arXiv subjects

Alexandre Dauphin

Publications and source records attributed to Alexandre Dauphin.

63 records · Page 4Linked to original sources

arXiv2019

Intertwined Topological Phases induced by Emergent Symmetry Protection

The dual role played by symmetry in many-body physics manifests itself through two fundamental mechanisms: spontaneous symmetry breaking and topological symmetry protection. These two concepts, ubiquitous in both condensed matter and high energy physics, have been applied successfully in the last decades to unravel a plethora of complex phenomena. Their interplay, however, remains largely unexplored. Here we report how, in the presence of strong correlations, symmetry protection emerges dynamically from a set of configurations enforced by another broken symmetry. This novel mechanism spawns different intertwined topological phases, where topological properties coexist with long-range order. Such a singular interplay gives rise to interesting static and dynamical effects, including interaction-induced topological phase transitions constrained by symmetry breaking, as well as a self-adjusted fractional pumping. This work paves the way for further exploration of exotic topological features in strongly-correlated quantum systems.

cond-mat.str-el↗

arXiv2019

Symmetry-Breaking Topological Insulators in the $\mathbb{Z}_2$ Bose-Hubbard Model

In this work, we study a one-dimensional model of interacting bosons coupled to a dynamical $\mathbb{Z}_2$ field, the $\mathbb{Z}_2$ Bose-Hubbard model, and analyze the interplay between spontaneous symmetry breaking and topological symmetry protection. In a previous work, we showed how this model exhibits a spontaneous breaking of the translational symmetry through a bosonic Peierls transition. Here we find how, at half filling, the resulting phase also displays topological features that coexist with the presence of long-range order and yields a topological bond order wave. Using both analytical and numerical methods, we describe the properties of this phase, showing that it cannot be adiabatically connected to a bosonic topological phase with vanishing Hubbard interactions, and thus constitutes an instance of an interaction-induced symmetry-breaking topological insulator.

cond-mat.quant-gas↗

arXiv2019

Strongly Correlated Bosons on a Dynamical Lattice

We study a one-dimensional system of strongly correlated bosons on a dynamical lattice. To this end, we extend the standard Bose-Hubbard Hamiltonian to include extra degrees of freedom on the bonds of the lattice. We show that this minimal model exhibits phenomena reminiscent of fermion-phonon models. In particular, we discover a bosonic analog of the Peierls transition, where the translational symmetry of the underlying lattice is spontaneously broken. This provides a dynamical mechanism to obtain a topological insulator in the presence of interactions, analogous to the Su-Schrieffer-Heeger model for electrons. We characterize the phase diagram numerically, showing different types of bond order waves and topological solitons. Finally, we study the possibility of implementing the model using atomic systems.

cond-mat.quant-gas↗

arXiv2018

Identifying Quantum Phase Transitions with Adversarial Neural Networks

The identification of phases of matter is a challenging task, especially in quantum mechanics, where the complexity of the ground state appears to grow exponentially with the size of the system. We address this problem with state-of-the-art deep learning techniques: adversarial domain adaptation. We derive the phase diagram of the whole parameter space starting from a fixed and known subspace using unsupervised learning. The input data set contains both labeled and unlabeled data instances. The first kind is a system that admits an accurate analytical or numerical solution, and one can recover its phase diagram. The second type is the physical system with an unknown phase diagram. Adversarial domain adaptation uses both types of data to create invariant feature extracting layers in a deep learning architecture. Once these layers are trained, we can attach an unsupervised learner to the network to find phase transitions. We show the success of this technique by applying it on several paradigmatic models: the Ising model with different temperatures, the Bose-Hubbard model, and the SSH model with disorder. The input is the ground state without any manual feature engineering, and the dimension of the parameter space is unrestricted. The method finds unknown transitions successfully and predicts transition points in close agreement with standard methods. This study opens the door to the classification of physical systems where the phases boundaries are complex such as the many-body localization problem or the Bose glass phase.

cond-mat.stat-mech↗

arXiv2018

Observation of the topological Anderson insulator in disordered atomic wires

Topology and disorder have deep connections and a rich combined influence on quantum transport. In order to probe these connections, we synthesized one-dimensional chiral symmetric wires with controllable disorder via spectroscopic Hamiltonian engineering, based on the laser-driven coupling of discrete momentum states of ultracold atoms. We characterize the system's topology through measurement of the mean chiral displacement of the bulk density extracted from quench dynamics. We find evidence for the topological Anderson insulator phase, in which the band structure of an otherwise trivial wire is driven topological by the presence of added disorder. In addition, we observed the robustness of topological wires to weak disorder and measured the transition to a trivial phase in the presence of strong disorder. Atomic interactions in this quantum simulation platform will enable future realizations of strongly interacting topological fluids.

cond-mat.quant-gas↗

arXiv2018

Topological characterization of chiral models through their long time dynamics

We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk observable, the mean chiral displacement. The derivation of this result is done in terms of spectral projectors, allowing for a detailed understanding of the physics. We show that the proposed detection converges rapidly and it can be implemented in a wide class of chiral systems. Furthermore, it can measure arbitrary winding numbers and topological boundaries, it applies to all non-interacting systems, independently of their quantum statistics, and it requires no additional elements, such as external fields, nor filled bands.

cond-mat.other↗

arXiv2017

Measuring Chern numbers in Hofstadter strips

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wavepacket exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.

cond-mat.quant-gas↗

arXiv2015

Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal

We investigate the properties of a two-dimensional quasicrystal in the presence of a uniform magnetic field. In this configuration, the density of states (DOS) displays a Hofstadter butterfly-like structure when it is represented as a function of the magnetic flux per tile. We show that the low-DOS regions of the energy spectrum are associated with chiral edge states, in direct analogy with the Chern insulators realized with periodic lattices. We establish the topological nature of the edge states by computing the topological Chern number associated with the bulk of the quasicrystal. This topological characterization of the non-periodic lattice is achieved through a local (real-space) topological marker. This work opens a route for the exploration of topological insulating materials in a wide range of non-periodic lattice systems, including photonic crystals and cold atoms in optical lattices.

cond-mat.mes-hall↗

arXiv2013

Extracting the Chern number from the dynamics of a Fermi gas: Implementing a quantum Hall bar for cold atoms

We propose a scheme to measure the quantized Hall conductivity of an ultracold Fermi gas initially prepared in a topological (Chern) insulating phase, and driven by a constant force. We show that the time evolution of the center of mass, after releasing the cloud, provides a direct and clear signature of the topologically invariant Chern number. We discuss the validity of this scheme, highlighting the importance of driving the system with a sufficiently strong force to displace the cloud over measurable distances while avoiding band-mixing effects. The unusual shapes of the driven atomic cloud are qualitatively discussed in terms of a semi-classical approach.

cond-mat.quant-gas↗