Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

Petrescu, Alexandru; Piraud, Marie; Roux, Guillaume; McCulloch, Ian P.; Hur, Karyn Le

doi:10.1103/physrevb.96.014524

Cited by 57 publications

(53 citation statements)

References 127 publications

(263 reference statements)

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“…In particular, the proposal that Laughlin-like phases exist in this model as conjectured in Ref. [69][70][71]78] offers exciting further possibilities for studies of this apparently simple yet ultimately very rich two-leg ladder model. line.…”

Section: Discussionmentioning

confidence: 99%

“…Here, ν = N/N φ is the ratio of particle number over flux quanta. For this ratio, the results of [78] may hint at the presence of another commensurate phase in the hard-core boson limit. In our case, i.e., for the parameters of have encountered studying hard-core bosons close to the boundary between Meissner and vortex-liquid phases for low particle densities [68], which is also the regime discussed by Petrescu et al [78].…”

Section: B Momentum Distribution Function: Experimental Observable Amentioning

confidence: 99%

“…A particular interest has been in the possible existence of one-dimensional versions of fractional quantum Hall states [69][70][71]74]. Whether topologically nontrivial states that resemble properties of, e.g., the ν = 1/2 Laughlin state are indeed realized in bosonic or fermionic ladders remains a topic of ongoing research [78].…”

Section: Introductionmentioning

confidence: 99%

“…These include the Meissner superfluid (M-SF), the MeissnerMott insulator (M-MI), vortex-liquid superfluids (V-SF) and vortex liquids on top of Mott insulators (V-MI), vortex-lattice superfluids at a vortex density ρ v (V ρ v -SF) as well as the VL 1/2 -MI that sits on top of a Mott-insulating state, the charge-density-wave state (CDW 1/4 ), and the biased-ladder superfluid phase (BLP). Other states that have also been proposed to exist in this model [71,78] are not at the main focus of the work and are thus not included in the table. The terminology for these phases as well as the acronyms already suggest the existence of transitions in two sectors:…”

Section: Introductionmentioning

confidence: 99%

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Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

et al. 2016

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We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

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Section: Discussionmentioning

confidence: 99%

Section: B Momentum Distribution Function: Experimental Observable Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

et al. 2016

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“…Since all particles on the same synthetic dimensional rung share the same optical lattice site, contact interactions lead to exotic long-ranged interactions along the rungs, which for typical systems [10,11] may be assumed to be SUðMÞ symmetric. The interplay of long-ranged interactions along the synthetic dimension and homogeneous gauge fields has attracted considerable attention recently, as it gives rise to the ground states bearing analogies with quantum Hall-like behavior [13][14][15][16][17][18][19][20][21], or exhibiting exotic quantum magnetism [4,18,[22][23][24][25][26][27][28][29][30][31].…”

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confidence: 99%

Vortex-Hole Duality: A Unified Picture of Weak- and Strong-Coupling Regimes of Bosonic Ladders with Flux

Greschner

Vekua

2017

Phys. Rev. Lett.

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Two-leg bosonic ladders with flux harbor a remarkable vortex-hole duality between the weak-coupling vortex lattice superfluids and strong-coupling charge-density-wave crystals. The strong-coupling crystalline states, which are realized in the vicinity of π flux, are independent of particle statistics, and are related to the incompressible fractional quantum Hall states in the thin-cylinder limit. These fully gapped ground states, away from π flux, develop nonzero chiral (spin) currents. Contact-interacting quantum gases permit exploration of this vortex-hole duality in experiments. DOI: 10.1103/PhysRevLett.119.073401 Dualities encode important nonperturbative information in statistical, condensed matter and high-energy physics, by mapping weak and strong coupling regimes and providing a way for their unified description [1].A quantum system, depending on conditions, can manifest one of its dual natures profoundly. In a weakly coupled gas or liquid, where positions of particles are not fixed, at sufficiently low temperatures quantum effects set in, and, as a result, Bose particles can develop phase coherence and superfluidity. For strong repulsive interparticle interactions, crystals can form, where each particle is localized to a certain position in space to get as far as possible from the others. Phases of particles, being conjugate variables of densities, fluctuate strongly in crystals. Fluids can develop eddy currents, or vortices when excited. In superfluids with global phase coherence, vortices get topological protection by quantization. Crystals also harbour excitations of topological nature-e.g., point defects such as vacancies (holes).The purpose of this Letter is to demonstrate a spectacular correspondence between the topological defects of superfluids and crystals, referred in the following as a vortexhole duality, realized between weak and strong-coupling regimes of bosonic ladders with flux. Figure 1 shows the microscopic configurations of local particle currents (arrows) and densities (filled circles) of a few dual weak and strong-coupling ground states of bosonic ladders with flux. In the weak-coupling limit the phases of particles are the relevant degrees of freedom, whereas in strong-coupling particle densities they play a dominant role. Vortices are indicated by the letter V in those plaquettes of Fig. 1, wherewhere Θ is local phase and integration is along the boundary l of the plaquette □. Holes, defects of the local particle density distribution, are localized on rungs, indicated by the letter H. Vortices (elementary loop currents), topological excitations of a weak-coupling regime, repel each other [2] (like same pole magnets) and vortex lattices (VLs) at a commensurate vortex density ρ V are dual to hole crystals of chargedensity-wave (CDW) states at ρ H ¼ ρ V realized in a strong-coupling regime, as we will show. Table I summarizes the weak and strong-coupling duality relations. In the weak coupling regime of bosonic ladders few VL superfluids were observed [3,4] to survive quantum fluc...

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Driven dissipative dynamics and topology of quantum impurity systems

Hur

Henriet

Herviou

et al. 2018

Comptes Rendus. Physique

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In this review, we provide an introduction and overview to some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin-boson and related models, which describes a single spin-1/2 coupled to an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin-bath coupling. In these situations, the non-perturbative stochastic Schroedinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields h z (t) of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling to a common bath. In the second part of this review, we discuss quantum engineering of spin-boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose-Einstein condensate, a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott-Superfluid transition.

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Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

Cited by 57 publications

References 127 publications

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

Vortex-Hole Duality: A Unified Picture of Weak- and Strong-Coupling Regimes of Bosonic Ladders with Flux

Driven dissipative dynamics and topology of quantum impurity systems

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