Is the continuum SSH model topological?

• URL: http://arxiv.org/abs/2107.09146v2
• Date: Fri, 7 Oct 2022 14:08:11 GMT
• Title: Is the continuum SSH model topological?
• Authors: Jacob Shapiro, Michael I. Weinstein
• Abstract summary: The discrete Hamiltonian of Su, Schrieffer and Heeger (SSH) is a well-known one-dimensional translation-invariant model in condensed matter physics. The model consists of two atoms per unit cell and describes in-cell and out-of-cell electron-hopping between two sub-lattices.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The discrete Hamiltonian of Su, Schrieffer and Heeger (SSH) is a well-known one-dimensional translation-invariant model in condensed matter physics. The model consists of two atoms per unit cell and describes in-cell and out-of-cell electron-hopping between two sub-lattices. It is among the simplest models exhibiting a non-trivial topological phase; to the SSH Hamiltonian one can associate a winding number, the Zak phase, which depends on the ratio of hopping coefficients and takes on the values $0$ and $1$ labeling the two distinct phases. We display two homotopically equivalent continuum Hamiltonians whose tight binding limits are SSH models with different topological indices. The topological character of the SSH model is therefore an emergent rather than fundamental property, associated with emergent chiral or sublattice symmetry in the tight-binding limit. In order to establish that the tight-binding limit of these continuum Hamiltonians is the SSH model, we extend our recent results on the tight-binding approximation to lattices which depend on the tight-binding asymptotic parameter.

Related papers

• Exceptional Luttinger Liquids from sublattice dependent interaction [0.0]
  Exceptional Points (EPs) naturally occur in the Luttinger Liquid (LL) theory. EPs are non-Hermitian topological properties of the single-particle Green Function (GF)
  arXiv  Detail & Related papers  (2024-08-01T18:00:01Z)
• Wave packet dynamics and long-range tunneling within the SSH model using Rydberg-atom synthetic dimensions [0.0]
  An atom is first excited to a Rydberg state that lies within the lattice then subject to the microwave dressing fields. The measurements show the existence of long-lived symmetry-protected edge states and reveal the existence of direct long-distance tunneling between the edge states.
  arXiv  Detail & Related papers  (2023-11-13T01:25:08Z)
• Latent Su-Schrieffer-Heeger models [0.0]
  Su-Schrieffer-Heeger (SSH) chain is the reference model of a one-dimensional topological insulator. Here, we harness recent graph-theoretical results to construct families of setups whose unit cell features neither of these symmetries. This causes the isospectral reduction -- akin to an effective Hamiltonian -- of the resulting lattice to have the form of an SSH model.
  arXiv  Detail & Related papers  (2023-10-11T16:00:21Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Higher-order topological Peierls insulator in a two-dimensional atom-cavity system [58.720142291102135]
  We show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The pattern opens a non-trivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states. Our work shows how atomic quantum simulators can be harnessed to investigate novel strongly-correlated topological phenomena.
  arXiv  Detail & Related papers  (2023-05-05T10:25:14Z)
• Interactions and Topology in Quantum Matter: Auxiliary Field Approach & Generalized SSH Models [0.0]
  This thesis presents a set of projects which lie at the intersection between strong correlations and topological phases of matter. The first of these projects is a treatment of an infinite dimensional generalization of the SSH model with local Coulomb interactions which is solved exactly using DMFT-NRG. The second set of projects involves the development of methods for formulating non-interacting auxiliary models for strongly correlated systems.
  arXiv  Detail & Related papers  (2022-12-09T18:38:31Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings [0.0]
  In this work, we investigate a special sort of a disorder when inter-cell hopping amplitudes are random. Using a definition for $mathbbZ$-topological invariant $nuin 0; 1$ in terms of a non-Hermitian part of the total Hamiltonian, we calculate $langlenurangle averaged by random realizations.
  arXiv  Detail & Related papers  (2021-11-30T15:35:58Z)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.