2010

Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems

Guan, X. -W., Batchelor, M. T.

Understand

We demonstrate that the thermodynamics of one-dimensional Lieb-Liniger bosons can be accurately calculated in analytic fashion using the polylog function in the framework of the thermodynamic Bethe ansatz.

The approach does away with the need to numerically solve the thermodynamic Bethe ansatz (Yang-Yang) equation.
The expression for the equation of state allows the exploration of Tomonaga-Luttinger liquid physics and quantum criticality in an archetypical quantum system.
In particular, the low-temperature phase diagram is obtained, along with the scaling functions for the density and compressibility.

Built on

Lieb E H and Liniger W 1963 Phys. Rev
1963
Earlier work this paper cites.
Yang C N 1967 Phys. Rev. Lett
1967
Earlier work this paper cites.
Gaudin M 1967 Phys. Lett
1967
Earlier work this paper cites.
Yang C N and Yang C P 1969 J. Math. Phys
1969
Earlier work this paper cites.
Lewin L 1981 Polylogarithms and Associated Functions
1981
Earlier work this paper cites.
Korepin V E, Izergin A G and Bogoliubov N M 1993 Quantum Inverse Scattering Method and Correlation Functions
1993
Earlier work this paper cites.
Takahashi M 1999 Thermodynamics of One-Dimensional Solvable Models
1999
Earlier work this paper cites.
Cazalilla M A 2004 J. Phys. B
2004
Earlier work this paper cites.
Petrov D S, Gangardt D M and Shlyapnikov G V 2004 J. Phys. IV France
2004
Earlier work this paper cites.
Kinoshita T, Wenger T and Weiss D S 2004 Science
2004
Earlier work this paper cites.
Giamarchi T 2004 Quantum Physics in One Dimension
2004
Earlier work this paper cites.
Kinoshita T, Wenger T and Weiss D S 2005 Phys. Rev. Lett
2005
Earlier work this paper cites.
Gangardt D M and Shlyapnikov G V 2003 Phys. Rev. Lett
2005
Earlier work this paper cites.

Similar

Batchelor M T 2007 Physics Today
2007
Cited alongside, same era.
Guan X W, Batchelor M T and Takahashi M 2007 Phys. Rev. A
2007
Cited alongside, same era.
Batchelor M T and Guan X W 2006 Phys. Rev. B
2007
Cited alongside, same era.
Guan X W, Batchelor M T, Lee C and Bortz M 2007 Phys. Rev. B
2007
Cited alongside, same era.
Orso G 2007 Phys. Rev. Lett
2007
Cited alongside, same era.
Hu H, Liu X J and Drummond P D 2007 Phys. Rev. Lett
2007
Cited alongside, same era.
Yurovsky V A, Olshanii M and Weiss D S 2008 Adv. Atom. Mole. Opt. Phys. 55
2008
Cited alongside, same era.
Pethick C J and Smith H 2008 Bose-Einstein Condensation in Dilute Gases
2008
Cited alongside, same era.
van Amerongen A H, van Es JJP, Wicke P, Kheruntsyan K V and van Druten N J 2008 Phys. Rev. Lett
2008
Cited alongside, same era.
Iida T and Wadati M 2008 J Phys. Soc. Jpn
2008
Cited alongside, same era.
Casula M, Ceperley D M and Mueller E J 2008 Phys. Rev. A
2008
Cited alongside, same era.
Feiguin A E and Heidrich-Meisner F 2008 Phys. Rev. B 76
2008
Cited alongside, same era.

Then

Haller E, Gustavsson M, Mark M J, Danzl J G, Hart R, Pupillo G and Nagerl H C 2009 Science
2009
Later among the works it cites.
Zhao E, Guan X W, Liu W V, Batchelor M T and Oshikawa M 2009 Phys. Rev. Lett
2009
Later among the works it cites.
Kormos M, Mussardo G and Trombettoni A 2009 Phys Rev. Lett
2009
Later among the works it cites.
Kakashvili P and Bolech C J 2009 Phys. Rev. A
2009
Later among the works it cites.
Edge J M and Cooper N R 2009 Phys. Rev. Lett
2009
Later among the works it cites.
Guan L, Chen S, Wang Y P and Ma Z-Q 2009 Phys. Rev. Lett
2009
Later among the works it cites.
Ma Z-Q and Yang C N 2009 Chinese Phys. Lett
2009
Later among the works it cites.
Guan X W, Lee J Y, Batchelor M T, Yin X G and Chen S 2010 Phys. Rev. A
2010
Closest in time.
Liao Y et al., Nature 467
2010
Closest in time.
Nascimbene S, Navon N, Jiang K J, Chevy F and Salomon C 2010 Nature
2010
Closest in time.
Horikoshi M, Nakajima S, Ueda M and Mukaiyama T 2010 Science
2010
Closest in time.
T L Ho and Q Zhou 2010 Nature Physics
Original
2010
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…