Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2207.12443 · Physical Review Letters

Superconducting Transition Temperature of the Bose One-Component Plasma

Chao Zhang, Barbara Capogrosso-Sansone, Massimo Boninsegni, Nikolay V. Prokof'ev, Boris V. Svistunov

Published Jun 9, 2023• 20 citations
arXivHTMLPDF

Abstract

We present results of numerically exact simulations of the Bose one-component plasma, i.e., a Bose gas with pairwise Coulomb interactions among particles and a uniform neutralizing background. We compute the superconducting transition temperature for a wide range of densities, in two and three dimensions, for both continuous and lattice versions of the model. The Coulomb potential causes the weakly interacting limit to be approached at high density, but gives rise to no qualitatively different behavior, vis-à-vis the superfluid transition, with respect to short-ranged interactions. Our results are of direct relevance to quantitative studies of bipolaron mechanisms of (high-temperature) superconductivity.

DOI
10.1103/physrevlett.130.236001

Related papers

Superfluid Region for a Bose-Coulomb Gas with Hard Cores

B. J. Alder, Doug Peters

The superconducting region of the high-temperature superconductors can be semi-quantitatively modeled by holes paired in real space to form bosons which interact mutually via a long-range Coulomb potential with a short-range hard-core cut-off. The bosons are localized at low carrier density by Wigner crystallization and by ordinary crystallization at high carrier densities although dissociation is also predicted. At intermediate densities the superfluid/superconducting transition follows the Kosterlitz-Thouless criterion with a reasonable effective mass.

Europhysics Letters (EPL)•Sep 1, 1989•17 citations

Superfluid transition temperature of bond bipolarons with Coulomb interaction

Chao Zhang

Using numerically exact diagrammatic Monte Carlo simulations in the two-electron (single-bipolaron) sector, we explore the impact of long-range Coulomb repulsion on the dilute-limit Berezinskii-Kosterlitz-Thouless transition temperature T c of bipolarons on a two-dimensional square lattice. We study the bond Su-Schrieffer-Heeger model, in which bond phonons modulate the electron hopping. In the absence of long-range repulsion, this model was shown to support small, light bipolarons with a comparatively high transition temperature [C. Zhang, J. Sous, D. R. Reichman, M. Berciu, A. J. Millis, N. V. Prokof’ev, and B. V. Svistunov, Bipolaronic high-temperature superconductivity, ]. Here, we find that long-range Coulomb repulsion suppresses the optimal T c but leaves it appreciable over a broad parameter window, including the adiabatic regime ω / t = 0.5 at a representative Coulomb strength V = U / 10 (with U the on-site repulsion). Our results provide controlled single-bipolaron inputs for dilute-limit T c estimates in the presence of long-range repulsion.

arXiv:2407.10444•APS Open Science•May 20, 2026•0 citations

Critical Temperature of Interacting Bose Gases in Two and Three Dimensions

Sebastiano Pilati, S. Giorgini, Nikolay V. Prokof'ev

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.

arXiv:0801.3424•Physical Review Letters•Apr 9, 2008•75 citations

Dilute Bose gas in two dimensions

Daniel S. Fisher, Pierre C. Hohenberg

The weakly interacting Bose gas in two dimensions is considered in the dilute limit ${n}^{1/2}$a\ensuremath{\ll}1, where n is the particle density and a is the range of the potential. The standard many-body perturbation theory for this system has two separate divergences: the first, associated with classical phase fluctuations, is responsible for the vanishing of the long-range order; the second is quantum mechanical and is connected with the vanishing of the scattering t matrix at long wavelengths and low energies. An earlier diagrammatic theory of Popov, which provides a consistent description of the system in the dilute limit, is rederived heuristically from a quasiparticle picture, and also using the renormalization group. It is shown that the superfluid transition temperature is ${T}_{c}$\ensuremath{\approxeq}4\ensuremath{\pi}(${\ensuremath{\Elzxh}}^{2}$/2m)n/[ln ln(1/${\mathrm{na}}^{2}$)], and the condition of validity of the dilute limit is ln ln(1/${\mathrm{na}}^{2}$)\ensuremath{\gg}1. The connection to the dilute Bose gas in dimensions d>2 and the universal behavior beyond the extreme asymptotic low-density domain are also discussed.

Physical review. B, Condensed matter•Apr 1, 1988•388 citations

Quantum Phase Transition in a Low-Dimensional Weakly Interacting Bose Gas

Luca Fontanesi

This thesis is devoted to the study of the effect of disorder on low-dimensional weakly interacting Bose gases. In particular, the disorder triggers a quantum phase transition in one dimension at zero temperature that is investigated here through the study of the long-range behaviour of the one-body density matrix. An algebraic spatial decay of the coherence marks the quasicondensate, whereas, in the case of strong disorder, an exponential decay is recovered and it characterizes the insulating Bose-glass phase. This analysis is performed using an extended Bogoliubov theory to treat low dimensional Bose gases within a density-phase approach. A systematic numerical study allowed to draw the phase diagram of 1D weakly interacting bosons. The phase boundary obeys two different power laws between interaction and disorder strength depending on the regime of the gas where the transition occurs. These relations can be explained by means of scaling arguments valid in the white noise limit and in the Thomas-Fermi regime of the Bose gas. The phase transition to a quasicondensed phase comes along with the onset of superfluidity: the inspection of the superfluid fraction of the gas is consistent with these predictions for the boundary. The finite temperature case and the scenario in two dimensions are briefly discussed. The quantum phase transition is caused by low-energy phase fluctuations that destroy the quasi-long-range order characterizing the uniform system. Within the approach presented here, the phase fluctuations are identified as the low-lying Bogoliubov modes. Their properties have been investigated in detail to understand which changes trigger the phase transition and we found that the transition to the insulating phase is accompanied by a diverging density of states and a localization length, measured through the inverse participation ratio, that diverges as a power-law with power – 1 for vanishing energy. The fragmentation of the gas is also studied: this notion is very often associated with the onset of the insulating phase. The characterization of the density fragmentation is performed by analyzing the probability distribution of the density. A density profile is defined as fragmented when the probability distribution at vanishing density is finite or divergent and this happens for a gas in the Bose-glass phase. On the contrary, the superfluid phase is characterized by a zero limiting probability of having vanishing densities. This definition is derived analytically, and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments: when a harmonic trap is included, the transition to the insulating phase can be extracted from the statistics of the local density distribution.

•Jan 1, 2011•1 citation

On the Charged Bose Liquid

Arkady A Shanenko

A new approach developed in Ref.1 for investigating the spatial boson correlations at low temperatures is considered in the particular case of the Coulomb interaction potential. This approach is based on integro–differential equations for the radial distribution function and can be used beyond the weak coupling regime. PACS: 05.30.Jp, 67.90.+z Description of the charged Bose liquid, or, in other words, of the strongly correlated many–boson system with the Coulomb interparticle potential, is a long–standing problem of the condensed matter physics. Recently, interest in this problem has been renewed in the connection with the noteworthy results of applying the Bose and Bose–Fermi liquid models [2] to the explanation of various phenomena inherent in the superconductors with high critical temperatures. These models are based on the Bogoliubov approach [3] implying the weak coupling regime. For the system of charged bosons the weak coupling approximation can be used at small values of the Brueckner parameter rS ∼ 0.1. However, questions requiring detailed investigations often concern the materials with relatively low densities of charge carriers which correspond to rS−values even larger than those of the electron gas at 1 the metallic densities. For example, there are the results [4] testifying to the possibility of forming the so–called large bipolaron (e.g. the two–electron cluster with a large radius of electron–electron separation, see papers in Ref. [5]) inside the polaron environment at the electron densities ∼ 10 19 cm −3 close to the carrier densities of the heavily doped degenerate polar semiconductors. To investigate the possible phase transition of the charge carrier system from the polaron state to the bipolaron phase at these densities, one should operate with the charged Bose liquid of large bipolarons for rS ≫ 1. Indeed, the ”large–bipolaron“ Bohr radius can be expressed [4] as abip =

•Jan 1, 1997•0 citations
We present results of numerically exact simulations of the Bose one-component plasma, i.e., a Bose gas with pairwise Coulomb interactions among particles and a uniform neutralizing background. We compute the superconducting transition temperature for a wide range of densities, in two and three dimensions, for both continuous and lattice versions of the model. The Coulomb potential causes the weakly interacting limit to be approached at high density, but gives rise to no qualitatively different behavior, vis-à-vis the superfluid transition, with respect to short-ranged interactions. Our results are of direct relevance to quantitative studies of bipolaron mechanisms of (high-temperature) superconductivity.
The superconducting region of the high-temperature superconductors can be semi-quantitatively modeled by holes paired in real space to form bosons which interact mutually via a long-range Coulomb potential with a short-range hard-core cut-off. The bosons are localized at low carrier density by Wigner crystallization and by ordinary crystallization at high carrier densities although dissociation is also predicted. At intermediate densities the superfluid/superconducting transition follows the Kosterlitz-Thouless criterion with a reasonable effective mass.
Using numerically exact diagrammatic Monte Carlo simulations in the two-electron (single-bipolaron) sector, we explore the impact of long-range Coulomb repulsion on the dilute-limit Berezinskii-Kosterlitz-Thouless transition temperature T c of bipolarons on a two-dimensional square lattice. We study the bond Su-Schrieffer-Heeger model, in which bond phonons modulate the electron hopping. In the absence of long-range repulsion, this model was shown to support small, light bipolarons with a comparatively high transition temperature [C. Zhang, J. Sous, D. R. Reichman, M. Berciu, A. J. Millis, N. V. Prokof’ev, and B. V. Svistunov, Bipolaronic high-temperature superconductivity, ]. Here, we find that long-range Coulomb repulsion suppresses the optimal T c but leaves it appreciable over a broad parameter window, including the adiabatic regime ω / t = 0.5 at a representative Coulomb strength V = U / 10 (with U the on-site repulsion). Our results provide controlled single-bipolaron inputs for dilute-limit T c estimates in the presence of long-range repulsion.
We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.
The weakly interacting Bose gas in two dimensions is considered in the dilute limit n1/2{n}^{1/2}n1/2a\ensuremath{\ll}1, where n is the particle density and a is the range of the potential. The standard many-body perturbation theory for this system has two separate divergences: the first, associated with classical phase fluctuations, is responsible for the vanishing of the long-range order; the second is quantum mechanical and is connected with the vanishing of the scattering t matrix at long wavelengths and low energies. An earlier diagrammatic theory of Popov, which provides a consistent description of the system in the dilute limit, is rederived heuristically from a quasiparticle picture, and also using the renormalization group. It is shown that the superfluid transition temperature is Tc{T}_{c}Tc​\ensuremath{\approxeq}4\ensuremath{\pi}(${\ensuremath{\Elzxh}}^{2}$/2m)n/[ln ln(1/na2{\mathrm{na}}^{2}na2)], and the condition of validity of the dilute limit is ln ln(1/na2{\mathrm{na}}^{2}na2)\ensuremath{\gg}1. The connection to the dilute Bose gas in dimensions d>2 and the universal behavior beyond the extreme asymptotic low-density domain are also discussed.
This thesis is devoted to the study of the effect of disorder on low-dimensional weakly interacting Bose gases. In particular, the disorder triggers a quantum phase transition in one dimension at zero temperature that is investigated here through the study of the long-range behaviour of the one-body density matrix. An algebraic spatial decay of the coherence marks the quasicondensate, whereas, in the case of strong disorder, an exponential decay is recovered and it characterizes the insulating Bose-glass phase. This analysis is performed using an extended Bogoliubov theory to treat low dimensional Bose gases within a density-phase approach. A systematic numerical study allowed to draw the phase diagram of 1D weakly interacting bosons. The phase boundary obeys two different power laws between interaction and disorder strength depending on the regime of the gas where the transition occurs. These relations can be explained by means of scaling arguments valid in the white noise limit and in the Thomas-Fermi regime of the Bose gas. The phase transition to a quasicondensed phase comes along with the onset of superfluidity: the inspection of the superfluid fraction of the gas is consistent with these predictions for the boundary. The finite temperature case and the scenario in two dimensions are briefly discussed. The quantum phase transition is caused by low-energy phase fluctuations that destroy the quasi-long-range order characterizing the uniform system. Within the approach presented here, the phase fluctuations are identified as the low-lying Bogoliubov modes. Their properties have been investigated in detail to understand which changes trigger the phase transition and we found that the transition to the insulating phase is accompanied by a diverging density of states and a localization length, measured through the inverse participation ratio, that diverges as a power-law with power – 1 for vanishing energy. The fragmentation of the gas is also studied: this notion is very often associated with the onset of the insulating phase. The characterization of the density fragmentation is performed by analyzing the probability distribution of the density. A density profile is defined as fragmented when the probability distribution at vanishing density is finite or divergent and this happens for a gas in the Bose-glass phase. On the contrary, the superfluid phase is characterized by a zero limiting probability of having vanishing densities. This definition is derived analytically, and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments: when a harmonic trap is included, the transition to the insulating phase can be extracted from the statistics of the local density distribution.
A new approach developed in Ref.1 for investigating the spatial boson correlations at low temperatures is considered in the particular case of the Coulomb interaction potential. This approach is based on integro–differential equations for the radial distribution function and can be used beyond the weak coupling regime. PACS: 05.30.Jp, 67.90.+z Description of the charged Bose liquid, or, in other words, of the strongly correlated many–boson system with the Coulomb interparticle potential, is a long–standing problem of the condensed matter physics. Recently, interest in this problem has been renewed in the connection with the noteworthy results of applying the Bose and Bose–Fermi liquid models [2] to the explanation of various phenomena inherent in the superconductors with high critical temperatures. These models are based on the Bogoliubov approach [3] implying the weak coupling regime. For the system of charged bosons the weak coupling approximation can be used at small values of the Brueckner parameter rS ∼ 0.1. However, questions requiring detailed investigations often concern the materials with relatively low densities of charge carriers which correspond to rS−values even larger than those of the electron gas at 1 the metallic densities. For example, there are the results [4] testifying to the possibility of forming the so–called large bipolaron (e.g. the two–electron cluster with a large radius of electron–electron separation, see papers in Ref. [5]) inside the polaron environment at the electron densities ∼ 10 19 cm −3 close to the carrier densities of the heavily doped degenerate polar semiconductors. To investigate the possible phase transition of the charge carrier system from the polaron state to the bipolaron phase at these densities, one should operate with the charged Bose liquid of large bipolarons for rS ≫ 1. Indeed, the ”large–bipolaron“ Bohr radius can be expressed [4] as abip =