Symmetry-breaking topological insulators in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>Bose-Hubbard model

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

doi:10.1103/physrevb.99.045139

Cited by 59 publications

(61 citation statements)

References 111 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the last section we know that in this limit the Zak phase of quasiparticle excitations is directly related to the many-body Zak phase of the groundstate. Here we study dimerized Mott insulators (MIs) which are generic examples for states with non-trivial manybody Zak phases [53,71].…”

Section: Dimerized Mott Insulatorsmentioning

confidence: 99%

Topological polarons, quasiparticle invariants, and their detection in one-dimensional symmetry-protected phases

2019

View full text Add to dashboard Cite

In the presence of symmetries, one-dimensional quantum systems can exhibit topological order, which in many cases can be characterized by a quantized value of the many-body geometric Zak or Berry phase. We establish that this topological Zak phase is directly related to the Zak phase of an elementary quasiparticle excitation in the system. By considering various systems, we establish this connection for a number of different interacting phases including: the Su-Schrieffer-Heeger model, p-wave topological superconductors, and the Haldane chain. Crucially, in contrast to the bulk many-body Zak phase associated with the ground state of such systems, the topological invariant associated with quasiparticle excitations (above this ground-state) exhibit a more natural route for direct experimental detection. To this end, we build upon recent work [Nature Communications 7, 11994 (2016)] and demonstrate that mobile quantum impurities can be used, in combination with Ramsey interferometry and Bloch oscillations, to directly measure these quasiparticle topological invariants. Finally, a concrete experimental realization of our protocol for dimerized Mott insulators in ultracold atomic systems is discussed and analyzed.

show abstract

Section: Dimerized Mott Insulatorsmentioning

confidence: 99%

Topological polarons, quasiparticle invariants, and their detection in one-dimensional symmetry-protected phases

2019

View full text Add to dashboard Cite

show abstract

“…An alternative technique was recently proposed for digital quantum simulation [34]. Z 2 LGTs are of high interest in condensed matter physics [13,[35][36][37] and topological quantum computation [38]. Our scheme is based on densitydependent laser-assisted tunneling techniques [39][40][41][42].…”

mentioning

confidence: 99%

Floquet approach to ℤ2 lattice gauge theories with ultracold atoms in optical lattices

et al. 2019

View full text Add to dashboard Cite

Quantum simulation has the potential to investigate gauge theories in strongly-interacting regimes, which are up to now inaccessible through conventional numerical techniques. Here, we take a first step in this direction by implementing a Floquet-based method for studying Z 2 lattice gauge theories using two-component ultracold atoms in a double-well potential. For resonant periodic driving at the on-site interaction strength and an appropriate choice of the modulation parameters, the effective Floquet Hamiltonian exhibits Z 2 symmetry. We study the dynamics of the system for different initial states and critically contrast the observed evolution with a theoretical analysis of the full time-dependent Hamiltonian of the periodically-driven lattice model. We reveal challenges that arise due to symmetrybreaking terms and outline potential pathways to overcome these limitations. Our results provide important insights for future studies of lattice gauge theories based on Floquet techniques.Lattice gauge theories (LGTs) [1,2] are fundamental for our understanding of quantum many-body physics across different disciplines ranging from condensed matter [3-6] to high-energy physics [7]. However, theoretical studies of LGTs can be extremely challenging in particular in strongly-interacting regimes, where conventional computational methods are limited [8,9]. To overcome these limitations alternative numerical tools are currently developed, which enable out-of-equilibrium and finite density computations [10][11][12][13]. In parallel, the rapid progress in the field of quantum simulation [14][15][16][17] has sparked a growing interest in designing experimental platforms to explore the rich physics of LGTs [18][19][20][21][22][23][24][25]. State-of-the-art experiments are now able to explore the physics of static [26] as well as density-dependent gauge fields [27] and have engineered controlled few-body interactions [28][29][30], which are the basis for many proposed schemes to realize LGTs. First studies of the Schwinger model have been performed with quantum-classical algorithms [31] and a digital quantum computer composed of four trapped ions [32]. The challenge for analog quantum simulators mainly lies in the complexity to engineer gauge-invariant interactions between matter and gauge fields.Here, we explore the dynamics of a minimal model for Z 2 LGTs coupled to matter with ultracold atoms in periodically-driven double-well potentials [33]. An alternative technique was recently proposed for digital quantum simulation [34]. Z 2 LGTs are of high interest in condensed matter physics [13,[35][36][37] and topological quantum computation [38]. Our scheme is based on densitydependent laser-assisted tunneling techniques [39][40][41][42]. We use a mixture of bosonic atoms in two different internal states to encode the matter and gauge field degrees of freedom. The interaction between these states is engineered via resonant periodic modulation [43][44][45][46] of the on-site potential at the inter-species Hubbard interaction [47][48...

show abstract

“…screened Coulomb interactions, or truncated versions thereof, such as Hubbardtype couplings). More recently, some studies [12][13][14][15] have started to explore strongly-correlated SPT phases with interparticle interactions that are carried by auxiliary fields locally coupled to the matter sector, avoiding in this way the action at a distance of effective models with instantaneous interactions. This leads to interesting scenarios with intertwined topological phases that simultaneously display symmetry breaking, as characterised by a local order parameter, and topological symmetry protection, as described by a non-zero topological invariant [14,15].…”

mentioning

confidence: 99%

“…More recently, some studies [12][13][14][15] have started to explore strongly-correlated SPT phases with interparticle interactions that are carried by auxiliary fields locally coupled to the matter sector, avoiding in this way the action at a distance of effective models with instantaneous interactions. This leads to interesting scenarios with intertwined topological phases that simultaneously display symmetry breaking, as characterised by a local order parameter, and topological symmetry protection, as described by a non-zero topological invariant [14,15]. This more general framework of interacting SPT phases also allows one to explore models where interparticle interactions are carried by gauge bosons, and constrained by imposing invariance under local gauge symmetries [12,13].…”

mentioning

confidence: 99%

ZN gauge theories coupled to topological fermions: QED2 with a quantum mechanical θ angle

et al. 2019

View full text Add to dashboard Cite

We present a detailed study of the topological Schwinger model [Phys. Rev. D 99, 014503 (2019)], which describes (1+1) quantum electrodynamics of an Abelian U(1) gauge field coupled to a symmetry-protected topological matter sector, by means of a class of Z N lattice gauge theories. Employing density-matrix renormalization group techniques that exactly implement Gauss' law, we show that these models host a correlated topological phase for different values of N, where fermion correlations arise through inter-particle interactions mediated by the gauge field. Moreover, by a careful finite-size scaling, we show that this phase is stable in the large-N limit, and that the phase boundaries are in accordance to bosonization predictions of the U(1) topological Schwinger model. Our results demonstrate that Z N finite-dimensional gauge groups offer a practical route for an efficient classical simulation of equilibrium properties of electromagnetism with topological fermions. Additionally, we describe a scheme for the quantum simulation of a topological Schwinger model exploiting spin-changing collisions in boson-fermion mixtures of ultra-cold atoms in optical lattices. Although technically challenging, this quantum simulation would provide an alternative to classical density-matrix renormalization group techniques, providing also an efficient route to explore real-time non-equilibrium phenomena. :1906.07005v1 [cond-mat.quant-gas] CONTENTS arXiv

show abstract

Symmetry-breaking topological insulators in theZ2Bose-Hubbard model

Cited by 59 publications

References 111 publications

Topological polarons, quasiparticle invariants, and their detection in one-dimensional symmetry-protected phases

Topological polarons, quasiparticle invariants, and their detection in one-dimensional symmetry-protected phases

Floquet approach to ℤ2 lattice gauge theories with ultracold atoms in optical lattices

ZN gauge theories coupled to topological fermions: QED2 with a quantum mechanical θ angle

Contact Info

Product

Resources

About