One-dimensional Bose-Hubbard model with nearest-neighbor interaction

Kühner, Till D.; White, Steven R.; Monien, H.

doi:10.1103/physrevb.61.12474

Cited by 397 publications

(624 citation statements)

References 38 publications

(65 reference statements)

Supporting

Mentioning

584

Contrasting

Order By: Relevance

“…The MF transition between the SF phase and the Mott phase is independent of the dimension of the system and is located at U c Ϸ 5.83, while a DMRG [17] study locates it at U c / z Ϸ 3.36 in one dimension and a strong-coupling expansion [10] locates it at U c / z Ϸ 4.18 in two dimensions. We have performed a simulation at U / z = 5.0 in one, two, and three dimensions.…”

Section: Fig 3 Uppermentioning

confidence: 99%

“…In view of the enormous success of DMRG [25] in bosonic [17] and fermionic [26] real-space lattice models in one dimension, DMRG has been extended beyond these models, towards applications in metallic grains [27], quantum chemistry [28,29], and first attempts have even been undertaken towards applications in nuclear physics [30]. Unfortunately, an exact DMRG study in all three dimensions of the Bose-Hubbard model is not feasible with current computer power.…”

Section: Introductionmentioning

confidence: 99%

“…Strong coupling expansions [9,10] gave a better quantitative picture, while quantum Monte Carlo simulations [11][12][13][14][15] were carried out in one and two dimensions. The one-dimensional case was recently investigated using the density-matrix renormalization group (DMRG) [16,17], yielding the most accurate results at present. Longer-range interactions can cause charge density wave, stripe or even supersolid order [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…The one-dimensional case was recently investigated using the density-matrix renormalization group (DMRG) [16,17], yielding the most accurate results at present. Longer-range interactions can cause charge density wave, stripe or even supersolid order [17][18][19]. Disorder and impurities can have dramatic effects [6,11,17,[20][21][22] and lead to even other phases.…”

Section: Introductionmentioning

confidence: 99%

“…Longer-range interactions can cause charge density wave, stripe or even supersolid order [17][18][19]. Disorder and impurities can have dramatic effects [6,11,17,[20][21][22] and lead to even other phases. The model with a quadratic confining potential [2] has been addressed in one dimension [23] and for a small lattice in three dimensions [24], using quantum Monte Carlo methods.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bosons confined in optical lattices: The numerical renormalization group revisited

Pollet¹,

Rombouts²,

Heyde³

et al. 2004

Phys. Rev. A

View full text Add to dashboard Cite

A Bose-Hubbard model, describing bosons in a harmonic trap with a superimposed optical lattice, is studied using a fast and accurate variational technique (MFϩNRG): the Gutzwiller mean-field (MF) ansatz is combined with a numerical renormalization group (NRG) procedure in order to improve on both. Results are presented for one, two, and three dimensions, with particular attention to the experimentally accessible momentum distribution and possible satellite peaks in this distribution. In one dimension, a comparison is made with exact results obtained using stochastic series expansion.

show abstract

Section: Fig 3 Uppermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bosons confined in optical lattices: The numerical renormalization group revisited

Pollet¹,

Rombouts²,

Heyde³

et al. 2004

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

Nonlocal Correlation and Entanglement of Ultracold Bosons in the 2D Bose–Hubbard Lattice at Finite Temperature

2022

View full text Add to dashboard Cite

The temperature‐dependent behavior emerging in the vicinity of the superfluid (SF) to Mott‐insulator (MI) transition of interacting bosons in a 2D optical lattice, described by the Bose–Hubbard model is investigated. The equilibrium phase diagram at finite‐temperature is computed using the cluster mean‐field (CMF) theory including a finite‐cluster‐size‐scaling. The SF, MI, and normal fluid (NF) phases are characterized as well as the transition or crossover temperatures between them are estimated by computing physical quantities such as the superfluid fraction, compressibility and sound velocity using the CMF method. It is found that the nonlocal correlations included in a finite cluster, when extrapolated to infinite size, leads to quantitative agreement of the phase boundaries with quantum Monte Carlo (QMC) results as well as with experiments. Moreover, it is shown that the von Neumann entanglement entropy within a cluster corresponds to the system's entropy density and that it is enhanced near the SF–MI quantum critical point (QCP) and at the SF–NF boundary. The behavior of the transition lines near this QCP, at and away from the particle‐hole (p–h) symmetric point located at the Mott‐tip, is also discussed. The results obtained by using the CMF theory can be tested experimentally using the quantum gas microscopy method.

show abstract

Capturing the re‐entrant behavior of one‐dimensional Bose–Hubbard model

Pino

Prior

Clark

2012

Physica Status Solidi (b)

View full text Add to dashboard Cite

The Bose Hubbard model (BHM) is an archetypal quantum lattice system exhibiting a quantum phase transition between its superfluid (SF) and Mott-insulator (MI) phase. Unlike in higher dimensions the phase diagram of the BHM in one dimension possesses regions in which increasing the hopping amplitude can result in a transition from MI to SF and then back to a MI. This type of re-entrance is well known in classical systems like liquid crystals yet its origin in quantum systems is still not well understood. Moreover, this unusual re-entrant character of the BHM is not easily captured in approximate analytical or numerical calculations.Here we study in detail the predictions of three different and widely used approximations; a multi-site meanfield decoupling, a finite-sized cluster calculation, and a real-space renormalization group (RG) approach. It is found that mean-field calculations do not reproduce reentrance while finite-sized clusters display a precursor to re-entrance. Here we show for the first time that RG does capture the re-entrant feature and constitutes one of the simplest approximation able to do so. The differing abilities of these approaches reveals the importance of describing short-ranged correlations relevant to the kinetic energy of a MI in a particle-number symmetric way.Copyright line will be provided by the publisher 1 Introduction Re-entrance is a novel phenomenon in which a succession of transitions between two phases A and B, such as A-B-A-B, can occur by monotonically increasing just one parameter. Such a series of transitions implies a non-linearity which allows a single parameter to produce opposite effects depending on its initial value and is often a reflection of the interacting character of the system. In the context of classical thermal phase transitions the natural parameter to vary is temperature. It is then expected that the low temperature phase A will be ordered, while increasing the temperature will drive the system to a disordered phase B. However, the appearance of re-entrance means that increasing the temperature can in fact unexpectedly stabilize the ordered phase A again. This sequence of phase transitions has been observed in liquid crystals between the A = Smectic (ordered) phase and B =

show abstract

One-dimensional Bose-Hubbard model with nearest-neighbor interaction

Cited by 397 publications

References 38 publications

Bosons confined in optical lattices: The numerical renormalization group revisited

Bosons confined in optical lattices: The numerical renormalization group revisited

Nonlocal Correlation and Entanglement of Ultracold Bosons in the 2D Bose–Hubbard Lattice at Finite Temperature

Capturing the re‐entrant behavior of one‐dimensional Bose–Hubbard model

Contact Info

Product

Resources

About