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arXiv:1908.02186 · Physical review. B./Physical review. B

Zn solitons in intertwined topological phases

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

Published Dec 23, 2020• 15 citations
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Abstract

Topological phases of matter can support fractionalized quasiparticles localized at topological defects. The current understanding of these exotic excitations, based on the celebrated bulk-defect correspondence, typically relies on crude approximations where such defects are replaced by a static classical background coupled to the matter sector. In this work, we explore the strongly correlated nature of symmetry-protected topological defects by focusing on situations where such defects arise spontaneously as dynamical solitons in intertwined topological phases, where symmetry breaking coexists with topological symmetry protection. In particular, we focus on the ${\mathbb{Z}}_{2}$ Bose-Hubbard model, a one-dimensional chain of interacting bosons coupled to ${\mathbb{Z}}_{2}$ fields, and show how solitons with ${\mathbb{Z}}_{n}$ topological charges appear for particle/hole dopings about certain commensurate fillings, extending the results in D. Gonz\'alez-Cuadra et al. [Phys. Rev. Lett. 125, 265301 (2020)] beyond half filling. We show that these defects host fractionalized bosonic quasiparticles, forming bound states that travel through the system unless externally pinned, and repel each other giving rise to a fractional soliton lattice for sufficiently high densities. Moreover, we uncover the topological origin of these fractional bound excitations through a pumping mechanism, where the quantization of the intersoliton transport allows us to establish a generalized bulk-defect correspondence. This in-depth analysis of dynamical topological defects bound to fractionalized quasiparticles, together with the possibility of implementing our model in cold-atomic experiments, paves the way for further exploration of exotic topological phenomena in strongly correlated systems.

DOI
10.1103/physrevb.102.245137

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Topological phases of matter can support fractionalized quasiparticles localized at topological defects. The current understanding of these exotic excitations, based on the celebrated bulk-defect correspondence, typically relies on crude approximations where such defects are replaced by a static classical background coupled to the matter sector. In this work, we explore the strongly correlated nature of symmetry-protected topological defects by focusing on situations where such defects arise spontaneously as dynamical solitons in intertwined topological phases, where symmetry breaking coexists with topological symmetry protection. In particular, we focus on the Z2{\mathbb{Z}}_{2}Z2​ Bose-Hubbard model, a one-dimensional chain of interacting bosons coupled to Z2{\mathbb{Z}}_{2}Z2​ fields, and show how solitons with Zn{\mathbb{Z}}_{n}Zn​ topological charges appear for particle/hole dopings about certain commensurate fillings, extending the results in D. Gonz'alez-Cuadra et al. [Phys. Rev. Lett. 125, 265301 (2020)] beyond half filling. We show that these defects host fractionalized bosonic quasiparticles, forming bound states that travel through the system unless externally pinned, and repel each other giving rise to a fractional soliton lattice for sufficiently high densities. Moreover, we uncover the topological origin of these fractional bound excitations through a pumping mechanism, where the quantization of the intersoliton transport allows us to establish a generalized bulk-defect correspondence. This in-depth analysis of dynamical topological defects bound to fractionalized quasiparticles, together with the possibility of implementing our model in cold-atomic experiments, paves the way for further exploration of exotic topological phenomena in strongly correlated systems.
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.
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.
Symmetry-protected topology and deconfined solitons in a multi-link Z2\mathbb{Z}_2Z2​ gauge theory
With the advent of quantum simulators, exploring exotic collective phenomena in lattice models with local symmetries and unconventional geometries is at reach of near-term experiments. Motivated by recent progress in this direction, we study a Z2\mathbb{Z}_2Z2​ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell hosting the Z2\mathbb{Z}_2Z2​ gauge fields. Elementary Wilson loops along pairs of these bonds allow to identify a dynamical gauge-invariant flux, responsible for Aharonov-Bohm-like interference effects in the tunneling dynamics of charged matter residing on the vertices. Focusing on an odd number of links, we show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability. We find inhomogeneous phases in which an ordered pattern of the gauge fluxes spontaneously breaks translational invariance, and intertwines with a bond order wave for the gauge-invariant kinetic matter operators. Long-range order is shown to coexist with symmetry protected topological order, which survives the quantum fluctuations of the gauge flux induced by an external electric field. Doping the system above half filling leads to the formation of topological soliton/anti-soliton pairs interpolating between different inhomogeneous orderings of the gauge fluxes. By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization. Quasiparticles carrying fractional charge and bound at the soliton centers can be arbitrarily separated without feeling a confining force, in spite of the long-range attractive interactions set by the small electric field on the individual integer charges.
Abstract 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.
Understanding the interplay between symmetries and phases lies at the heart of characterizing states of matter. The conventional Landau's paradigm associates local ordered states with symmetry breaking, but this paradigm fails to include gapped topological phases, which can only be distinguished by the global topological invariant and the present of gapless edge modes at open boundaries. In this thesis, variety of states of matter is enriched from two aspects: a new paradigm of phases that incorporates both symmetry broken phase and topological phase, and exotic topological phases that are realized in different degree of freedoms of the same system. The two aspects are explored by studying corresponding one dimensional fermionic models. Besides gapped phases, exotic quasiparticle interferences of gapless topological systems are also investigated. \n \nThe first chapter serves as a theoretical basis for the next two chapters by giving an introduction to topological phases in one dimension. In particular, a bosonization method is introduced to describe topological degeneracy and edge zero modes, which is favoured by the ability to deal with interactions as well as to uncover the phenomena of spin-charge separation. \n \nIn the second chapter a new paradigm of phases is proposed and investigated that incorporates both symmetry broken phases and symmetry-protected topological phases. Through exact-solvable models bond spin density wave(BSDW) states are proposed as candidates for this new paradigm, which are ZZ2\\ZZ_2ZZ2​ symmetry breaking due to spontaneous dimerization and yet each is topological nontrivial with edge zero modes of fractional fermions. More general lattice models are constructed, and it is shown that BSDW exists in a considerable regime of parameters for a family of lattice models, from both mean-field analysis and bosonization. \n \nIn the third chapter, we give an effective field description for spin-charge separated edge modes consisting of both Majorana modes and fractional fermions, and demonstrate how to harvest both simultaneously in a spinless fermionic ladder with particle-hole symmetry and single-chain fermion parity. Further, the idea of spin-charge separated edge modes is applied to reinterpret the prominent Haldane phase of spin-1 chain in its equivalent spin-frac12\\frac{1}{2}frac12 fermionic model. \n \nIn contrast to the above two theoretically oriented topics that aim to add variety to topological phases, the third topic establishes a bridge between abstract concepts for topological systems to remarkable features that can be detected in experiments. The last chapter reveals how topological charges for topological Fermi points, through exhibiting exotic quasiparticle interference in the presence of impurities, could be visualized in STS measurements. \nThe generalized joint density of states(GJDOS) is applied to address effects from the geometry of band dispersion and topological charges separately. Both analytical results and numerical simulation suggest distinct and robust quasiparticle interference features as indicators for topological charges that can be accessed by FT-STS experiments.
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.