Homogeneous and domain-wall topological Haldane conductors with dressed Rydberg atoms

Arianna Montorsi, Serena Fazzini, and Luca Barbiero

Phys. Rev. A 101, 043618 – Published 24 April 2020

Abstract

The interplay between antiferromagnetic interaction and hole motion is capable of inducing conducting Haldane phases with topological features described by a finite nonlocal string order parameter. Here we show that these states of matter are captured by the one-dimensional $t − J_{z}$ model, which can be experimentally realized with dressed Rydberg atoms trapped onto a one-dimensional optical lattice. In the sector with vanishing total magnetization, exact calculations associated with the bosonization technique allow us to predict that both metallic and superconducting topological Haldane states can be achieved. With the addition of an appropriate magnetic field, the system enters a domain-wall structure with finite total magnetization. In this regime, the conducting Haldane states are confined in domains separated by regions where a fully polarized Luttinger liquid occurs. A procedure to dynamically stabilize such topological phases starting from a confined Ising state is also described.

Received 31 October 2019
Revised 23 March 2020
Accepted 30 March 2020

DOI:https://doi.org/10.1103/PhysRevA.101.043618

Physics Subject Headings (PhySH)

Dipolar gases Topological superconductors

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Arianna Montorsi ¹, Serena Fazzini², and Luca Barbiero ³

¹Institute for Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino I-10129, Italy
²Physics Department and Research Center OPTIMAS, University of Kaiserslautern, D-67663 Kaiserslautern, Germany
³Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium

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Vol. 101, Iss. 4 — April 2020

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Images

Figure 1
Phase diagram of the $t − J_{z}$ model Eq. (1) with $δ = 0$ as a function of the filling $n$ and $J_{z}$ . Here the topological conducting phase ( $J_{z} < 2$ ) is denoted as a Haldane liquid (HL), hosting in particular a Haldane triplet superconducting regime (HTS; see text). The state with $J_{z} > 2$ is characterized by phase separation into an Ising antiferromagnet and empty sites, and is denoted as IPS. The illustrations reproduce a generic state in the HL and IPS phases; the three possible values of $S_{i}^{z}$ , namely $+ 1$ , 0, and $- 1$ are depicted as $↑$ , 0, and $↓$ , respectively. The shorter arrows at the edges emphasize the fractional edge spins, in this case $+ n$ at left and $- n$ at right. All the interaction parameters are in units of the hopping strength $t$ .
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Figure 2
Upper panel: decay of $O_{S}^{s} (r)$ for different $J_{z}$ and $δ = 0$ with $L = 81$ , $N = (L + 1) / 2$ particles and keeping only the central sites of the system. To pin the Ising domain in the right part of the lattice, we also include weak antiparallel magnetic fields at the systems edges. Lower panel: values of the entanglement spectrum for different $J_{z}$ and $δ = 0$ with $L = 81$ and $N = (L + 1) / 2$ particles. All the interaction parameters are in units of the hopping strength $t$ .
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Figure 3
Density distribution for different values of $δ$ at fixed $J_{z} = 1.5$ , $L = 80$ , and $N = L / 2$ . In all cases, a weak positive local magnetic field $μ = 0.01$ is applied in the system center to lift the GS degeneracy. All the interaction parameters are in units of the hopping strength $t$ .
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Figure 4
Decay of $O_{S}^{s} (r)$ , $O_{TS} (r)$ , and $C_{S} (r)$ for $δ = 0.4$ , $L = 80$ , and $N = L / 2$ for two different values of $J_{z}$ . The correlations are evaluated in the central region of the system where $N_{↑} = N_{↓}$ . In both cases, a weak positive local magnetic field $μ = 0.01$ is applied in the system center to lift the GS degeneracy. All the interaction parameters are in units of the hopping strength $t$ .
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Figure 5
Phase diagram of the $t − J_{z}$ model equation (1) as a function of $δ$ and $J_{z}$ with density $n = 0.5$ and $L = 80$ . Here also regions characterized by phase-separated states are reported: the $+$ symbol is used to emphasize this aspect. All the interaction parameters are in units of the hopping strength $t$ .
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Figure 6
Upper panel: Time evolution of $C_{s}$ and $O_{S}^{s}$ in a system with $L = 40$ and $N = L / 2 + 1$ particles and starting with an initial state with fixed $J_{z}$ and a strong harmonic potential to confine the particles in the central part of the system. The evolution is performed by keeping the same value of $J_{z}$ and removing the harmonic potential. Both quantities are evaluated in the central 10 sites of the systems. The numerical simulations are performed by keeping up to 512 DMRG states in the evolution and a time step $δ t = 0.01$ . All the interaction parameters and the time are in units of the hopping strength $t$ .
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