Exact diagonalization plus renormalization-group theory: Accurate method for a one-dimensional superfluid-insulator-transition study

Kashurnikov, V. A.; Svistunov, Boris

doi:10.1103/physrevb.53.11776

Cited by 64 publications

(74 citation statements)

References 13 publications

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“…For numerical simplicity, we truncate the local bosonic Hilbert space to four states. This does not change the relevant physics significantly [7,8,9].…”

Section: Modelmentioning

confidence: 99%

“…The transition at zero temperature (T = 0) has been analyzed in onedimensional systems [7,8,9,10,11]. But there is still a multitude of open questions.…”

Section: Introductionmentioning

confidence: 99%

“…There are many theoretical treatments of these issues, ranging from mean-field approaches [5] to more sophisticated techniques [6,7,8,9,10,11]. The transition at zero temperature (T = 0) has been analyzed in onedimensional systems [7,8,9,10,11].…”

Section: Introductionmentioning

confidence: 99%

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Temperature in one-dimensional bosonic Mott insulators

Reischl

Schmidt²,

Uhrig³

2005

Phys. Rev. A

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The Mott insulating phase of a one-dimensional bosonic gas trapped in optical lattices is described by a Bose-Hubbard model. A continuous unitary transformation is used to map this model onto an effective model conserving the number of elementary excitations. We obtain quantitative results for the kinetics and for the spectral weights of the low-energy excitations for a broad range of parameters in the insulating phase. By these results, recent Bragg spectroscopy experiments are explained. Evidence for a significant temperature of the order of the microscopic energy scales is found.

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“…For numerical simplicity, we truncate the local bosonic Hilbert space to four states. This does not change the relevant physics significantly [7,8,9].…”

Section: Modelmentioning

confidence: 99%

“…The transition at zero temperature (T = 0) has been analyzed in onedimensional systems [7,8,9,10,11]. But there is still a multitude of open questions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Temperature in one-dimensional bosonic Mott insulators

Reischl

Schmidt²,

Uhrig³

2005

Phys. Rev. A

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“…Three works find somewhat bigger values t c = 0.298 11 , t c = 0.304±0.002 15 and t = 0.300 ± 0.005 10 . Early QMC simulations resulted in t c = 0.215 ± 0.01 16 .…”

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confidence: 99%

Phases of the one-dimensional Bose-Hubbard model

1998

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The zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with nearestneighbor interaction is investigated using the Density-Matrix Renormalization Group. Recently normal phases without long-range order have been conjectured between the charge density wave phase and the superfluid phase in one-dimensional bosonic systems without disorder. Our calculations demonstrate that there is no intermediate phase in the one-dimensional Bose-Hubbard model but a simultaneous vanishing of crystalline order and appearance of superfluid order. The complete phase diagrams with and without nearest-neighbor interaction are obtained. Both phase diagrams show reentrance from the superfluid phase to the insulator phase.PACS numbers: 05.30. Jp, 05.70.Jk, 67.40.Db Quantum phase transitions in strongly correlated systems have attracted a lot of interest in recent years. Usually the basic particles are electrons, but in some interesting cases the relevant particles are not fermions but bosons. Examples of experimental systems with superfluid and insulating phases are Cooper pairs in thin granular superconducting films 1 and cooper pairs or fluxes in Josephson junction arrays 2 . While in dimensions greater than one the existence of supersolids 3 , i.e. phases with simultaneous superfluid and crystalline order, has been established in theoretical work, the situation in one dimension is less clear. Recently normal phases that are neither crystalline nor superfluid have been found in a one-dimensional model of Josephson junction arrays 4 in the region where supersolids are found in higher dimensions. In this paper we will verify whether supersolids or normal phases exist in the more general Bose-Hubbard model in one dimension.The Bose-Hubbard model contains the basic physics of interacting bosons on a lattice. It is a minimal bosonic many-particle model that cannot be reduced to a single particle model. The bosons have repulsive interactions, and they can gain energy by hopping to neighboring sites on the lattice. The Hamiltonian with on-site and nearestneighbor interactions iswhere b i are the annihilation operators of bosons on site i,n i = b † i b i the number of particles on site i, t is the hopping matrix element. U and V are on-site and nearestneighbor repulsion, and µ is the chemical potential. The energy scale is set by choosing U = 1.The range of the interactions depends on the individual experimental situation. In general the lattice underlying the system is not an atomic lattice, but a larger structure like a Josephson-junction or a grain in a superconductor. In Josephson-junctions the relevant bosons can be cooper pairs or fluxes, resulting in different interactions.As a starting point we first consider the case of onsite repulsion only. In the (µ, t)-plane Mott-insulating regions are surrounded by the superfluid phase 5 . These phases are separated by two types of phase transitions. On the constant density line the transition is driven by phase fluctuations and is of the Berezinskii-KosterlitzThouless (BKT...

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“…2,5,[7][8][9][10][11] In particular, if V = 0 and there is no disorder, only an SF phase is obtained at noninteger densities. For integer densities an MI phase is obtained at large U; as U is lowered the system shows an MI-SF transition, which is of the Kosterlitz-Thouless type 23 in one dimension.…”

Section: Resultsmentioning

confidence: 99%

The one-dimensional extended Bose-Hubbard model

Pai

Pandit

2003

J Chem Sci

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Abstract.We use the finite-size, density-matrix-renormalization-group (DMRG) method to obtain the zero-temperature phase diagram of the one-dimensional, extended Bose-Hubbard model, for mean boson density ρ = 1, in the U-V plane (U and V are respectively, onsite and nearest-neighbour repulsive interactions between bosons). The phase diagram includes superfluid (SF), bosonic-Mott-insulator (MI), and mass-density-wave (MDW) phases. We determine the natures of the quantum phase transitions between these phases.Keywords. Boson systems; quantum statistical theory; ground state; elementary excitations; other topics in quantum fluids and solids; liquid and solid helium.

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Exact diagonalization plus renormalization-group theory: Accurate method for a one-dimensional superfluid-insulator-transition study

Cited by 64 publications

References 13 publications

Temperature in one-dimensional bosonic Mott insulators

Temperature in one-dimensional bosonic Mott insulators

Phases of the one-dimensional Bose-Hubbard model

The one-dimensional extended Bose-Hubbard model

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