Bose-glass phase of a one-dimensional disordered Bose fluid: Metastable states, quantum tunneling, and droplets

Dupuis, N.; Daviet, Romain

doi:10.1103/physreve.101.042139

Cited by 13 publications

(37 citation statements)

References 96 publications

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“…A proper treatment of the phase field ϑ is an important step in the FRG analysis of lowdimensional quantum fluids in the framework of bosonization. For instance, this will allow us to study the phase fluctuations and the superfluid properties more accurately in the Bose-glass phase of a one-dimensional disordered Bose fluid [4,5]. This also opens up the possibility to study strongly anisotropic two-or three-dimensional systems, consisting of weakly coupled one-dimensional chains, where the interchain kinetic coupling gives rise to an action that depends nontrivially on ϑ.…”

Section: Discussionmentioning

confidence: 99%

“…Bosonization is one of the most popular methods to describe one-dimensional quantum fluids [1]. It has recently been used in combination with the nonperturbative functional renormalization (FRG) group to study the Mott-insulating phase induced by a periodic potential (in the framework of the sine-Gordon model) [2,3] and the Bose-glass phase of disordered bosons [4][5][6][7][8]. These studies are based on an action S[ϕ] expressed solely in terms of the "density" field ϕ, its conjugate partner, the phase ϑ of the superfluid order parameter (the field operator ψ for bosons), being integrated out from the outset.…”

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confidence: 99%

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Flowing bosonization in the nonperturbative functional renormalization-group approach

Daviet,

Dupuis

2021

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Bosonization allows one to describe the low-energy physics of one-dimensional quantum fluids within a bosonic effective field theory formulated in terms of two fields: the "density" field ϕ and its conjugate partner, the phase ϑ of the superfluid order parameter. We discuss the implementation of the nonperturbative functional renormalization group in this formalism, considering a Luttinger liquid in a periodic potential as an example. We show that in order for ϑ and ϕ to remain conjugate variables at all energy scales, one must dynamically redefine the field ϑ along the renormalization-group flow. We derive explicit flow equations using a derivative expansion of the scale-dependent effective action to second order and show that they reproduce the flow equations of the sine-Gordon model (obtained by integrating out the field ϑ from the outset) derived within the same approximation. Only with the scale-dependent (flowing) reparametrization of the phase field ϑ do we obtain the standard phenomenology of the Luttinger liquid (when the periodic potential is sufficiently weak so as to avoid the Mott-insulating phase) characterized by two low-energy parameters, the velocity of the sound mode and the renormalized Luttinger parameter.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Flowing bosonization in the nonperturbative functional renormalization-group approach

Daviet,

Dupuis

2021

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“…In this paper, we have shown that the FRG approach is also a very powerful method, notably at zero temperature, to determine the physical properties of the massive sine-Gordon model, which is the bosonized version of the massive Schwinger model. More generally, the FRG is very useful to study quantum systems in d = 1 + 1 dimensions where soliton-like excitations may play a crucial role [45] By computing the critical exponents, we confirm that the phase transition ocurring in the massive Schwinger model for a value θ = π of the vacuum angle belongs to the two-dimensional Ising universality class, as had been shown in several previous studies [13,15]. Though the precision of the critical exponents is typical of a secondorder derivative expansion (DE), more accurate results could be obtained by pushing the expansion to higher orders [46,47].…”

Section: Discussionmentioning

confidence: 99%

Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group

et al. 2022

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We investigate the massive Schwinger model in d = 1 + 1 dimensions using bosonization and the non-perturbative functional renormalization group. In agreement with previous studies we find that the phase transition, driven by a change of the ratio m/e between the mass and the charge of the fermions, belongs to the two-dimensional Ising universality class. The temperature and vacuum angle dependence of various physical quantities (chiral density, electric field, entropy density) are also determined and agree with results obtained from density matrix renormalization group studies. Screening of fractional charges and deconfinement occur only at infinite temperature.

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“…Following previous FRG studies of one-dimensional disordered boson systems [10,20,21], we consider the following truncation of the effective action,…”

Section: S[{ϕmentioning

confidence: 99%

“…the finite localization length and the gapless conductivity, this fixed point is characterized by a renormalized disorder correlator that assumes a cuspy functional form whose origin lies in the existence of metastable states associated with glassy properties [20,21].…”

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Mott-glass phase of a one-dimensional quantum fluid with long-range interactions

Daviet,

Dupuis

2020

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We investigate the ground-state properties of quantum particles interacting via a long-range repulsive potential Vσ(x) ∼ 1/|x| 1+σ (−1 < σ) or Vσ(x) ∼ −|x| −1−σ (−2 ≤ σ < −1) that interpolates between the Coulomb potential V0(x) and the linearly confining potential V−2(x) of the Schwinger model. In the absence of disorder the ground state is a Wigner crystal when σ ≤ 0. Using bosonization and the nonperturbative functional renormalization group we show that any amount of disorder suppresses the Wigner crystallization when −3/2 < σ ≤ 0; the ground state is then a Mott glass, i.e., a state that has a vanishing compressibility and a gapless optical conductivity. For σ < −3/2 the ground state remains a Wigner crystal.

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Bose-glass phase of a one-dimensional disordered Bose fluid: Metastable states, quantum tunneling, and droplets

Cited by 13 publications

References 96 publications

Flowing bosonization in the nonperturbative functional renormalization-group approach

Flowing bosonization in the nonperturbative functional renormalization-group approach

Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group

Mott-glass phase of a one-dimensional quantum fluid with long-range interactions

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