Helicity modulus of the quasi-one-dimensional 
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 model: Protection by an energy barrier

Hirashima, Dai S.

doi:10.1103/physrevb.102.104506

Cited by 5 publications

(3 citation statements)

References 41 publications

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“…parameter K, in this case is ∼ 1.85, again inferred from the low-k behavior of S(k), It need be stressed that observing numerically the 1D limiting behavior of cylindrically-shaped 3D systems with a significant spatial extension in the radial direction, requires that computer simulations be carried out on systems of sufficient length L. In particular, as shown by Hirashima [52] in the context of the XY model, L must be significantly greater than a characteristic L c , which grows proportionally to the perimeter (area) of an empty (filled) cylindrical shell (we review this theoretical result in Appendix B).…”

Section: A Dimensionalitymentioning

confidence: 71%

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Quasi-one-dimensional $^4$He in nanopores

Nava,

Giuliano,

Nguyen

et al. 2021

Preprint

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Low temperature structural and superfluid properties of 4 He confined in cylindrical nanopores are theoretically investigated by means of first principle Quantum Monte Carlo (QMC) simulations. We vary the density of 4 He inside the pore, as well as the pore diameter and the potential describing the interaction of each 4 He atom with the pore surface. Accordingly, the 4 He fluid inside the pore forms either a single channel along the axis, or a series of concentric cylindrical shells, with varying degrees of shell overlap. In the limit of pore length greatly exceeding its radius, the 4 He fluid always displays markedly one-dimensional behavior, with no "dimensional crossover" above some specific pore radius and/or as multiple concentric shells form, in contrast to what recently claimed by other authors [Phys. Rev. B 101, 104505 (2020)]. Indeed, the predicted robustness of one-dimensional physics suggests that this system may offer a broadly viable pathway to the experimental observation of exotic behavior of, e.g., junctions of interacting Tomonaga-Luttinger liquids, in an appropriately designed network of nanopores.

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Section: A Dimensionalitymentioning

confidence: 71%

“…ν,µ e −(K/2)[ M L (2πν) 2 + L M (2πµ) 2 ]−KMs(2πν)−(K/2)MLs 2 ν,µ e −(K/2)[ M L (2πν) 2 + L M (2πµ) 2 ]Expanding up to second-order in s and extracting the superfluid fraction, we therefore obtainρ S (L, M, T ) = − 2T LM (2πν) 2 exp − KM 2L (2πν) 2 ν exp − KM 2L (2πν) 2 ≡ ρ S (L ef f , T ) ,(B6)with L ef f = L/M[52].…”

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confidence: 99%

Quasi-one-dimensional $^4$He in nanopores

Nava,

Giuliano,

Nguyen

et al. 2021

Preprint

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“…These long relaxation times must be taken into account in modeling experiments in cold atom systems [49,50] and 4 He nanopores [51][52][53][54]. One approach is to introduce "dynamical" superfluidity [55][56][57][58].…”

Section: Non-equilibrium Considerationsmentioning

confidence: 99%

Superfluidity in the 1D Bose-Hubbard Model

Kiely,

Mueller

2022

Preprint

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We study superfluidity in the 1D Bose-Hubbard model using a variational matrix product state technique. We determine the superfluid density as a function of the Hubbard parameters by calculating the energy cost of phase twists in the thermodynamic limit. As the system is critical, correlation functions decay as power laws and the entanglement entropy grows with the bond dimension of our variational state. We relate the resulting scaling laws to the superfluid density. We compare two different algorithms for optimizing the infinite matrix product state and develop a physical explanation why one of them (VUMPS) is more efficient than the other (iDMRG). Finally, we comment on finite-temperature superfluidity in one dimension and how our results can be realized in cold atom experiments.

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