Quantum magnetism of bosons with synthetic gauge fields in one-dimensional optical lattices: A density-matrix renormalization-group study

Piraud, Marie; Cai, Zi; McCulloch, Ian P.; Schollwöck, Ulrich

doi:10.1103/physreva.89.063618

Cited by 55 publications

(61 citation statements)

References 62 publications

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“…Recently, we became aware of the similar DMRG calculations of [49][50][51][52]. Our results and theirs agree for the parameter regimes where they overlap.…”

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confidence: 68%

Mott-superfluid transition for spin-orbit-coupled bosons in one-dimensional optical lattices

Cole

Zhang

2014

Phys. Rev. A

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We study the effects of spin-orbit coupling on the Mott-superfluid transition of bosons in a onedimensional optical lattice. We determine the strong-coupling magnetic phase diagram by a combination of exact analytic and numerical means. Smooth evolution of the magnetic structure into the superfluid phases is investigated with the density matrix renormalization group technique. Other magnetic phases are seen and phase transitions between them within the superfluid regime are discussed. Possible experimental detection is discussed.

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“…Recently, we became aware of the similar DMRG calculations of [49][50][51][52]. Our results and theirs agree for the parameter regimes where they overlap.…”

supporting

confidence: 68%

Mott-superfluid transition for spin-orbit-coupled bosons in one-dimensional optical lattices

Cole

Zhang

2014

Phys. Rev. A

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“…Magnetism of the unit filled Mott phase in Abelian and non-Abelian gauge fields has been studied in Ref. [54] using DMRG. Vortex lattice states, in which the discrete lattice translation symmetry is spontaneously broken, exist for U finite [55].…”

Section: Model and Previous Resultsmentioning

confidence: 99%

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

et al. 2017

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We study hard core bosons on a two-leg ladder lattice under the orbital effect of a uniform magnetic field. At densities which are incommensurate with flux, the ground state is a Meissner state, or a vortex state, depending on the strength of the flux. When the density is commensurate with the flux, analytical arguments predict the possibility to stabilize a ground state of central charge c = 1, which is a precursor of the two-dimensional Laughlin state at ν = 1/2. This differs from the coupled wire construction of the Laughlin state in that there exists a nonzero backscattering term in the edge Hamiltonian. By using a combination of bosonization and density matrix renormalization group (DMRG) calculations, we construct a phase diagram versus density and flux from local observables and central charge. We delimit the region where the finite-size ground state displays signatures compatible with this precursor to the Laughlin state. We show how bipartite charge fluctuations allow access to the Luttinger parameter for the edge Luttinger liquid corresponding to the precursor Laughlin state. The properties studied with local observables are confirmed by the long distance behavior of correlation functions. Our findings are consistent with an exact-diagonalization calculation of the many body ground state transverse conductivity in a thin torus geometry for parameters corresponding to the precursor Laughlin state. The model considered is simple enough such that the precursor to the Laughlin state could be realized in current ultracold atom, Josephson junction array, and quantum circuit experiments.

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“…During the completion of this manuscript we became aware of three works where one-dimensional lattice bosons with spin-orbit coupling are studied by means of densitymatrix renormalization-group algorithms [50,51,52]. scaling in the text, we performed some simulations at m = 120, which were however computationally too demanding for a complete program of simulations (note also that the model does not conserve any magnetization, i.e.…”

Section: Discussionmentioning

confidence: 99%

The XYZ chain with Dzyaloshinsky–Moriya interactions: from spin–orbit-coupled lattice bosons to interacting Kitaev chains

et al. 2014

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Abstract. Using the density-matrix renormalization-group algorithm (DMRG) and a finite-size scaling analysis, we study the properties of the one-dimensional completelyanisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. The model shows a rich phase diagram: depending on the value of the coupling constants, the system can display different kinds of ferromagnetic order and Luttinger-liquid behavior. Transitions from ferromagnetic to Luttinger-liquid phases are first order. We thoroughly discuss the transition between different ferromagnetic phases, which, in the absence of DM interactions, belongs to the XX universality class. We provide evidence that the DM exchange term turns out to split this critical line into two separated Ising-like transitions and that in between a disordered phase may appear. Our study sheds light on the general problem of strongly-interacting spin-orbit-coupled bosonic gases trapped in an optical lattice and can be used to characterize the topological properties of superconducting nanowires in the presence of an imposed supercurrent and of interactions.

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Quantum magnetism of bosons with synthetic gauge fields in one-dimensional optical lattices: A density-matrix renormalization-group study

Cited by 55 publications

References 62 publications

Mott-superfluid transition for spin-orbit-coupled bosons in one-dimensional optical lattices

Mott-superfluid transition for spin-orbit-coupled bosons in one-dimensional optical lattices

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

The XYZ chain with Dzyaloshinsky–Moriya interactions: from spin–orbit-coupled lattice bosons to interacting Kitaev chains

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