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arXiv:1811.08392 · Physical review. B./Physical review. B

Symmetry-breaking topological insulators in the Z2 Bose-Hubbard model

Daniel González-Cuadra, Alexandre Dauphin, Przemysław R. Grzybowski, Paweł Wójcik, Maciej Lewenstein, A. Bermúdez

Published Jan 24, 2019• 61 citations
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Abstract

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 topological phase of noninteracting bosons, and thus constitutes an instance of an interaction-induced symmetry-breaking topological insulator.

DOI
10.1103/physrevb.99.045139

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We study a one-dimensional model of interacting bosons coupled to a dynamical Z2{\mathbb{Z}}_{2}Z2​ field, the Z2{\mathbb{Z}}_{2}Z2​ 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 topological phase of noninteracting bosons, and thus constitutes an instance of an interaction-induced symmetry-breaking topological insulator.
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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 from a set of configurations enforced by another broken symmetry. This 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.
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We study the Z_{2} Bose-Hubbard model, a chain of interacting bosons the tunneling of which is dressed by a dynamical Z_{2} field. The interplay between spontaneous symmetry breaking (SSB) and topological symmetry protection gives rise to interesting fractional topological phenomena when the system is doped to certain incommensurate fillings. In particular, we hereby show how topological defects in the Z_{2} field can appear in the ground state, connecting different SSB sectors. These defects are dynamical and can travel through the lattice carrying both a topological charge and a fractional particle number. In the hardcore limit, this phenomenon can be understood through a bulk-defect correspondence. Using a pumping argument, we show that it survives also for finite interactions, demonstrating how boson fractionalization induced by topological defects can occur in strongly correlated bosonic systems. Our results indicate the possibility of observing this phenomenon, which appears for fermionic matter in solid-state and high-energy physics, using ultracold atomic systems.
We propose an SSH-BCS-Hubbard chain model and theoretically study the interplay of topology and interaction therein. We obtain the exact solution of the model at the symmetric point. The exact solution reveals that the Hubbard interaction induces Z2{Z}_{2}Z2​ symmetry breaking, which leads to the coexistence and competition of antiferromagnetic order and $\ensuremath{\eta}$-pairing order. The interaction splits the zero-energy states into in-gap states and destroys the symmetry-protected topological state of the SSH-BCS chain. However, the symmetry analysis reveals that the interacting topological state can exist for small Hubbard interaction and dimerization. The topological phase transition of the perturbed SSH-BCS-Hubbard is studied via the spectral Z2{Z}_{2}Z2​ topological invariant. Our study uncovers a stable interacting topological state coexisting with symmetry-breaking induced intertwined orders.