metric deformation, and show explicitly the family of trial wavefunctions for the nematic modes with spatially varying nematic order. For short range interactions, the dynamics of the FQHN is determined by the long wavelength part of the ground state structure factor, leading to potentially more efficient numerical approaches. The special case of the FQHN at ν = 1/3 is discussed with theoretical insights from the Haffnian parent Hamiltonian, leading to a number of rigorous statements and experimental implications. This allows us to discuss the possibility of the linear Goldstone modes proposed in the effective theory from the microscopic perspective. (PR RESEARCH 2, 033362 (2020)) |
Wednesday, March 17, 2021 2:18PM - 2:30PM Live |
M43.00015: Fractional Quantum Hall Effect from Hilbert Space Algebra and Frustration-free Hamiltonians Ying-Hai Wu, Bo Yang, Zlatko Papic We show that model states of fractional quantum Hall (FQH) fluids for many topological phases can be uniquely determined by the Hilbert space algebra manifested as the classical reduced density matrix constraints, or the local exclusion constraint (LEC). The scheme allows us to identify filling factors, topological shifts and clustering of topological quantum fluids universally without resorting to microscopic Hamiltonians. Elementary excitations of the FQH phases can also be characterised by the LECs. More interestingly, the LEC formalism leads to a new perspective for the FQH model Hamiltonians, which can now be understood as a the von Neumann lattice of local potentials. The reformulation of the FQHE as a frustration free Hamiltonian as a sum of local projections opens up new path for rigorously proving the incompressibility of microscopic Hamiltonians in the thermodynamic limit. It may also potentially lead to new experimental ways of stabilising exotic FQH phases (related papers: Bo Yang, PRL. 125, 176402 (2020), PRB 100, 241302(R) (2019), Bo Yang, Ajit Balram, arXiv:1907.09493, Bo Yang, Ying-Hai Wu, Zlatko Papic, PRB. 100, 245303 (2019)). |
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