Population-imbalance instability in a Bose-Hubbard ladder in the presence of a magnetic flux

Uchino, Shun; Tokuno, Akiyuki

doi:10.1103/physreva.92.013625

Cited by 36 publications

(55 citation statements)

References 37 publications

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“…0 2 where we have kept only the most relevant term in the renormalization group sense [3]. For a model with equivalent up and down leg as equation (1), and in the absence of the spontaneous density imbalance between the chains found for weak repulsion [46,47], =   u u and =   K K , it is convenient to introduce the leg-symmetric and leg-antisymmetric representation: The Hamiltonian H c describes the gapless leg-symmetric density modes, while H s , which describes the legantisymmetric modes, has the form of a quantum sine-Gordon model [48][49][50] and is gapful for K s >1/4. In a model of bosons with spin-orbit coupling, H s would describe the spin modes, and H c the total density (i.e., the 'charge' in the bosonization literature) modes.…”

Section: Bosonization Of the Two-leg Boson Laddermentioning

confidence: 99%

Incommensurate phases of a bosonic two-leg ladder under a flux

et al. 2016

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A boson two-leg ladder in the presence of a synthetic magnetic flux is investigated by means of bosonization techniques and density matrix renormalization group (DMRG). We follow the quantum phase transition from the commensurate Meissner to the incommensurate vortex phase with increasing flux at different fillings. When the applied flux is ρπ and close to it, where ρ is the filling per rung, we find a second incommensuration in the vortex state that affects physical observables such as the momentum distribution, the rung-rung correlation function and the spin-spin and chargecharge static structure factors.A remarkable characteristic of charged systems with broken U(1) global gauge symmetry such as superconductors is the Meissner-Ochsenfeld effect [1]. In the Meissner phase, below the critical field H c1 , a superconductor behaves as a perfect diamagnet, i.e. it develops surface currents that fully screen the external magnetic field. In a type-II superconductor, for fields above H>H c1 , an Abrikosov vortex lattice phase is formed in the system, where the magnetic field penetrates into vortex cores. In quasi one-dimensional systems, analogues of the Meissner and Abrikosov vortex lattice have been predicted for the bosonic two-leg ladder [2-5], the simplest system where orbital magnetic field effects are allowed. It was shown that in this model, the quantum phase transition between the Meissner and the Vortex phase is a commensurate-incommensurate (C-IC) transition [6][7][8]. For ladder systems at commensurate filling, a chiral Mott insulator phase with currents circulating in loops commensurate with the ladder was obtained [9][10][11][12]. Initially, Josephson junction arrays [13][14][15][16] were proposed as experimental realizations of bosonic one-dimensional systems [17,18]. However, Josephson junctions are dissipative and open systems [19-21] that cannot be described using a Hermitian manybody Hamiltonian in a canonical formalism. Moreover, the quantum effects in the vortex phase of the Josephson ladder are weak [22]. Fortunately, with the recent advent of ultracold atomic gases, another route to realize low dimensional strongly interacting bosonic systems has opened [23][24][25]. Atoms being neutral, it is necessary to find a way to realize an artificial magnetic flux acting on the ladder. Alternatively, one can consider the mapping of the two-leg ladder bosonic model to a two-component spinor boson model in which the bosons in the upper leg become spin-up bosons and the bosons in the lower leg spin-down bosons. Under such mapping, the magnetic flux of the ladder becomes a spin-orbit coupling for the spinor bosons. Theoretical proposals to realize either artificial gauge fields or artificial spin-orbit coupling have been put forward [26,27], and an artificial spinorbit coupling has been achieved in a cold atoms experiment [28,29]. Recently, the Meissner effect and the formation of a vortex state have been observed for non-interacting ultracold bosonic atoms bosons on a two leg ladder in artificial gauge fi...

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Section: Bosonization Of the Two-leg Boson Laddermentioning

confidence: 99%

Incommensurate phases of a bosonic two-leg ladder under a flux

et al. 2016

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“…The BLP phase was studied previously in several works [63,76,77,91]. In framework valid in the regime of a dilute Bose gas to describe this state and to obtain the phase diagram in the dilute-gas limit.…”

Section: Biased-ladder Phasementioning

confidence: 99%

“…The experiments on bosonic [44,48] and fermionic ladders [47] have led to numerous theoretical studies of the strongly correlated quantum phases of such systems [67][68][69][70][71][72][73][74][75][76][77]. A particular interest has been in the possible existence of one-dimensional versions of fractional quantum Hall states [69][70][71]74].…”

Section: Introductionmentioning

confidence: 99%

“…Another state that breaks a discrete symmetry is the biased-ladder phase (BLP), first discussed by Wei and Mueller [76] and also studied in [63,77,91]. In this state, the density between the two legs of the ladder is imbalanced, which serves as an order parameter.…”

Section: Introductionmentioning

confidence: 99%

“…1(e). We determined the phase boundaries of the BLP phase at intermediate interaction strength in [63] from accurate DMRG simulations, thus providing robust evidence for its existence beyond mean-field [76] and bosonization [77,91] predictions. In our present work we also introduce a theory of the emergence of the Meissner state, vortex fluids, and the biased-ladder phase based on the limit of a dilute Bose gas that some of us originally developed for the description of frustrated spin chains just below their saturation magnetization [92,93].…”

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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