Critical phenomena in one dimension from a Bethe ansatz perspective

Guan, Xi‐Wen

doi:10.1142/s0217979214300151

Cited by 14 publications

(16 citation statements)

References 199 publications

(309 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…5-6 we report the temperature dependence of the chemical potential of the system described by Hamiltonian (1) as obtained numerically from the Bethe-ansatz (BA) approach first developed by Yang-Yang [5][6][7]23] for several characteristic values of γ. The Yang-Yang description has been probed experimentally [24,25] and allows not only to investigate the thermodynamics, but also the Luttinger liquid physics and the quantum criticality of the system [26][27][28]. The numerical results for the thermodynamics have been derived recently in an analytic fashion by using the polylog functions at finite temperature by Guan and Batchelor [26,28].…”

Section: Low-temperature Expansion Of the Chemical Potentialmentioning

confidence: 99%

Thermodynamic behavior of a one-dimensional Bose gas at low temperature

2017

View full text Add to dashboard Cite

We show that the chemical potential of a one-dimensional (1D) interacting Bose gas exhibits a non-monotonic temperature dependence which is peculiar of superfluids. The effect is a direct consequence of the phononic nature of the excitation spectrum at large wavelengths exhibited by 1D Bose gases. For low temperatures T , we demonstrate that the coefficient in T 2 expansion of the chemical potential is entirely defined by the zero-temperature density dependence of the sound velocity. We calculate that coefficient along the crossover between the Bogoliubov weaklyinteracting gas and the Tonks-Girardeau gas of impenetrable bosons. Analytic expansions are provided in the asymptotic regimes. The theoretical predictions along the crossover are confirmed by comparison with the exactly solvable Yang-Yang model in which the finite-temperature equation of state is obtained numerically by solving Bethe-ansatz equations. A 1D ring geometry is equivalent to imposing periodic boundary conditions and arising finite-size effects are studied in details. At T = 0 we calculated various thermodynamic functions, including the inelastic structure factor, as a function of the number of atoms, pointing out the occurrence of important deviations from the thermodynamic limit.

show abstract

Section: Low-temperature Expansion Of the Chemical Potentialmentioning

confidence: 99%

Thermodynamic behavior of a one-dimensional Bose gas at low temperature

2017

View full text Add to dashboard Cite

show abstract

“…In this system, R W also depends on the temperature. Recently the effect of the polarization on the Wilson ratio of Fermi gases in 1D has been studied [34][35][36] . It is found that R W exhibits anomalous enhancement at critical points.…”

Section: Resultsmentioning

confidence: 99%

Theoretical investigation of the behavior of CuSe 2 O 5 compound in high magnetic fields

Saghafi

Jahangiri

Mahdavifar

et al. 2016

Journal of Magnetism and Magnetic Materials

View full text Add to dashboard Cite

Based on analytical and numerical approaches, we investigate thermodynamic properties of CuSe2O5 at high magnetic fields which is a candidate for the strong intra-chain interaction in quasi one-dimensional (1D) quantum magnets. Magnetic behavior of the system can be described by the 1D spin-1/2 XXZ model in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Under these circumstances, there is one quantum critical field in this compound. Below the quantum critical field the spin chain system is in the gapless Luttinger liquid (LL) regime, whereas above it one observes a crossover to the gapped saturation magnetic phase. Indications on the thermodynamic curves confirm the occurrence of such a phase transition. The main characteristics of the LL phase are gapless and spin-spin correlation functions decay algebraic. The effects of zero-temperature quantum phase transition are observed even at rather high temperatures in comparison with the counterpart compounds. In addition, we calculate the Wilson ratio in the model. The Wilson ratio at a fixed temperature remains almost independent of the field in the LL region. In the vicinity of the quantum critical field, the Wilson ratio increases and exhibits anomalous enhancement.

show abstract

“…This method, however, is restricted to uniform systems in the ground state (or close to it [37,38]). Finitetemperature analyses require the thermodynamic Bethe ansatz, which involves solving an infinite tower of coupled nonlinear integral equations [37,38], which leads to potentially uncontrolled approximations [39][40][41][42][43][44][45]. The Monte Carlo techniques used here, on the other hand, have well-controlled systematic and statistical uncertainties.…”

Section: Discussionmentioning

confidence: 99%

Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions

et al. 2017

View full text Add to dashboard Cite

Motivated by advances in the manipulation and detection of ultracold atoms with multiple internal degrees of freedom, we present a finite-temperature lattice Monte Carlo calculation of the density and pressure equations of state, as well as Tan's contact, of attractively interacting SU(4)-and SU(6)-symmetric fermion systems in one spatial dimension. We also furnish a nonperturbative proof of a universal relation whereby quantities computable in the SU(2) case completely determine the virial coefficients of the SU(N f ) case. These one-dimensional systems are appealing because they can be experimentally realized in highly constrained traps and because of the dominant role played by correlations. The latter are typically nonperturbative and are crucial for understanding ground states and quantum phase transitions. While quantum fluctuations are typically overpowered by thermal ones in one and two dimensions at any finite temperature, we find that quantum effects do leave their imprint in thermodynamic quantities. Our calculations show that the additional degrees of freedom, relative to the SU(2) case, provide a dramatic enhancement of the density and pressure (in units of their noninteracting counterparts) in a wide region around vanishing βµ, where β is the inverse temperature and µ the chemical potential. As shown recently in experiments, the thermodynamics we explore here can be measured in a controlled and precise fashion in highly constrained traps and optical lattices. Our results are a prediction for such experiments in one dimension with atoms of high nuclear spin.

show abstract

Critical phenomena in one dimension from a Bethe ansatz perspective

Cited by 14 publications

References 199 publications

Thermodynamic behavior of a one-dimensional Bose gas at low temperature

Thermodynamic behavior of a one-dimensional Bose gas at low temperature

Theoretical investigation of the behavior of CuSe 2 O 5 compound in high magnetic fields

Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions

Contact Info

Product

Resources

About