Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session W50: Correlated Chains and 1D Models |
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Sponsoring Units: DCMP Chair: Daniel Agterberg, University of Wisconsin - Milwaukee Room: Mile High Ballroom 1C |
Friday, March 6, 2020 8:00AM - 8:12AM |
W50.00001: Spin chains with long range RKKY interaction Luhang Yang, Adrian Feiguin Spin-chains are not well ordered antiferromagnets: their correlations decay algebraically and they do not develop true long-range order. Higher dimensional magnets may develop long-range order and, in such a case, the excitations are gapless magnons with well-defined Goldstone modes. To reconcile these two pictures we interpret magnons as bound states of spinons. The introduction of antiferromagnetic long-range RKKY interactions effectively increases the dimensionality of the chains and allow them to develop long range AFM order without violating Mermin-Wagner’s theorem. We study the transition from gapless disordered to gapless ordered phases through the spin dynamical structure factor with the DMRG method. We identify signatures of bound states leaking out from the spinon continuum and the formation of coherent Goldstone modes. We also consider the effects of easy-axis anisotropy and we compare to predictions from spin-wave theory. |
Friday, March 6, 2020 8:12AM - 8:24AM |
W50.00002: Dynamics of a tunable spin chain with three-body interactions Khagendra Adhikari, Kevin Stuart David Beach We formulate a projective Monte Carlo scheme for a spin-half chain with tunable 3-body interactions that encompass the Fredkin model and its t-deformed extension. Dynamical correlation functions are measured directly in various regions of the phase diagram. We report a high-quality numerical estimate of the large dynamical exponent at the Fredkin point. |
Friday, March 6, 2020 8:24AM - 8:36AM |
W50.00003: Universality and Quantum Criticality in Quasiperiodic Spin Chains Utkarsh Agrawal, Romain Vasseur, Sarang Gopalakrishnan Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems as well as disordered ones. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization group transformation. These discrete sequences are therefore fixed points of a functional renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition. |
Friday, March 6, 2020 8:36AM - 8:48AM |
W50.00004: Universal Spin Dynamics in Infinite-Temperature One-Dimensional Quantum Magnets Maxime Dupont, Joel Moore We address the nature of spin dynamics in various integrable and non-integrable, isotropic and anisotropic quantum spin-S chains, beyond the paradigmatic S=1/2 Heisenberg model. In particular, we investigate the algebraic long-time decay ~ t-1/z of the spin-spin correlation function at infinite temperature, using state-of-the-art simulations based on tensor network methods. We identify three universal regimes for the spin transport, independent of the exact microscopic model: (i) superdiffusive with z=3/2, as in the Kardar-Parisi-Zhang universality class, when the model is integrable with extra symmetries such as spin isotropy that drive the Drude weight to zero, (ii) ballistic with z=1 when the model is integrable with a finite Drude weight, and (iii) diffusive with z=2 with easy-axis anisotropy or without integrability, at variance with previous observations. |
Friday, March 6, 2020 8:48AM - 9:00AM |
W50.00005: Excitations of critical quantum spin chains from non-equilibrium classical dynamics Stéphane Vinet, Gabriel Longpré, William Witczak-Krempa We study critical quantum spin chains with spin 1/2 that are dual to the non-equilibrium dynamics of a classical spin chain coupled to a bath. One example is the Kawasaki dynamics of an Ising chain. We give the exact groundstates, and single magnon excitations. Solutions for the two-magnon spectra are derived via the Bethe Ansatz. We discuss the corresponding dynamical critical exponents, which suggest that these chains host multiple dynamics at low energy. We also discuss a generalization to higher dimensions. |
Friday, March 6, 2020 9:00AM - 9:12AM |
W50.00006: Critical quantum spin chains from non-equilibrium classical dynamics: level statistics and entanglement entropy Gabriel Longpré, Stéphane Vinet, William Witczak-Krempa A critical quantum spin 1/2 chain dual to the non-equilibrium Kawasaki dynamics of an Ising chain coupled to a bath is presented. Its level spacing distributions are analysed in the context of random matrix theory. The implications on the integrability of the system are discussed. Scaling of the entanglement entropy of exact states is studied against the eigenstate thermalization hypothesis. |
Friday, March 6, 2020 9:12AM - 9:24AM |
W50.00007: 1D spin chain with topologically constrained dynamics Zhehao Dai, Adam Nahum We discuss a new type of quantum critical point in 1+1D realizing topologically constrained dynamics different from blastic or diffusive transport. We discuss the scaling structure and intuitive understandings of the operator contents. |
Friday, March 6, 2020 9:24AM - 9:36AM |
W50.00008: Dynamical properties of a driven dissipative dimerized S = 1/2 chain Bruce Normand, Mohsen Yarmohammadi, Constantin Meyer, Benedikt Fauseweh, Goetz S Uhrig We consider the dynamical properties of a gapped quantum spin system coupled to the electric field of a laser, which drives the resonant excitation of specific phonon modes that modulate the magnetic interactions. We deduce the quantum master equations governing the time-evolution of both the lattice and spin sectors, by developing a Lindblad formalism with bath operators providing an explicit description of their respective phonon-mediated damping terms. We investigate the non-equilibrium steady states (NESS) of the spin system established by a continuous driving, delineating parameter regimes in driving frequency, damping, and spin-phonon coupling for the establishment of non-trivial properties. We characterize these NESS by their frequency and wave-vector content, explore the timescales for transient and relaxation behavior, and discuss the critical role of the type of bath adopted. Our study lays a foundation for the quantitative modelling of experiments currently being designed to control coherent many-body spin states in quantum magnetic materials. |
Friday, March 6, 2020 9:36AM - 9:48AM |
W50.00009: Generalization of the Haldane conjecture to SU(n) chains Kyle Wamer, Miklós Lajkó, Frederic Mila, Ian Affleck Recently, SU(3) chains in the symmetric and self-conjugate representations have been studied using field theory techniques. For certain representations, namely rank-p symmetric ones with p not a multiple of 3, it was argued that the the ground state exhibits gapless excitations. For the remaining representations considered, a finite energy gap exists above the ground state. In this paper, we extend these results to SU(n) chains in the symmetric representation. For a rank-p symmetric representation with n and p coprime, we predict gapless excitations above the ground state. If p is a multiple of n, we predict a unique ground state with a finite energy gap. Finally, if p and n have a greatest common divisor 1<q<n, we predict a ground state degeneracy of n/q, with a finite energy gap. To arrive at these results, we derive a non-Lorentz invariant flag manifold sigma model description of the SU(n) chains, and use the renormalization group to show that Lorentz invariance is restored at low energies. We then make use of recently developed anomaly matching conditions for these Lorentz-invariant models. We also review the Lieb-Shultz-Mattis-Affleck theorem, and extend it to SU(n) models with longer range interactions. |
Friday, March 6, 2020 9:48AM - 10:00AM |
W50.00010: Constructing Low-Energy Effective Models for the Hydrogen Chain using sb-DMRG Randy Sawaya, Steven Robert White Sliced-basis DMRG(sb-DMRG) is used to simulate a chain of hydrogen atoms which is then transformed to an effective low-energy model. The downfolding procedure involves a change of basis from the real-space grid of the hydrogen chain to a set of atom-centered Wannier functions. Instead of conventional Wannier functions constructed from mean-field bands, we construct them directly from the exact DMRG one particle density matrix. We consider two versions of this. In the first, we use only the ground state to construct the density matrix. This more conventional approach produces a model which poorly reproduces spin and charge gaps. We obtain much better models using Wannier functions constructed from an average density matrix over a small set of low lying DMRG eigenstates. |
Friday, March 6, 2020 10:00AM - 10:12AM |
W50.00011: Fractons from confinement in one dimension Shriya Pai, Michael Pretko Recent work has shown that two seemingly different physical mechanisms, namely fracton behavior and confinement, can give rise to non-ergodicity in one-dimensional quantum many-body systems. We demonstrate an intrinsic link between these two mechanisms by studying the dynamics of 1d confining theories, such as lattice gauge theories. We show that, within certain parameter regimes, these models exhibit effective fracton dynamics, characterized by immobility of stable single-particle excitations and free motion of dipolar bound states. By perturbatively integrating out the linearly confining field, we obtain an effective fracton Hamiltonian for the confined charges which exhibits conservation of dipole moment. We discuss an intuitive understanding of these results in terms of the motion of the confining strings, leading to potential extensions to higher dimensions. We thereby interpret recent observations of nonthermal eigenstates and glassy dynamics in confining theories in terms of corresponding results in the fracton literature. |
Friday, March 6, 2020 10:12AM - 10:24AM |
W50.00012: Emptiness Formation Probability in 1D Bose Liquids. Hsiu-Chung Yeh, Alex Kamenev We study emptiness formation probability (EFP) in interacting 1D Bose liquids. That is the probability that a snapshot of its ground state reveals exactly zero number of particles within the interval |x| < R. For a weakly interacting liquid there is parametrically wide regime 1/n < R < ξ (here n is the average density and ξ is the healing length), where EFP exhibits a non-trivial crossover from the Poisson to the Gaussian behavior. We employ the instanton technique [A. Abanov, 2004] to study quantitative details of these regime and compare it with previously reported limited cases. |
Friday, March 6, 2020 10:24AM - 10:36AM |
W50.00013: One-dimensional repulsive Hubbard model with mass imbalance Yuchi He, David Pekker, Roger Mong We investigate the phase diagram of the one-dimensional repulsive Hubbard model with mass imbalance away from half-filling. Using DMRG we show that this model has a triplet paired phase at generic fillings, consistent with previous theoretical analyses. |
Friday, March 6, 2020 10:36AM - 10:48AM |
W50.00014: Dielectric breakdown of strongly correlated insulators in one dimension: Universal formula from non-Hermitian sine-Gordon theory Kazuaki Takasan, Masaya Nakagawa, Norio Kawakami Application of sufficiently strong electric fields to insulators induces finite currents and then the insulators become metallic. This phenomenon is called dielectric breakdown. In this talk, we present our recent study about the dielectric breakdown of generic strongly correlated insulators in one dimension [1]. Combining bosonization techniques with a theory of quantum tunneling, we develop an effective field-theoretical description of dielectric breakdown with a non-Hermitian sine-Gordon theory. Then, we derive an analytic formula of the threshold field which is a many-body generalization of the Landau-Zener formula. Importantly, we point out that the threshold field contains a previously overlooked factor originating from charges of elementary excitations, which should be significant when a system has fractionalized excitations. We apply our results to integrable lattice models and confirm that our formula is valid in a broad range including the weak coupling regime, indicating its wide and potential applicability. Our results unveil universal aspects in nonlinear and nonequilibrium transport phenomena for various strongly correlated insulators. |
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W50.00015: Deconfined quantum criticality in a spin chain with long-range interactions Sibin Yang, Dao-Xin Yao, Anders W Sandvik We study a 1D spin-1/2 model with long-range power-law decaying unfrustrated (bipartite) Heisenberg exchange interactions Jr ∝ r-α (for odd distances r) and a competing multi-spin interaction Q favoring a dimerized (valence-bond solid, VBS) ground state. Employing quantum Monte Carlo techniques and Lanczos exact diagonalization, we analyze order parameters and excited-state level crossings to characterize quantum phase transitions between the different ground states hosted by the model in the (α, Q) plane. For 1 < α < 1.3, we find a direct continuous quantum phase transition between a long-range ordered antiferromagnetic state and a VBS state, providing an analogy to the two-dimensional deconfined quantum-critical point. Unlike previous 1D analogies of deconfined quantum criticality, where the two ordered phases both have fractional excitations, in our model the excitations fractionalize at the critical point, changing from anomalous, sublinealy dispersing spin waves in the antiferromagnetic phase to deconfined spinons in the VBS phase. We extract critical exponents and also use order-parameter histograms to study possible emergent symmetries. |
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