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

Finkel, Federico; González‐López, A.; León, Israel De; Rodrı́guez, Miguel Á.

doi:10.1088/1742-5468/aab3f4

Cited by 14 publications

(44 citation statements)

References 56 publications

(132 reference statements)

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“…In analogy with Eq. (4.1), we may now construct a one-to-one mapping between branched border strips like xk 1 , ..., k r |ly and branched motifs like pδ 1 , δ 2 , ..., δ N´1 |lq as xk 1 , ..., k r |ly ñ¨0, ..., 0 lo omo on 20) with degeneracy factor given by N pm 1 ,m 2 |n 1 ,n 2 q pδ 1 ,δ 2 ,...,δ N´1 |lq " N pm 1 ,m 2 |n 1 ,n 2 q xk 1 ,...,kr|ly , which can be computed by using Eq. (4.22).…”

Section: Spectra Of the Bc N Type Of Ferromagnetic Pf Spin Chainsmentioning

confidence: 99%

“…Moreover, by applying a rather general framework, it is possible to show that all energy eigenvalues for a class of HS like Yangian invariant quantum spin chains can be reproduced from the energy functions of some one-dimensional classical vertex models having only local interactions [18]. The above mentioned equivalence between the eigenvalues of Yangian invariant spin chains with long-range interactions and energy functions of onedimensional vertex models with only local interactions can be extended even in the presence of chemical potentials [19,20]. As a result, by using transfer matrices associated with those vertex models, one can calculate various thermodynamic quantities of this type of spin chains even in the presence of chemical potentials and investigate the critical properties of those systems [19,20,41,42].…”

Section: Introductionmentioning

confidence: 98%

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Appearance of branched motifs in the spectra of BC type Polychronakos spin chains

Basu-Mallick

Sinha

2020

Nuclear Physics B

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As is well known, energy levels appearing in the highly degenerate spectra of the A N´1 type of Haldane-Shastry and Polychronakos spin chains can be classified through the motifs, which are characterized by some sequences of the binary digits like '0' and '1'. In a similar way, at present we classify all energy levels appearing in the spectra of the BC N type of Polychronakos spin chains with Hamiltonians containing supersymmetric analogue of polarized spin reversal operators. To this end, we show that the BC N type of multivariate super Rogers-Szegö (SRS) polynomials, which at a certain limit reduce to the partition functions of the later type of Polychronakos spin chains, satisfy some recursion relation involving a q-deformation of the elementary supersymmetric polynomials. Subsequently, we use a Jacobi-Trudi like formula to define the corresponding q-deformed super Schur polynomials and derive a novel expression for the BC N type of multivariate SRS polynomials as suitable linear combinations of the q-deformed super Schur polynomials. Such an expression for SRS polynomials leads to a complete classification of all energy levels appearing in the spectra of the BC N type of Polychronakos spin chains through the 'branched' motifs, which are characterized by some sequences of integers of the form pδ 1 , δ 2 , ..., δ N´1 |lq, where δ i P t0, 1u and l P t0, 1, ..., Nu. Finally, we derive an extended boson-fermion duality relation among the restricted super Schur polynomials and show that the partition functions of the BC N type of Polychronakos spin chains also exhibit similar type of duality relation.

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Section: Spectra Of the Bc N Type Of Ferromagnetic Pf Spin Chainsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Appearance of branched motifs in the spectra of BC type Polychronakos spin chains

Basu-Mallick

Sinha

2020

Nuclear Physics B

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“…Note, finally, that the description of the spectrum of the su(m) KY model in terms of supersymmetric motifs and their associated Young tableaux derived in this paper makes it possible to compute in closed form the model's thermodynamic functions at finite temperature, by means of the transfer matrix method developed in Refs. [22,43]. In fact, work on this problem is currently in progress and shall be presented in a forthcoming publication.…”

Section: Discussionmentioning

confidence: 99%

Supersymmetric t-J models with long-range interactions: partition function and spectrum

Basu-Mallick¹,

Bondyopadhaya²,

Carrasco³

et al. 2019

J. Stat. Mech.

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We study the spectrum of the long-range supersymmetric su(m) t-J model of Kuramoto and Yokoyama in the presence of an external magnetic field and a charge chemical potential. To this end, we first establish the precise equivalence of a large class of models of this type to a family of su(1|m) spin chains with long-range exchange interactions and a suitable chemical potential term. We exploit this equivalence to compute in closed form the partition function of the long-range t-J model, which we then relate to that of an inhomogeneous vertex model with simple interactions. From the structure of this partition function we are able to deduce an exact formula for the restricted partition function of the long-range t-J model in subspaces with well-defined magnon content in terms of its analogue for the equivalent vertex model. This yields a complete analytical description of the spectrum in the latter subspaces, including the precise degeneracy of each level, by means of the supersymmetric version of Haldane's motifs and their related skew Young tableaux. As an application, we determine the structure of the motifs associated with the ground state of the spin 1/2 model in the thermodynamic limit in terms of the magnetic field strength and the charge chemical potential. This leads to a complete characterization of the distinct ground state phases, determined by their spin content, in terms of the magnetic field strength and the charge chemical potential.Keywords: integrable spin chains and vertex models, solvable lattice models arXiv:1811.10297v2 [cond-mat.str-el]

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“…As shown in Refs. [10] and [21], the spectrum of the su(1|m) spin chain (2.8), and hence of the equivalent Hamiltonian (2.5), can be generated from the formula The vectors δ(s) with components δ(s i , s i+1 ) (1 i N − 1) in Eq. (2.11) are su(1|m) motifs [13,14,34].…”

Section: Free Energymentioning

confidence: 99%

“…Equation (2.11) is the key ingredient in the exact computation of the free energy in the thermodynamic limit through the (site-dependent) transfer matrix method developed in Ref. [21]. Indeed, from Eq.…”

Section: Free Energymentioning

confidence: 99%

Supersymmetric t-J models with long-range interactions: thermodynamics and criticality

et al. 2019

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We analyze the thermodynamics and the critical behavior of the supersymmetric su(m) t-J model with long-range interactions. Using the transfer matrix formalism, we obtain a closed-form expression for the free energy per site both for a finite number of sites and in the thermodynamic limit. Our approach, which is different from the usual ones based on the asymptotic Bethe ansatz and generalized exclusion statistics, can in fact be applied to a large class of models whose spectrum is described in terms of supersymmetric Young tableaux and their associated Haldane motifs. In the simplest and most interesting su(2) case, we identify the five ground state phases of the model and derive the complete low-temperature asymptotic series of the free energy per site, the magnetization and charge densities, and their susceptibilities. We verify the model's characteristic spin-charge separation at low temperatures, and show that it holds to all orders in the asymptotic expansion. Using the low-temperature asymptotic expansions of the free energy, we also analyze the critical behavior of the model in each of its ground state phases. While the standard su(1|2) phase is described by two independent CFTs with central charge c = 1 in correspondence with the spin and charge sectors, we find that the low-energy behavior of the su(2) and su(1|1) phases is that of a single c = 1 CFT. We show that the model exhibits an even richer behavior on the boundary between zero-temperature phases, where it can be non-critical but gapless, critical in the spin sector but not in the charge one, or critical with central charge c = 3/2. arXiv:1903.12541v1 [cond-mat.str-el] Supersymmetric t-J models with long-range interactions ‡ Here and in what follows, unless otherwise stated, sums and products over Latin indexes run over the set 1, . . . , N while Greek indices range from 1 to m.

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

Cited by 14 publications

References 56 publications

Appearance of branched motifs in the spectra of BC type Polychronakos spin chains

Appearance of branched motifs in the spectra of BC type Polychronakos spin chains

Supersymmetric t-J models with long-range interactions: partition function and spectrum

Supersymmetric t-J models with long-range interactions: thermodynamics and criticality

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