Modern Physics Letters B

CRITICAL BEHAVIOR OF A TWO-DIMENSIONAL DILUTE BOSE GAS

M. Crişan, I. Ţifrea, D. Bodea, I. Grosu

Published Aug 30, 2001• 1 citation

Abstract

We applied the Renormalization Group method at finite temperature to reconsider the two-dimensional dilute Bose gas. The general flow equations are obtained for the case of arbitrary dimensions, and by considering the two-dimensional limit, we estimate the value of the critical temperature, coherence length and specific heat. The value of the critical temperature is in agreement with previous calculations performed using the t-matrix method. The coherence length and the specific heat present a non-universal behavior, a logarithmic temperature dependence in the critical region being identified.

DOI: 10.1142/s0217984901002634

Related papers

Renormalization-group analysis of the dilute Bose system inddimensions at finite temperature

M. Crişan, D. Bodea, I. Grosu +1 more

arXiv:cond-mat/0101391Journal of Physics A Mathematical and GeneralJan 7, 200217 citations

Three-dimensional dilute Bose liquid at finite temperature: a Renormalization Group approach

M. Crişan, Marina Bianca Trif, I. Grosu +1 more

Physics and Chemistry of LiquidsFeb 1, 20070 citations

QUANTUM EFFECTS IN THE THREE-DIMENSIONAL DILUTE BOSE SYSTEM AT FINITE TEMPERATURE: RENORMALIZATION GROUP APPROACH

M. Crişan, Marina Bianca Trif, I. Grosu

Modern Physics Letters BAug 30, 20060 citations

Thermodynamics and renormalized quasiparticles in the vicinity of the dilute Bose gas quantum critical point in two dimensions

Jan Krieg, Dominik Straßel, Simon Streib +2 more

arXiv:1607.01015Physical review. B./Physical review. BJan 13, 20173 citations

Universal thermodynamics of a two-dimensional Bose gas

Adam Rançon, N. Dupuis

arXiv:1203.1788Physical Review AJun 5, 201255 citations

Critical temperature and thermodynamic properties of a homogeneous dilute weakly interacting Bose gas within the improved Hartree-Fock approximation at finite temperature

Nguyễn Văn Thụ, Thanh, Pham Duy

arXiv:2311.13822Nov 23, 20230 citations

Modern Physics Letters B

CRITICAL BEHAVIOR OF A TWO-DIMENSIONAL DILUTE BOSE GAS

M. Crişan, I. Ţifrea, D. Bodea, I. Grosu

Published Aug 30, 2001• 1 citation

Publisher

Abstract

DOI: 10.1142/s0217984901002634

Related papers

Renormalization-group analysis of the dilute Bose system inddimensions at finite temperature

M. Crişan, D. Bodea, I. Grosu +1 more

We study the d -dimensional Bose gas at finite temperature using the renormalization-group method. The flow-equations and the free energy are obtained for dimension d , and the cases d < 2 and d = 2 have been analysed in the limit of low and high temperatures. The critical temperature, the coherence length and the specific heat of a two-dimensional Bose gas are obtained using a regular solution for the coupling constant which is obtained from the scaling equations. The relevance of the dilute Bose gas for recent experimental results is also discussed.We study the d -dimensional Bose gas at finite temperature using the renormalization-group method. The flow-equations and the free energy are obtained for dimension d , and the cases d < 2 and d = 2 have been analysed in the limit of low and high temperatures. The critical temperature, the coherence length and the specific heat of a two-dimensional Bose gas are obtained using a regular solution for the coupling constant which is obtained from the scaling equations. The relevance of the dilute Bose gas for recent experimental results is also discussed.

arXiv:cond-mat/0101391Journal of Physics A Mathematical and GeneralJan 7, 200217 citations

Three-dimensional dilute Bose liquid at finite temperature: a Renormalization Group approach

M. Crişan, Marina Bianca Trif, I. Grosu +1 more

We consider the influence of temperature on the critical behavior of a weakly interacting three dimensional Bose system. Using the flow equations of the Renormalization Group and a Φ4 model with dynamical critical exponent z = 2, we calculated the critical exponent ν, and the thermodynamical parameters near the critical temperature, taking in consideration the quantum effects. The quantum effects considered using this method gives for ν the value 0.75, which is close to the value 0.73 obtained by the polynomial method. The critical temperature shift ΔT c was obtained, in the lowest-order approximation, and turns out to be proportional to the scattering length.We consider the influence of temperature on the critical behavior of a weakly interacting three dimensional Bose system. Using the flow equations of the Renormalization Group and a Φ4 model with dynamical critical exponent z = 2, we calculated the critical exponent ν, and the thermodynamical parameters near the critical temperature, taking in consideration the quantum effects. The quantum effects considered using this method gives for ν the value 0.75, which is close to the value 0.73 obtained by the polynomial method. The critical temperature shift ΔT c was obtained, in the lowest-order approximation, and turns out to be proportional to the scattering length.

Physics and Chemistry of LiquidsFeb 1, 20070 citations

QUANTUM EFFECTS IN THE THREE-DIMENSIONAL DILUTE BOSE SYSTEM AT FINITE TEMPERATURE: RENORMALIZATION GROUP APPROACH

M. Crişan, Marina Bianca Trif, I. Grosu

We consider the influence of temperature on the critical behavior of the weakly interacting three-dimensional Bose system. Using the flow equations of the Renormalization group and a Φ4 model with dynamical critical exponent z = 2, we calculated the critical exponent ν, and the thermodynamic parameters near the critical temperature, taking into consideration the quantum effects. The quantum effects considered in this method gives ν the value 0.75, which is close to the value 0.73 obtained by the polynomial method. The critical temperature shift ΔTc was obtained, in the lowest order approximation, proportional to the scattering length.We consider the influence of temperature on the critical behavior of the weakly interacting three-dimensional Bose system. Using the flow equations of the Renormalization group and a Φ4 model with dynamical critical exponent z = 2, we calculated the critical exponent ν, and the thermodynamic parameters near the critical temperature, taking into consideration the quantum effects. The quantum effects considered in this method gives ν the value 0.75, which is close to the value 0.73 obtained by the polynomial method. The critical temperature shift ΔTc was obtained, in the lowest order approximation, proportional to the scattering length.

Modern Physics Letters BAug 30, 20060 citations

Thermodynamics and renormalized quasiparticles in the vicinity of the dilute Bose gas quantum critical point in two dimensions

Jan Krieg, Dominik Straßel, Simon Streib +2 more

We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wave-function renormalization and effective mass) of interacting bosons in two dimensions as a function of temperature $T$ and chemical potential $\ensuremath{\mu}$. We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization-group calculations for thermodynamic observables at $\ensuremath{\mu}=0$ to finite values of $\ensuremath{\mu}$. To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, susceptibility, and correlation length of the two-dimensional spin- $1/2$ quantum $XY$ model with coupling $J$ in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for $\ensuremath{\mu}\ensuremath{\le}0$ rather accurately up to relatively high temperatures $T\ensuremath{\lesssim}0.1J$.We use the functional renormalization group (FRG) to derive analytical expressions for thermodynamic observables (density, pressure, entropy, and compressibility) as well as for single-particle properties (wave-function renormalization and effective mass) of interacting bosons in two dimensions as a function of temperature $T$ and chemical potential $\ensuremath{\mu}$. We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization-group calculations for thermodynamic observables at $\ensuremath{\mu}=0$ to finite values of $\ensuremath{\mu}$. To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, susceptibility, and correlation length of the two-dimensional spin-$1/2$ quantum $XY$ model with coupling $J$ in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for $\ensuremath{\mu}\ensuremath{\le}0$ rather accurately up to relatively high temperatures $T\ensuremath{\lesssim}0.1J$.

arXiv:1607.01015Physical review. B./Physical review. BJan 13, 20173 citations

Universal thermodynamics of a two-dimensional Bose gas

Adam Rançon, N. Dupuis

Using renormalization-group arguments we show that the low-temperature thermodynamics of a three- or two-dimensional dilute Bose gas is fully determined by a universal scaling function ${\mathcal{F}}_{d}(\ensuremath{\mu}/{k}_{B}T,\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}(T))$ once the mass $m$ and the $s$ -wave scattering length ${a}_{d}$ of the bosons are known ( $d$ is the space dimension). Here $\ensuremath{\mu}$ and $T$ denote the chemical potential and temperature of the gas, and the temperature-dependent dimensionless interaction constant $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}(T)$ is a function of $m{a}_{d}^{2}{k}_{B}T/{\ensuremath{\hbar}}^{2}$. We compute the scaling function ${\mathcal{F}}_{2}$ using a nonperturbative renormalization-group approach and find that both the $\ensuremath{\mu}/{k}_{B}T$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}(T)$ dependencies are in very good agreement with recent experimental data obtained for a quasi-two-dimensional Bose gas with or without optical lattice. We also show that the nonperturbative renormalization-group estimate of the Berezinskii-Kosterlitz-Thouless transition temperature compares well with the result obtained from a quantum Monte Carlo simulation of an effective classical field theory.Using renormalization-group arguments we show that the low-temperature thermodynamics of a three- or two-dimensional dilute Bose gas is fully determined by a universal scaling function ${\mathcal{F}}_{d}(\ensuremath{\mu}/{k}_{B}T,\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}(T))$ once the mass $m$ and the $s$-wave scattering length ${a}_{d}$ of the bosons are known ($d$ is the space dimension). Here $\ensuremath{\mu}$ and $T$ denote the chemical potential and temperature of the gas, and the temperature-dependent dimensionless interaction constant $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}(T)$ is a function of $m{a}_{d}^{2}{k}_{B}T/{\ensuremath{\hbar}}^{2}$. We compute the scaling function ${\mathcal{F}}_{2}$ using a nonperturbative renormalization-group approach and find that both the $\ensuremath{\mu}/{k}_{B}T$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}(T)$ dependencies are in very good agreement with recent experimental data obtained for a quasi-two-dimensional Bose gas with or without optical lattice. We also show that the nonperturbative renormalization-group estimate of the Berezinskii-Kosterlitz-Thouless transition temperature compares well with the result obtained from a quantum Monte Carlo simulation of an effective classical field theory.

arXiv:1203.1788Physical Review AJun 5, 201255 citations

Critical temperature and thermodynamic properties of a homogeneous dilute weakly interacting Bose gas within the improved Hartree-Fock approximation at finite temperature

Nguyễn Văn Thụ, Thanh, Pham Duy

By means of Cornwall-Jackiw-Tomboulis effective action approach we investigate a homogeneous dilute weakly interacting Bose gas at finite temperature in vicinity of critical region. A longstanding debate, the shift of critical temperature, is considered and obtained in the universal form $ΔT_C/T_C^{(0)} = cn_0^{1/3}a_s$ with constants $c$ and $a$ . The non-condensate fraction is contributed by quantum fluctuations as well as thermal exitations and can be expressed in sum of three terms. These terms correspond to the quantum fluctuations, thermal fluctuations and both. Indeed, the specific heat capacity and critical exponents are calculated and in excellent agreement with those in previous works and experimental data.By means of Cornwall-Jackiw-Tomboulis effective action approach we investigate a homogeneous dilute weakly interacting Bose gas at finite temperature in vicinity of critical region. A longstanding debate, the shift of critical temperature, is considered and obtained in the universal form $ΔT_C/T_C^{(0)} = cn_0^{1/3}a_s$ with constants $c$ and $a$. The non-condensate fraction is contributed by quantum fluctuations as well as thermal exitations and can be expressed in sum of three terms. These terms correspond to the quantum fluctuations, thermal fluctuations and both. Indeed, the specific heat capacity and critical exponents are calculated and in excellent agreement with those in previous works and experimental data.

arXiv:2311.13822Nov 23, 20230 citations

T

and chemical potential $\ensuremath{\mu}$. We focus on the quantum disordered and the quantum critical regime close to the dilute Bose gas quantum critical point. Our approach is based on a truncated vertex expansion of the hierarchy of FRG flow equations and the decoupling of the two-body contact interaction in the particle-particle channel using a suitable Hubbard-Stratonovich transformation. Our analytic FRG results extend previous analytical renormalization-group calculations for thermodynamic observables at $\ensuremath{\mu}=0$ to finite values of $\ensuremath{\mu}$. To confirm the validity of our FRG approach, we have also performed quantum Monte Carlo simulations to obtain the magnetization, susceptibility, and correlation length of the two-dimensional spin-

1/2

quantum

XY

model with coupling

J

in a regime where its quantum critical behavior is controlled by the dilute Bose gas quantum critical point. We find that our analytical results describe the Monte Carlo data for $\ensuremath{\mu}\ensuremath{\le}0$ rather accurately up to relatively high temperatures $T\ensuremath{\lesssim}0.1J$.

m

and the

s

-wave scattering length

{a}_{d}

of the bosons are known (

d

is the space dimension). Here $\ensuremath{\mu}$ and

T

denote the chemical potential and temperature of the gas, and the temperature-dependent dimensionless interaction constant $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}(T)$ is a function of $m{a}_{d}^{2}{k}_{B}T/{\ensuremath{\hbar}}^{2}$. We compute the scaling function

{\mathcal{F}}_{2}

using a nonperturbative renormalization-group approach and find that both the $\ensuremath{\mu}/{k}_{B}T$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}(T)$ dependencies are in very good agreement with recent experimental data obtained for a quasi-two-dimensional Bose gas with or without optical lattice. We also show that the nonperturbative renormalization-group estimate of the Berezinskii-Kosterlitz-Thouless transition temperature compares well with the result obtained from a quantum Monte Carlo simulation of an effective classical field theory.

ΔT_C/T_C^{(0)} = cn_0^{1/3}a_s

with constants

c

and

a

. The non-condensate fraction is contributed by quantum fluctuations as well as thermal exitations and can be expressed in sum of three terms. These terms correspond to the quantum fluctuations, thermal fluctuations and both. Indeed, the specific heat capacity and critical exponents are calculated and in excellent agreement with those in previous works and experimental data.