A new set of renormalization equations for the two-dimensional Coulomb gas is derived and solved numerically. These equations give a new picture of the Kosterlitz-Thouless transition. A new temperature ${T}^{\mathrm{*}}$ is found. Above ${T}^{\mathrm{*}}$ the value of the dielectric constant at the transition is ${\ensuremath{\epsilon}}_{c}$=1/(4 ${T}_{c}$ ) as before whereas below ${T}^{\mathrm{*}}$ the new result ${\ensuremath{\epsilon}}_{c} $1/(4$ {T}_{c}$) is obtained. The singular behavior at ${T}^{\mathrm{*}}$ is explored. The results are translated into a renormalization-group flow diagram. An interesting consequence is that the universal jump prediction for the Kosterlitz-Thouless transition turns into a nonuniversal jump prediction for critical temperatures below ${T}^{\mathrm{*}}$ .A new set of renormalization equations for the two-dimensional Coulomb gas is derived and solved numerically. These equations give a new picture of the Kosterlitz-Thouless transition. A new temperature ${T}^{\mathrm{*}}$ is found. Above ${T}^{\mathrm{*}}$ the value of the dielectric constant at the transition is ${\ensuremath{\epsilon}}_{c}$=1/(4${T}_{c}$) as before whereas below ${T}^{\mathrm{*}}$ the new result ${\ensuremath{\epsilon}}_{c}$1/(4${T}_{c}$) is obtained. The singular behavior at ${T}^{\mathrm{*}}$ is explored. The results are translated into a renormalization-group flow diagram. An interesting consequence is that the universal jump prediction for the Kosterlitz-Thouless transition turns into a nonuniversal jump prediction for critical temperatures below ${T}^{\mathrm{*}}$.

Physical review. B, Condensed matterSep 1, 198559 citations

Berezinskii-Kosterlitz-Thouless Transition

Pedro D Sacramento

Springer eBooksJan 1, 20250 citations

Observation of the universal jump across the Berezinskii-Kosterlitz-Thouless transition in two-dimensional Bose gases

Jiho Noh, Jeongwon Lee, Jongchul Mun

The physics in two-dimensional (2D) systems is very different from what we observe in three-dimensional (3D) systems. Thermal fluctuations in 2D systems are enhanced, and they prevent the conventional Bose-Einstein condensation (BEC) at non-zero temperatures by destroying the long-range order. However, a phase transition to a superfluid phase is still expected to occur in a 2D system along with an emergence of a quasi-long-range order, explained by the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. Within the BKT mechanism, a universal jump of the superfluid density in a 2D Bosonic system was theoretically predicted by Nelson and Kosterlitz, and was first observed in 2D \textsuperscript{4}He films by Bishop and Reppy. Recent experiments in trapped ultracold 2D Bose gas systems have shown signatures of the BKT transition, and its superfluidity. However, the universal jump in the superfluid density was not observed in these systems. Here we report the first observation of the universal jump in the superfluid density using an optically trapped ultracold 2D Bose gas. The measured superfluid phase space density at the BKT transition agrees well with the predicted value within our measurement uncertainty. Additionally, we measure the phase fluctuations in our density profiles to show that the BKT transition occurs first, followed by the BEC transition.The physics in two-dimensional (2D) systems is very different from what we observe in three-dimensional (3D) systems. Thermal fluctuations in 2D systems are enhanced, and they prevent the conventional Bose-Einstein condensation (BEC) at non-zero temperatures by destroying the long-range order. However, a phase transition to a superfluid phase is still expected to occur in a 2D system along with an emergence of a quasi-long-range order, explained by the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. Within the BKT mechanism, a universal jump of the superfluid density in a 2D Bosonic system was theoretically predicted by Nelson and Kosterlitz, and was first observed in 2D \textsuperscript{4}He films by Bishop and Reppy. Recent experiments in trapped ultracold 2D Bose gas systems have shown signatures of the BKT transition, and its superfluidity. However, the universal jump in the superfluid density was not observed in these systems. Here we report the first observation of the universal jump in the superfluid density using an optically trapped ultracold 2D Bose gas. The measured superfluid phase space density at the BKT transition agrees well with the predicted value within our measurement uncertainty. Additionally, we measure the phase fluctuations in our density profiles to show that the BKT transition occurs first, followed by the BEC transition.

arXiv:1305.1423May 7, 20130 citations

The Quantum Spring

The MIT Press eBooksOct 13, 20260 citations

Kosterlitz-Thouless transition in a dilute Bose gas

Henk T. C. Stoof, M. Bijlsma

We study the two-dimensional dilute Bose gas using the ladder or T-matrix approximation, which is valid if ln(1/ ${\mathit{na}}^{2}$ )\ensuremath{\gg}1, and show that this approximation can describe also the critical region of the Kosterlitz-Thouless transition accurately. In particular, we consider the superfluid properties of the gas and find that the superfluid density shows the square-root cusp together with the universal jump at the critical temperature. The theory is applied to spin-polarized atomic hydrogen adsorbed on a superfluid helium film, since this appears to be one of the most promising experimental setups to achieve the Kosterlitz-Thouless transition in a weakly interacting Bose gas.We study the two-dimensional dilute Bose gas using the ladder or T-matrix approximation, which is valid if ln(1/${\mathit{na}}^{2}$)\ensuremath{\gg}1, and show that this approximation can describe also the critical region of the Kosterlitz-Thouless transition accurately. In particular, we consider the superfluid properties of the gas and find that the superfluid density shows the square-root cusp together with the universal jump at the critical temperature. The theory is applied to spin-polarized atomic hydrogen adsorbed on a superfluid helium film, since this appears to be one of the most promising experimental setups to achieve the Kosterlitz-Thouless transition in a weakly interacting Bose gas.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsFeb 1, 199344 citations

{T}^{\mathrm{*}}

is found. Above

{T}^{\mathrm{*}}

the value of the dielectric constant at the transition is ${\ensuremath{\epsilon}}_{c}$=1/(4

{T}_{c}

) as before whereas below

{T}^{\mathrm{*}}

the new result ${\ensuremath{\epsilon}}_{c}

1/(4

{T}_{c}$) is obtained. The singular behavior at

{T}^{\mathrm{*}}

is explored. The results are translated into a renormalization-group flow diagram. An interesting consequence is that the universal jump prediction for the Kosterlitz-Thouless transition turns into a nonuniversal jump prediction for critical temperatures below

{T}^{\mathrm{*}}

We study the two-dimensional dilute Bose gas using the ladder or T-matrix approximation, which is valid if ln(1/

{\mathit{na}}^{2}

)\ensuremath{\gg}1, and show that this approximation can describe also the critical region of the Kosterlitz-Thouless transition accurately. In particular, we consider the superfluid properties of the gas and find that the superfluid density shows the square-root cusp together with the universal jump at the critical temperature. The theory is applied to spin-polarized atomic hydrogen adsorbed on a superfluid helium film, since this appears to be one of the most promising experimental setups to achieve the Kosterlitz-Thouless transition in a weakly interacting Bose gas.