Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Asymptotic form of level density distributions for a class of inhomogeneous 1D vertex models

Pratyay Banerjee, B. Basu-Mallick

Published Jan 28, 2013• 0 citations
Publisher

Abstract

Level density distributions for some Haldane-Shastry like spin chains associated with A N −1 root system have been computed recently by Enciso et al. , using the connection of these spin chains with inhomogeneous one-dimensional vertex models. The energy functions of such vertex models are given by specific polynomials of first or second degree. Here we consider a much broader class of one-dimensional vertex models whose energy functions are given by arbitrary polynomials of any possible degree and show that the level densities for this class of vertex models asymptotically follow the Gaussian distribution for large number of vertices.

DOI
10.1088/1742-6596/411/1/012005

Related papers

Level density distribution for one-dimensional vertex models related to Haldane-Shastry like spin chains

Pratyay Banerjee, B. Basu-Mallick

The energy level density distributions of some Haldane-Shastry like spin chains associated with the AN − 1 root system have been computed recently by Enciso et al., exploiting the connection of these spin systems with inhomogeneous one-dimensional vertex models whose energy functions depend on the vertices through specific polynomials of first or second degree. Here we consider a much broader class of one-dimensional vertex models whose energy functions depend on the vertices through arbitrary polynomials of any possible degree. We estimate the order of mean and variance for such energy functions and show that the level density distribution of all vertex models belonging to this class asymptotically follow the Gaussian pattern for large number of vertices. We also present some numerical evidence in support of this analytical result.

arXiv:1111.4376•Journal of Mathematical Physics•Aug 1, 2012•9 citations

One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains

B. Basu-Mallick

We define a class of Y (sl (m|n) ) Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials.Using some properties of the super Schur polynomials, we show that the partition functions of this class of spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions.We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by using their correspondence with onedimensional vertex models.

arXiv:1008.5285•Symmetry Integrability and Geometry Methods and Applications•Dec 10, 2010•10 citations

Level density of spin chains of Haldane-Shastry type

Alberto Enciso B, Federico Finkel, Artemio González-López

We provide a rigorous proof of the fact that the level density of all known su(m) spin chains of Haldane-Shastry type associated with the A(N-1) root system approaches a Gaussian distribution as the number of spins N tends to infinity. Our approach is based on the study of the large-N limit of the characteristic function of the level density, using the description of the spectrum in terms of motifs and the asymptotic behavior of the transfer matrix.

arXiv:1005.3202•Physical Review E•Nov 15, 2010•23 citations

Spin chains of Haldane-Shastry type and a generalized central limit theorem

Alberto Enciso B, Federico Finkel, Artemio González-López

We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a variant of the central limit theorem which is especially suited to models whose partition function is explicitly known. In particular, we provide a theoretical explanation of the fact that the level density of several spin chains of Haldane-Shastry type is asymptotically Gaussian when the number of sites tends to infinity.

arXiv:0903.4761•Physical Review E•Jun 19, 2009•8 citations

Global properties of the spectrum of the Haldane-Shastry spin chain

Federico Finkel, Artemio González-López

We derive an exact expression for the partition function of the $\mathrm{su}(m)$ Haldane-Shastry spin chain, which we use to study the density of levels and the distribution of the spacing between consecutive levels. Our computations show that when the number of sites $N$ is large enough, the level density is Gaussian to a very high degree of approximation. More surprisingly, we also find that the nearest-neighbor spacing distribution is not Poissonian, so that this model departs from the typical behavior for an integrable system. We show that the cumulative spacing distribution of the model can be well approximated by a simple functional law involving only three parameters.

arXiv:cond-mat/0509032•Physical Review B•Nov 8, 2005•61 citations

Generalized Lipkin–Meshkov–Glick models of Haldane–Shastry type

José A Carrasco, Federico Finkel, Artemio González-López

Abstract We introduce a class of generalized Lipkin–Meshkov–Glick (gLMG) models with s u ( m ) interactions of Haldane–Shastry type. We compute the partition function of these models in closed form by exactly evaluating the partition function of the restriction of a spin chain Hamiltonian of Haldane–Shastry type to subspaces with well-defined magnon numbers. As a byproduct of our analysis, we obtain strong numerical evidence of the Gaussian character of the level density of the latter restricted Hamiltonians, and study the distribution of the spacings of consecutive unfolded levels. We also discuss the thermodynamic behavior of a large family of s u ( 2 ) and s u ( 3 ) gLMG models, showing that it is qualitatively similar to that of a two-level system.

arXiv:1706.08751•Journal of Statistical Mechanics Theory and Experiment•Oct 1, 2017•0 citations
Level density distributions for some Haldane-Shastry like spin chains associated with A N −1 root system have been computed recently by Enciso et al. , using the connection of these spin chains with inhomogeneous one-dimensional vertex models. The energy functions of such vertex models are given by specific polynomials of first or second degree. Here we consider a much broader class of one-dimensional vertex models whose energy functions are given by arbitrary polynomials of any possible degree and show that the level densities for this class of vertex models asymptotically follow the Gaussian distribution for large number of vertices.
The energy level density distributions of some Haldane-Shastry like spin chains associated with the AN − 1 root system have been computed recently by Enciso et al., exploiting the connection of these spin systems with inhomogeneous one-dimensional vertex models whose energy functions depend on the vertices through specific polynomials of first or second degree. Here we consider a much broader class of one-dimensional vertex models whose energy functions depend on the vertices through arbitrary polynomials of any possible degree. We estimate the order of mean and variance for such energy functions and show that the level density distribution of all vertex models belonging to this class asymptotically follow the Gaussian pattern for large number of vertices. We also present some numerical evidence in support of this analytical result.
We define a class of Y (sl (m|n) ) Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials.Using some properties of the super Schur polynomials, we show that the partition functions of this class of spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions.We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by using their correspondence with onedimensional vertex models.
We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a variant of the central limit theorem which is especially suited to models whose partition function is explicitly known. In particular, we provide a theoretical explanation of the fact that the level density of several spin chains of Haldane-Shastry type is asymptotically Gaussian when the number of sites tends to infinity.
We derive an exact expression for the partition function of the su(m)\mathrm{su}(m)su(m) Haldane-Shastry spin chain, which we use to study the density of levels and the distribution of the spacing between consecutive levels. Our computations show that when the number of sites NNN is large enough, the level density is Gaussian to a very high degree of approximation. More surprisingly, we also find that the nearest-neighbor spacing distribution is not Poissonian, so that this model departs from the typical behavior for an integrable system. We show that the cumulative spacing distribution of the model can be well approximated by a simple functional law involving only three parameters.
Abstract We introduce a class of generalized Lipkin–Meshkov–Glick (gLMG) models with s u ( m ) interactions of Haldane–Shastry type. We compute the partition function of these models in closed form by exactly evaluating the partition function of the restriction of a spin chain Hamiltonian of Haldane–Shastry type to subspaces with well-defined magnon numbers. As a byproduct of our analysis, we obtain strong numerical evidence of the Gaussian character of the level density of the latter restricted Hamiltonians, and study the distribution of the spacings of consecutive unfolded levels. We also discuss the thermodynamic behavior of a large family of s u ( 2 ) and s u ( 3 ) gLMG models, showing that it is qualitatively similar to that of a two-level system.