Low energy properties of the supersymmetric Haldane–Shastry spin chain

Basu-Mallick, B.; Bondyopadhaya, Nilanjan; Sen, Diptiman

doi:10.1016/j.nuclphysb.2007.11.021

Cited by 31 publications

(58 citation statements)

References 35 publications

(74 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A similar result was obtained in Ref. 31 for the supersymmetric su͉͑1͉1͒ ͑fer-romagnetic͒ HS chain, although in the latter case the energy of the ith fermion is E i = i͑N − i͒.…”

Section: ͑19͒supporting

confidence: 86%

Polychronakos-Frahm spin chain ofBCNtype and the Berry-Tabor conjecture

et al. 2008

View full text Add to dashboard Cite

We compute the partition function of the su͑m͒ Polychronakos-Frahm spin chain of BC N type by means of the freezing trick. We use this partition function to study several statistical properties of the spectrum, which turn out to be analogous to those of other spin chains of Haldane-Shastry type. In particular, we find that when the number of particles is sufficiently large the level density follows a Gaussian distribution with great accuracy. We also show that the distribution of ͑normalized͒ spacings between consecutive levels is of neither Poisson nor Wigner type but is qualitatively similar to that of the original Haldane-Shastry spin chain. This suggests that spin chains of Haldane-Shastry type are exceptional integrable models since they do not satisfy a well-known conjecture of Berry and Tabor, according to which the spacings distribution of a generic integrable system should be Poissonian. We derive a simple analytic expression for the cumulative spacings distribution of the BC N -type Polychronakos-Frahm chain using only a few essential properties of its spectrum such as the Gaussian character of the level density and the fact that the energy levels are equally spaced. This expression is shown to be in excellent agreement with the numerical data.

show abstract

“…A similar result was obtained in Ref. 31 for the supersymmetric su͉͑1͉1͒ ͑fer-romagnetic͒ HS chain, although in the latter case the energy of the ith fermion is E i = i͑N − i͒.…”

Section: ͑19͒supporting

confidence: 86%

Polychronakos-Frahm spin chain ofBCNtype and the Berry-Tabor conjecture

et al. 2008

View full text Add to dashboard Cite

show abstract

“…The same is true for the su(m|n) HS chain with m 1, by virtue of the relation between the partition functions of the supersymmetric PF and HS chains established in Ref. [7]. The criticality of the su(1|1) HS chain with a chemical potential was also proved in Ref.…”

Section: Introductionmentioning

confidence: 63%

Thermodynamics and criticality of supersymmetric spin chains with long-range interactions

Finkel¹,

González‐López²,

León³

et al. 2018

J. Stat. Mech.

View full text Add to dashboard Cite

We study the thermodynamics and critical behavior of su(m|n) supersymmetric spin chains of Haldane-Shastry type with a chemical potential term. We obtain a closed-form expression for the partition function and deduce a description of the spectrum in terms of the supersymmetric version of Haldane's motifs, which we apply to obtain an analytic expression for the free energy per site in the thermodynamic limit. By studying the low-temperature behavior of the free energy, we characterize the critical behavior of the chains with 1 m, n 2, determining the critical regions and the corresponding central charge. We also show that in the su(2|1), su(1|2) and su(2|2) chains the bosonic or fermionic densities can undergo first-order (discontinuous) phase transitions at T = 0, in contrast with the previously studied su(2) case.Keywords: integrable spin chains and vertex models, solvable lattice models, quantum criticality, quantum phase transitions arXiv:1712.08536v2 [cond-mat.stat-mech]

show abstract

“…Eqs. (16), (26)-(34), (47)-(48), (57)-(58). As a matter of fact, we have already proved that the number of distinct levels of the su(2) PF chain is a second degree polynomial in N; see Eq.…”

Section: Average Degeneracy Of Spin Chains Of Haldane-shastry Typementioning

confidence: 99%

“…This model appears in connection with a wide variety of topics in theoretical and mathematical physics, including one-dimensional anyons [3,5,8,14], conformal field theory [15][16][17][18], quantum chaos [19][20][21][22], quantum information theory [23], and quantum integrability [12,24,25]. A distinctive feature of the HS chain is the fact that it can be obtained from a dynamical model, namely the spin Sutherland (trigonometric) model [26][27][28], in the strong coupling limit [9].…”

Section: Introductionmentioning

confidence: 99%

Yangian-invariant spin models and Fibonacci numbers

Finkel

González‐López

2015

Annals of Physics

View full text Add to dashboard Cite

We study a wide class of finite-dimensional su(m|n)-supersymmetric models closely related to the representations of the Yangian Y(sl(m|n)) labeled by border strips. We quantitatively analyze the degree of degeneracy of these models arising from their Yangian invariance, measured by the average degeneracy of the spectrum. We compute in closed form the minimum average degeneracy of any such model, and show that in the non-supersymmetric case it can be expressed in terms of generalized Fibonacci numbers. Using several properties of these numbers, we show that (except in the simpler su(1|1) case) the minimum average degeneracy grows exponentially with the number of spins. We apply our results to several well-known spin chains of Haldane-Shastry type, quantitatively showing that their degree of degeneracy is much higher than expected for a generic Yangian-invariant spin model. Finally, we show that the set of distinct levels of a Yangian-invariant spin model is described by an effective model of quasi-particles. We study this effective model, discussing its connections to one-dimensional anyons and properties of generalized Fibonacci numbers.Comment: LaTex, 31 pages, 7 figures. Minor additions in Section 2, one reference also adde

show abstract

Low energy properties of the supersymmetric Haldane–Shastry spin chain

Cited by 31 publications

References 35 publications

Polychronakos-Frahm spin chain ofBCNtype and the Berry-Tabor conjecture

Polychronakos-Frahm spin chain ofBCNtype and the Berry-Tabor conjecture

Thermodynamics and criticality of supersymmetric spin chains with long-range interactions

Yangian-invariant spin models and Fibonacci numbers

Contact Info

Product

Resources

About